/**
 * REST API: WP_REST_Attachments_Controller class
 *
 * @package WordPress
 * @subpackage REST_API
 * @since 4.7.0
 */

/**
 * Core controller used to access attachments via the REST API.
 *
 * @since 4.7.0
 *
 * @see WP_REST_Posts_Controller
 */
class WP_REST_Attachments_Controller extends WP_REST_Posts_Controller {

	/**
	 * Whether the controller supports batching.
	 *
	 * @since 5.9.0
	 * @var false
	 */
	protected $allow_batch = false;

	/**
	 * Registers the routes for attachments.
	 *
	 * @since 5.3.0
	 *
	 * @see register_rest_route()
	 */
	public function register_routes() {
		parent::register_routes();
		register_rest_route(
			$this->namespace,
			'/' . $this->rest_base . '/(?P<id>[\d]+)/post-process',
			array(
				'methods'             => WP_REST_Server::CREATABLE,
				'callback'            => array( $this, 'post_process_item' ),
				'permission_callback' => array( $this, 'post_process_item_permissions_check' ),
				'args'                => array(
					'id'     => array(
						'description' => __( 'Unique identifier for the attachment.' ),
						'type'        => 'integer',
					),
					'action' => array(
						'type'     => 'string',
						'enum'     => array( 'create-image-subsizes' ),
						'required' => true,
					),
				),
			)
		);
		register_rest_route(
			$this->namespace,
			'/' . $this->rest_base . '/(?P<id>[\d]+)/edit',
			array(
				'methods'             => WP_REST_Server::CREATABLE,
				'callback'            => array( $this, 'edit_media_item' ),
				'permission_callback' => array( $this, 'edit_media_item_permissions_check' ),
				'args'                => $this->get_edit_media_item_args(),
			)
		);
	}

	/**
	 * Determines the allowed query_vars for a get_items() response and
	 * prepares for WP_Query.
	 *
	 * @since 4.7.0
	 *
	 * @param array           $prepared_args Optional. Array of prepared arguments. Default empty array.
	 * @param WP_REST_Request $request       Optional. Request to prepare items for.
	 * @return array Array of query arguments.
	 */
	protected function prepare_items_query( $prepared_args = array(), $request = null ) {
		$query_args = parent::prepare_items_query( $prepared_args, $request );

		if ( empty( $query_args['post_status'] ) ) {
			$query_args['post_status'] = 'inherit';
		}

		$media_types = $this->get_media_types();

		if ( ! empty( $request['media_type'] ) && isset( $media_types[ $request['media_type'] ] ) ) {
			$query_args['post_mime_type'] = $media_types[ $request['media_type'] ];
		}

		if ( ! empty( $request['mime_type'] ) ) {
			$parts = explode( '/', $request['mime_type'] );
			if ( isset( $media_types[ $parts[0] ] ) && in_array( $request['mime_type'], $media_types[ $parts[0] ], true ) ) {
				$query_args['post_mime_type'] = $request['mime_type'];
			}
		}

		// Filter query clauses to include filenames.
		if ( isset( $query_args['s'] ) ) {
			add_filter( 'wp_allow_query_attachment_by_filename', '__return_true' );
		}

		return $query_args;
	}

	/**
	 * Checks if a given request has access to create an attachment.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return true|WP_Error Boolean true if the attachment may be created, or a WP_Error if not.
	 */
	public function create_item_permissions_check( $request ) {
		$ret = parent::create_item_permissions_check( $request );

		if ( ! $ret || is_wp_error( $ret ) ) {
			return $ret;
		}

		if ( ! current_user_can( 'upload_files' ) ) {
			return new WP_Error(
				'rest_cannot_create',
				__( 'Sorry, you are not allowed to upload media on this site.' ),
				array( 'status' => 400 )
			);
		}

		// Attaching media to a post requires ability to edit said post.
		if ( ! empty( $request['post'] ) && ! current_user_can( 'edit_post', (int) $request['post'] ) ) {
			return new WP_Error(
				'rest_cannot_edit',
				__( 'Sorry, you are not allowed to upload media to this post.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		return true;
	}

	/**
	 * Creates a single attachment.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function create_item( $request ) {
		if ( ! empty( $request['post'] ) && in_array( get_post_type( $request['post'] ), array( 'revision', 'attachment' ), true ) ) {
			return new WP_Error(
				'rest_invalid_param',
				__( 'Invalid parent type.' ),
				array( 'status' => 400 )
			);
		}

		$insert = $this->insert_attachment( $request );

		if ( is_wp_error( $insert ) ) {
			return $insert;
		}

		$schema = $this->get_item_schema();

		// Extract by name.
		$attachment_id = $insert['attachment_id'];
		$file          = $insert['file'];

		if ( isset( $request['alt_text'] ) ) {
			update_post_meta( $attachment_id, '_wp_attachment_image_alt', sanitize_text_field( $request['alt_text'] ) );
		}

		if ( ! empty( $schema['properties']['featured_media'] ) && isset( $request['featured_media'] ) ) {
			$thumbnail_update = $this->handle_featured_media( $request['featured_media'], $attachment_id );

			if ( is_wp_error( $thumbnail_update ) ) {
				return $thumbnail_update;
			}
		}

		if ( ! empty( $schema['properties']['meta'] ) && isset( $request['meta'] ) ) {
			$meta_update = $this->meta->update_value( $request['meta'], $attachment_id );

			if ( is_wp_error( $meta_update ) ) {
				return $meta_update;
			}
		}

		$attachment    = get_post( $attachment_id );
		$fields_update = $this->update_additional_fields_for_object( $attachment, $request );

		if ( is_wp_error( $fields_update ) ) {
			return $fields_update;
		}

		$terms_update = $this->handle_terms( $attachment_id, $request );

		if ( is_wp_error( $terms_update ) ) {
			return $terms_update;
		}

		$request->set_param( 'context', 'edit' );

		/**
		 * Fires after a single attachment is completely created or updated via the REST API.
		 *
		 * @since 5.0.0
		 *
		 * @param WP_Post         $attachment Inserted or updated attachment object.
		 * @param WP_REST_Request $request    Request object.
		 * @param bool            $creating   True when creating an attachment, false when updating.
		 */
		do_action( 'rest_after_insert_attachment', $attachment, $request, true );

		wp_after_insert_post( $attachment, false, null );

		if ( wp_is_serving_rest_request() ) {
			/*
			 * Set a custom header with the attachment_id.
			 * Used by the browser/client to resume creating image sub-sizes after a PHP fatal error.
			 */
			header( 'X-WP-Upload-Attachment-ID: ' . $attachment_id );
		}

		// Include media and image functions to get access to wp_generate_attachment_metadata().
		require_once ABSPATH . 'wp-admin/includes/media.php';
		require_once ABSPATH . 'wp-admin/includes/image.php';

		/*
		 * Post-process the upload (create image sub-sizes, make PDF thumbnails, etc.) and insert attachment meta.
		 * At this point the server may run out of resources and post-processing of uploaded images may fail.
		 */
		wp_update_attachment_metadata( $attachment_id, wp_generate_attachment_metadata( $attachment_id, $file ) );

		$response = $this->prepare_item_for_response( $attachment, $request );
		$response = rest_ensure_response( $response );
		$response->set_status( 201 );
		$response->header( 'Location', rest_url( sprintf( '%s/%s/%d', $this->namespace, $this->rest_base, $attachment_id ) ) );

		return $response;
	}

	/**
	 * Inserts the attachment post in the database. Does not update the attachment meta.
	 *
	 * @since 5.3.0
	 *
	 * @param WP_REST_Request $request
	 * @return array|WP_Error
	 */
	protected function insert_attachment( $request ) {
		// Get the file via $_FILES or raw data.
		$files   = $request->get_file_params();
		$headers = $request->get_headers();

		$time = null;

		// Matches logic in media_handle_upload().
		if ( ! empty( $request['post'] ) ) {
			$post = get_post( $request['post'] );
			// The post date doesn't usually matter for pages, so don't backdate this upload.
			if ( $post && 'page' !== $post->post_type && substr( $post->post_date, 0, 4 ) > 0 ) {
				$time = $post->post_date;
			}
		}

		if ( ! empty( $files ) ) {
			$file = $this->upload_from_file( $files, $headers, $time );
		} else {
			$file = $this->upload_from_data( $request->get_body(), $headers, $time );
		}

		if ( is_wp_error( $file ) ) {
			return $file;
		}

		$name       = wp_basename( $file['file'] );
		$name_parts = pathinfo( $name );
		$name       = trim( substr( $name, 0, -( 1 + strlen( $name_parts['extension'] ) ) ) );

		$url  = $file['url'];
		$type = $file['type'];
		$file = $file['file'];

		// Include image functions to get access to wp_read_image_metadata().
		require_once ABSPATH . 'wp-admin/includes/image.php';

		// Use image exif/iptc data for title and caption defaults if possible.
		$image_meta = wp_read_image_metadata( $file );

		if ( ! empty( $image_meta ) ) {
			if ( empty( $request['title'] ) && trim( $image_meta['title'] ) && ! is_numeric( sanitize_title( $image_meta['title'] ) ) ) {
				$request['title'] = $image_meta['title'];
			}

			if ( empty( $request['caption'] ) && trim( $image_meta['caption'] ) ) {
				$request['caption'] = $image_meta['caption'];
			}
		}

		$attachment = $this->prepare_item_for_database( $request );

		$attachment->post_mime_type = $type;
		$attachment->guid           = $url;

		// If the title was not set, use the original filename.
		if ( empty( $attachment->post_title ) && ! empty( $files['file']['name'] ) ) {
			// Remove the file extension (after the last `.`)
			$tmp_title = substr( $files['file']['name'], 0, strrpos( $files['file']['name'], '.' ) );

			if ( ! empty( $tmp_title ) ) {
				$attachment->post_title = $tmp_title;
			}
		}

		// Fall back to the original approach.
		if ( empty( $attachment->post_title ) ) {
			$attachment->post_title = preg_replace( '/\.[^.]+$/', '', wp_basename( $file ) );
		}

		// $post_parent is inherited from $attachment['post_parent'].
		$id = wp_insert_attachment( wp_slash( (array) $attachment ), $file, 0, true, false );

		if ( is_wp_error( $id ) ) {
			if ( 'db_update_error' === $id->get_error_code() ) {
				$id->add_data( array( 'status' => 500 ) );
			} else {
				$id->add_data( array( 'status' => 400 ) );
			}

			return $id;
		}

		$attachment = get_post( $id );

		/**
		 * Fires after a single attachment is created or updated via the REST API.
		 *
		 * @since 4.7.0
		 *
		 * @param WP_Post         $attachment Inserted or updated attachment
		 *                                    object.
		 * @param WP_REST_Request $request    The request sent to the API.
		 * @param bool            $creating   True when creating an attachment, false when updating.
		 */
		do_action( 'rest_insert_attachment', $attachment, $request, true );

		return array(
			'attachment_id' => $id,
			'file'          => $file,
		);
	}

	/**
	 * Determines the featured media based on a request param.
	 *
	 * @since 6.5.0
	 *
	 * @param int $featured_media Featured Media ID.
	 * @param int $post_id        Post ID.
	 * @return bool|WP_Error Whether the post thumbnail was successfully deleted, otherwise WP_Error.
	 */
	protected function handle_featured_media( $featured_media, $post_id ) {
		$post_type         = get_post_type( $post_id );
		$thumbnail_support = current_theme_supports( 'post-thumbnails', $post_type ) && post_type_supports( $post_type, 'thumbnail' );

		// Similar check as in wp_insert_post().
		if ( ! $thumbnail_support && get_post_mime_type( $post_id ) ) {
			if ( wp_attachment_is( 'audio', $post_id ) ) {
				$thumbnail_support = post_type_supports( 'attachment:audio', 'thumbnail' ) || current_theme_supports( 'post-thumbnails', 'attachment:audio' );
			} elseif ( wp_attachment_is( 'video', $post_id ) ) {
				$thumbnail_support = post_type_supports( 'attachment:video', 'thumbnail' ) || current_theme_supports( 'post-thumbnails', 'attachment:video' );
			}
		}

		if ( $thumbnail_support ) {
			return parent::handle_featured_media( $featured_media, $post_id );
		}

		return new WP_Error(
			'rest_no_featured_media',
			sprintf(
				/* translators: %s: attachment mime type */
				__( 'This site does not support post thumbnails on attachments with MIME type %s.' ),
				get_post_mime_type( $post_id )
			),
			array( 'status' => 400 )
		);
	}

	/**
	 * Updates a single attachment.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function update_item( $request ) {
		if ( ! empty( $request['post'] ) && in_array( get_post_type( $request['post'] ), array( 'revision', 'attachment' ), true ) ) {
			return new WP_Error(
				'rest_invalid_param',
				__( 'Invalid parent type.' ),
				array( 'status' => 400 )
			);
		}

		$attachment_before = get_post( $request['id'] );
		$response          = parent::update_item( $request );

		if ( is_wp_error( $response ) ) {
			return $response;
		}

		$response = rest_ensure_response( $response );
		$data     = $response->get_data();

		if ( isset( $request['alt_text'] ) ) {
			update_post_meta( $data['id'], '_wp_attachment_image_alt', $request['alt_text'] );
		}

		$attachment = get_post( $request['id'] );

		if ( ! empty( $schema['properties']['featured_media'] ) && isset( $request['featured_media'] ) ) {
			$thumbnail_update = $this->handle_featured_media( $request['featured_media'], $attachment->ID );

			if ( is_wp_error( $thumbnail_update ) ) {
				return $thumbnail_update;
			}
		}

		$fields_update = $this->update_additional_fields_for_object( $attachment, $request );

		if ( is_wp_error( $fields_update ) ) {
			return $fields_update;
		}

		$request->set_param( 'context', 'edit' );

		/** This action is documented in wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php */
		do_action( 'rest_after_insert_attachment', $attachment, $request, false );

		wp_after_insert_post( $attachment, true, $attachment_before );

		$response = $this->prepare_item_for_response( $attachment, $request );
		$response = rest_ensure_response( $response );

		return $response;
	}

	/**
	 * Performs post processing on an attachment.
	 *
	 * @since 5.3.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function post_process_item( $request ) {
		switch ( $request['action'] ) {
			case 'create-image-subsizes':
				require_once ABSPATH . 'wp-admin/includes/image.php';
				wp_update_image_subsizes( $request['id'] );
				break;
		}

		$request['context'] = 'edit';

		return $this->prepare_item_for_response( get_post( $request['id'] ), $request );
	}

	/**
	 * Checks if a given request can perform post processing on an attachment.
	 *
	 * @since 5.3.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return true|WP_Error True if the request has access to update the item, WP_Error object otherwise.
	 */
	public function post_process_item_permissions_check( $request ) {
		return $this->update_item_permissions_check( $request );
	}

	/**
	 * Checks if a given request has access to editing media.
	 *
	 * @since 5.5.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return true|WP_Error True if the request has read access, WP_Error object otherwise.
	 */
	public function edit_media_item_permissions_check( $request ) {
		if ( ! current_user_can( 'upload_files' ) ) {
			return new WP_Error(
				'rest_cannot_edit_image',
				__( 'Sorry, you are not allowed to upload media on this site.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		return $this->update_item_permissions_check( $request );
	}

	/**
	 * Applies edits to a media item and creates a new attachment record.
	 *
	 * @since 5.5.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function edit_media_item( $request ) {
		require_once ABSPATH . 'wp-admin/includes/image.php';

		$attachment_id = $request['id'];

		// This also confirms the attachment is an image.
		$image_file = wp_get_original_image_path( $attachment_id );
		$image_meta = wp_get_attachment_metadata( $attachment_id );

		if (
			! $image_meta ||
			! $image_file ||
			! wp_image_file_matches_image_meta( $request['src'], $image_meta, $attachment_id )
		) {
			return new WP_Error(
				'rest_unknown_attachment',
				__( 'Unable to get meta information for file.' ),
				array( 'status' => 404 )
			);
		}

		$supported_types = array( 'image/jpeg', 'image/png', 'image/gif', 'image/webp', 'image/avif' );
		$mime_type       = get_post_mime_type( $attachment_id );
		if ( ! in_array( $mime_type, $supported_types, true ) ) {
			return new WP_Error(
				'rest_cannot_edit_file_type',
				__( 'This type of file cannot be edited.' ),
				array( 'status' => 400 )
			);
		}

		// The `modifiers` param takes precedence over the older format.
		if ( isset( $request['modifiers'] ) ) {
			$modifiers = $request['modifiers'];
		} else {
			$modifiers = array();

			if ( ! empty( $request['rotation'] ) ) {
				$modifiers[] = array(
					'type' => 'rotate',
					'args' => array(
						'angle' => $request['rotation'],
					),
				);
			}

			if ( isset( $request['x'], $request['y'], $request['width'], $request['height'] ) ) {
				$modifiers[] = array(
					'type' => 'crop',
					'args' => array(
						'left'   => $request['x'],
						'top'    => $request['y'],
						'width'  => $request['width'],
						'height' => $request['height'],
					),
				);
			}

			if ( 0 === count( $modifiers ) ) {
				return new WP_Error(
					'rest_image_not_edited',
					__( 'The image was not edited. Edit the image before applying the changes.' ),
					array( 'status' => 400 )
				);
			}
		}

		/*
		 * If the file doesn't exist, attempt a URL fopen on the src link.
		 * This can occur with certain file replication plugins.
		 * Keep the original file path to get a modified name later.
		 */
		$image_file_to_edit = $image_file;
		if ( ! file_exists( $image_file_to_edit ) ) {
			$image_file_to_edit = _load_image_to_edit_path( $attachment_id );
		}

		$image_editor = wp_get_image_editor( $image_file_to_edit );

		if ( is_wp_error( $image_editor ) ) {
			return new WP_Error(
				'rest_unknown_image_file_type',
				__( 'Unable to edit this image.' ),
				array( 'status' => 500 )
			);
		}

		foreach ( $modifiers as $modifier ) {
			$args = $modifier['args'];
			switch ( $modifier['type'] ) {
				case 'rotate':
					// Rotation direction: clockwise vs. counter clockwise.
					$rotate = 0 - $args['angle'];

					if ( 0 !== $rotate ) {
						$result = $image_editor->rotate( $rotate );

						if ( is_wp_error( $result ) ) {
							return new WP_Error(
								'rest_image_rotation_failed',
								__( 'Unable to rotate this image.' ),
								array( 'status' => 500 )
							);
						}
					}

					break;

				case 'crop':
					$size = $image_editor->get_size();

					$crop_x = (int) round( ( $size['width'] * $args['left'] ) / 100.0 );
					$crop_y = (int) round( ( $size['height'] * $args['top'] ) / 100.0 );
					$width  = (int) round( ( $size['width'] * $args['width'] ) / 100.0 );
					$height = (int) round( ( $size['height'] * $args['height'] ) / 100.0 );

					if ( $size['width'] !== $width || $size['height'] !== $height ) {
						$result = $image_editor->crop( $crop_x, $crop_y, $width, $height );

						if ( is_wp_error( $result ) ) {
							return new WP_Error(
								'rest_image_crop_failed',
								__( 'Unable to crop this image.' ),
								array( 'status' => 500 )
							);
						}
					}

					break;

			}
		}

		// Calculate the file name.
		$image_ext  = pathinfo( $image_file, PATHINFO_EXTENSION );
		$image_name = wp_basename( $image_file, ".{$image_ext}" );

		/*
		 * Do not append multiple `-edited` to the file name.
		 * The user may be editing a previously edited image.
		 */
		if ( preg_match( '/-edited(-\d+)?$/', $image_name ) ) {
			// Remove any `-1`, `-2`, etc. `wp_unique_filename()` will add the proper number.
			$image_name = preg_replace( '/-edited(-\d+)?$/', '-edited', $image_name );
		} else {
			// Append `-edited` before the extension.
			$image_name .= '-edited';
		}

		$filename = "{$image_name}.{$image_ext}";

		// Create the uploads sub-directory if needed.
		$uploads = wp_upload_dir();

		// Make the file name unique in the (new) upload directory.
		$filename = wp_unique_filename( $uploads['path'], $filename );

		// Save to disk.
		$saved = $image_editor->save( $uploads['path'] . "/$filename" );

		if ( is_wp_error( $saved ) ) {
			return $saved;
		}

		// Create new attachment post.
		$new_attachment_post = array(
			'post_mime_type' => $saved['mime-type'],
			'guid'           => $uploads['url'] . "/$filename",
			'post_title'     => $image_name,
			'post_content'   => '',
		);

		// Copy post_content, post_excerpt, and post_title from the edited image's attachment post.
		$attachment_post = get_post( $attachment_id );

		if ( $attachment_post ) {
			$new_attachment_post['post_content'] = $attachment_post->post_content;
			$new_attachment_post['post_excerpt'] = $attachment_post->post_excerpt;
			$new_attachment_post['post_title']   = $attachment_post->post_title;
		}

		$new_attachment_id = wp_insert_attachment( wp_slash( $new_attachment_post ), $saved['path'], 0, true );

		if ( is_wp_error( $new_attachment_id ) ) {
			if ( 'db_update_error' === $new_attachment_id->get_error_code() ) {
				$new_attachment_id->add_data( array( 'status' => 500 ) );
			} else {
				$new_attachment_id->add_data( array( 'status' => 400 ) );
			}

			return $new_attachment_id;
		}

		// Copy the image alt text from the edited image.
		$image_alt = get_post_meta( $attachment_id, '_wp_attachment_image_alt', true );

		if ( ! empty( $image_alt ) ) {
			// update_post_meta() expects slashed.
			update_post_meta( $new_attachment_id, '_wp_attachment_image_alt', wp_slash( $image_alt ) );
		}

		if ( wp_is_serving_rest_request() ) {
			/*
			 * Set a custom header with the attachment_id.
			 * Used by the browser/client to resume creating image sub-sizes after a PHP fatal error.
			 */
			header( 'X-WP-Upload-Attachment-ID: ' . $new_attachment_id );
		}

		// Generate image sub-sizes and meta.
		$new_image_meta = wp_generate_attachment_metadata( $new_attachment_id, $saved['path'] );

		// Copy the EXIF metadata from the original attachment if not generated for the edited image.
		if ( isset( $image_meta['image_meta'] ) && isset( $new_image_meta['image_meta'] ) && is_array( $new_image_meta['image_meta'] ) ) {
			// Merge but skip empty values.
			foreach ( (array) $image_meta['image_meta'] as $key => $value ) {
				if ( empty( $new_image_meta['image_meta'][ $key ] ) && ! empty( $value ) ) {
					$new_image_meta['image_meta'][ $key ] = $value;
				}
			}
		}

		// Reset orientation. At this point the image is edited and orientation is correct.
		if ( ! empty( $new_image_meta['image_meta']['orientation'] ) ) {
			$new_image_meta['image_meta']['orientation'] = 1;
		}

		// The attachment_id may change if the site is exported and imported.
		$new_image_meta['parent_image'] = array(
			'attachment_id' => $attachment_id,
			// Path to the originally uploaded image file relative to the uploads directory.
			'file'          => _wp_relative_upload_path( $image_file ),
		);

		/**
		 * Filters the meta data for the new image created by editing an existing image.
		 *
		 * @since 5.5.0
		 *
		 * @param array $new_image_meta    Meta data for the new image.
		 * @param int   $new_attachment_id Attachment post ID for the new image.
		 * @param int   $attachment_id     Attachment post ID for the edited (parent) image.
		 */
		$new_image_meta = apply_filters( 'wp_edited_image_metadata', $new_image_meta, $new_attachment_id, $attachment_id );

		wp_update_attachment_metadata( $new_attachment_id, $new_image_meta );

		$response = $this->prepare_item_for_response( get_post( $new_attachment_id ), $request );
		$response->set_status( 201 );
		$response->header( 'Location', rest_url( sprintf( '%s/%s/%s', $this->namespace, $this->rest_base, $new_attachment_id ) ) );

		return $response;
	}

	/**
	 * Prepares a single attachment for create or update.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Request object.
	 * @return stdClass|WP_Error Post object.
	 */
	protected function prepare_item_for_database( $request ) {
		$prepared_attachment = parent::prepare_item_for_database( $request );

		// Attachment caption (post_excerpt internally).
		if ( isset( $request['caption'] ) ) {
			if ( is_string( $request['caption'] ) ) {
				$prepared_attachment->post_excerpt = $request['caption'];
			} elseif ( isset( $request['caption']['raw'] ) ) {
				$prepared_attachment->post_excerpt = $request['caption']['raw'];
			}
		}

		// Attachment description (post_content internally).
		if ( isset( $request['description'] ) ) {
			if ( is_string( $request['description'] ) ) {
				$prepared_attachment->post_content = $request['description'];
			} elseif ( isset( $request['description']['raw'] ) ) {
				$prepared_attachment->post_content = $request['description']['raw'];
			}
		}

		if ( isset( $request['post'] ) ) {
			$prepared_attachment->post_parent = (int) $request['post'];
		}

		return $prepared_attachment;
	}

	/**
	 * Prepares a single attachment output for response.
	 *
	 * @since 4.7.0
	 * @since 5.9.0 Renamed `$post` to `$item` to match parent class for PHP 8 named parameter support.
	 *
	 * @param WP_Post         $item    Attachment object.
	 * @param WP_REST_Request $request Request object.
	 * @return WP_REST_Response Response object.
	 */
	public function prepare_item_for_response( $item, $request ) {
		// Restores the more descriptive, specific name for use within this method.
		$post = $item;

		$response = parent::prepare_item_for_response( $post, $request );
		$fields   = $this->get_fields_for_response( $request );
		$data     = $response->get_data();

		if ( in_array( 'description', $fields, true ) ) {
			$data['description'] = array(
				'raw'      => $post->post_content,
				/** This filter is documented in wp-includes/post-template.php */
				'rendered' => apply_filters( 'the_content', $post->post_content ),
			);
		}

		if ( in_array( 'caption', $fields, true ) ) {
			/** This filter is documented in wp-includes/post-template.php */
			$caption = apply_filters( 'get_the_excerpt', $post->post_excerpt, $post );

			/** This filter is documented in wp-includes/post-template.php */
			$caption = apply_filters( 'the_excerpt', $caption );

			$data['caption'] = array(
				'raw'      => $post->post_excerpt,
				'rendered' => $caption,
			);
		}

		if ( in_array( 'alt_text', $fields, true ) ) {
			$data['alt_text'] = get_post_meta( $post->ID, '_wp_attachment_image_alt', true );
		}

		if ( in_array( 'media_type', $fields, true ) ) {
			$data['media_type'] = wp_attachment_is_image( $post->ID ) ? 'image' : 'file';
		}

		if ( in_array( 'mime_type', $fields, true ) ) {
			$data['mime_type'] = $post->post_mime_type;
		}

		if ( in_array( 'media_details', $fields, true ) ) {
			$data['media_details'] = wp_get_attachment_metadata( $post->ID );

			// Ensure empty details is an empty object.
			if ( empty( $data['media_details'] ) ) {
				$data['media_details'] = new stdClass();
			} elseif ( ! empty( $data['media_details']['sizes'] ) ) {

				foreach ( $data['media_details']['sizes'] as $size => &$size_data ) {

					if ( isset( $size_data['mime-type'] ) ) {
						$size_data['mime_type'] = $size_data['mime-type'];
						unset( $size_data['mime-type'] );
					}

					// Use the same method image_downsize() does.
					$image_src = wp_get_attachment_image_src( $post->ID, $size );
					if ( ! $image_src ) {
						continue;
					}

					$size_data['source_url'] = $image_src[0];
				}

				$full_src = wp_get_attachment_image_src( $post->ID, 'full' );

				if ( ! empty( $full_src ) ) {
					$data['media_details']['sizes']['full'] = array(
						'file'       => wp_basename( $full_src[0] ),
						'width'      => $full_src[1],
						'height'     => $full_src[2],
						'mime_type'  => $post->post_mime_type,
						'source_url' => $full_src[0],
					);
				}
			} else {
				$data['media_details']['sizes'] = new stdClass();
			}
		}

		if ( in_array( 'post', $fields, true ) ) {
			$data['post'] = ! empty( $post->post_parent ) ? (int) $post->post_parent : null;
		}

		if ( in_array( 'source_url', $fields, true ) ) {
			$data['source_url'] = wp_get_attachment_url( $post->ID );
		}

		if ( in_array( 'missing_image_sizes', $fields, true ) ) {
			require_once ABSPATH . 'wp-admin/includes/image.php';
			$data['missing_image_sizes'] = array_keys( wp_get_missing_image_subsizes( $post->ID ) );
		}

		$context = ! empty( $request['context'] ) ? $request['context'] : 'view';

		$data = $this->filter_response_by_context( $data, $context );

		$links = $response->get_links();

		// Wrap the data in a response object.
		$response = rest_ensure_response( $data );

		foreach ( $links as $rel => $rel_links ) {
			foreach ( $rel_links as $link ) {
				$response->add_link( $rel, $link['href'], $link['attributes'] );
			}
		}

		/**
		 * Filters an attachment returned from the REST API.
		 *
		 * Allows modification of the attachment right before it is returned.
		 *
		 * @since 4.7.0
		 *
		 * @param WP_REST_Response $response The response object.
		 * @param WP_Post          $post     The original attachment post.
		 * @param WP_REST_Request  $request  Request used to generate the response.
		 */
		return apply_filters( 'rest_prepare_attachment', $response, $post, $request );
	}

	/**
	 * Retrieves the attachment's schema, conforming to JSON Schema.
	 *
	 * @since 4.7.0
	 *
	 * @return array Item schema as an array.
	 */
	public function get_item_schema() {
		if ( $this->schema ) {
			return $this->add_additional_fields_schema( $this->schema );
		}

		$schema = parent::get_item_schema();

		$schema['properties']['alt_text'] = array(
			'description' => __( 'Alternative text to display when attachment is not displayed.' ),
			'type'        => 'string',
			'context'     => array( 'view', 'edit', 'embed' ),
			'arg_options' => array(
				'sanitize_callback' => 'sanitize_text_field',
			),
		);

		$schema['properties']['caption'] = array(
			'description' => __( 'The attachment caption.' ),
			'type'        => 'object',
			'context'     => array( 'view', 'edit', 'embed' ),
			'arg_options' => array(
				'sanitize_callback' => null, // Note: sanitization implemented in self::prepare_item_for_database().
				'validate_callback' => null, // Note: validation implemented in self::prepare_item_for_database().
			),
			'properties'  => array(
				'raw'      => array(
					'description' => __( 'Caption for the attachment, as it exists in the database.' ),
					'type'        => 'string',
					'context'     => array( 'edit' ),
				),
				'rendered' => array(
					'description' => __( 'HTML caption for the attachment, transformed for display.' ),
					'type'        => 'string',
					'context'     => array( 'view', 'edit', 'embed' ),
					'readonly'    => true,
				),
			),
		);

		$schema['properties']['description'] = array(
			'description' => __( 'The attachment description.' ),
			'type'        => 'object',
			'context'     => array( 'view', 'edit' ),
			'arg_options' => array(
				'sanitize_callback' => null, // Note: sanitization implemented in self::prepare_item_for_database().
				'validate_callback' => null, // Note: validation implemented in self::prepare_item_for_database().
			),
			'properties'  => array(
				'raw'      => array(
					'description' => __( 'Description for the attachment, as it exists in the database.' ),
					'type'        => 'string',
					'context'     => array( 'edit' ),
				),
				'rendered' => array(
					'description' => __( 'HTML description for the attachment, transformed for display.' ),
					'type'        => 'string',
					'context'     => array( 'view', 'edit' ),
					'readonly'    => true,
				),
			),
		);

		$schema['properties']['media_type'] = array(
			'description' => __( 'Attachment type.' ),
			'type'        => 'string',
			'enum'        => array( 'image', 'file' ),
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['mime_type'] = array(
			'description' => __( 'The attachment MIME type.' ),
			'type'        => 'string',
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['media_details'] = array(
			'description' => __( 'Details about the media file, specific to its type.' ),
			'type'        => 'object',
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['post'] = array(
			'description' => __( 'The ID for the associated post of the attachment.' ),
			'type'        => 'integer',
			'context'     => array( 'view', 'edit' ),
		);

		$schema['properties']['source_url'] = array(
			'description' => __( 'URL to the original attachment file.' ),
			'type'        => 'string',
			'format'      => 'uri',
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['missing_image_sizes'] = array(
			'description' => __( 'List of the missing image sizes of the attachment.' ),
			'type'        => 'array',
			'items'       => array( 'type' => 'string' ),
			'context'     => array( 'edit' ),
			'readonly'    => true,
		);

		unset( $schema['properties']['password'] );

		$this->schema = $schema;

		return $this->add_additional_fields_schema( $this->schema );
	}

	/**
	 * Handles an upload via raw POST data.
	 *
	 * @since 4.7.0
	 * @since 6.6.0 Added the `$time` parameter.
	 *
	 * @param string      $data    Supplied file data.
	 * @param array       $headers HTTP headers from the request.
	 * @param string|null $time    Optional. Time formatted in 'yyyy/mm'. Default null.
	 * @return array|WP_Error Data from wp_handle_sideload().
	 */
	protected function upload_from_data( $data, $headers, $time = null ) {
		if ( empty( $data ) ) {
			return new WP_Error(
				'rest_upload_no_data',
				__( 'No data supplied.' ),
				array( 'status' => 400 )
			);
		}

		if ( empty( $headers['content_type'] ) ) {
			return new WP_Error(
				'rest_upload_no_content_type',
				__( 'No Content-Type supplied.' ),
				array( 'status' => 400 )
			);
		}

		if ( empty( $headers['content_disposition'] ) ) {
			return new WP_Error(
				'rest_upload_no_content_disposition',
				__( 'No Content-Disposition supplied.' ),
				array( 'status' => 400 )
			);
		}

		$filename = self::get_filename_from_disposition( $headers['content_disposition'] );

		if ( empty( $filename ) ) {
			return new WP_Error(
				'rest_upload_invalid_disposition',
				__( 'Invalid Content-Disposition supplied. Content-Disposition needs to be formatted as `attachment; filename="image.png"` or similar.' ),
				array( 'status' => 400 )
			);
		}

		if ( ! empty( $headers['content_md5'] ) ) {
			$content_md5 = array_shift( $headers['content_md5'] );
			$expected    = trim( $content_md5 );
			$actual      = md5( $data );

			if ( $expected !== $actual ) {
				return new WP_Error(
					'rest_upload_hash_mismatch',
					__( 'Content hash did not match expected.' ),
					array( 'status' => 412 )
				);
			}
		}

		// Get the content-type.
		$type = array_shift( $headers['content_type'] );

		// Include filesystem functions to get access to wp_tempnam() and wp_handle_sideload().
		require_once ABSPATH . 'wp-admin/includes/file.php';

		// Save the file.
		$tmpfname = wp_tempnam( $filename );

		$fp = fopen( $tmpfname, 'w+' );

		if ( ! $fp ) {
			return new WP_Error(
				'rest_upload_file_error',
				__( 'Could not open file handle.' ),
				array( 'status' => 500 )
			);
		}

		fwrite( $fp, $data );
		fclose( $fp );

		// Now, sideload it in.
		$file_data = array(
			'error'    => null,
			'tmp_name' => $tmpfname,
			'name'     => $filename,
			'type'     => $type,
		);

		$size_check = self::check_upload_size( $file_data );
		if ( is_wp_error( $size_check ) ) {
			return $size_check;
		}

		$overrides = array(
			'test_form' => false,
		);

		$sideloaded = wp_handle_sideload( $file_data, $overrides, $time );

		if ( isset( $sideloaded['error'] ) ) {
			@unlink( $tmpfname );

			return new WP_Error(
				'rest_upload_sideload_error',
				$sideloaded['error'],
				array( 'status' => 500 )
			);
		}

		return $sideloaded;
	}

	/**
	 * Parses filename from a Content-Disposition header value.
	 *
	 * As per RFC6266:
	 *
	 *     content-disposition = "Content-Disposition" ":"
	 *                            disposition-type *( ";" disposition-parm )
	 *
	 *     disposition-type    = "inline" | "attachment" | disp-ext-type
	 *                         ; case-insensitive
	 *     disp-ext-type       = token
	 *
	 *     disposition-parm    = filename-parm | disp-ext-parm
	 *
	 *     filename-parm       = "filename" "=" value
	 *                         | "filename*" "=" ext-value
	 *
	 *     disp-ext-parm       = token "=" value
	 *                         | ext-token "=" ext-value
	 *     ext-token           = <the characters in token, followed by "*">
	 *
	 * @since 4.7.0
	 *
	 * @link https://tools.ietf.org/html/rfc2388
	 * @link https://tools.ietf.org/html/rfc6266
	 *
	 * @param string[] $disposition_header List of Content-Disposition header values.
	 * @return string|null Filename if available, or null if not found.
	 */
	public static function get_filename_from_disposition( $disposition_header ) {
		// Get the filename.
		$filename = null;

		foreach ( $disposition_header as $value ) {
			$value = trim( $value );

			if ( ! str_contains( $value, ';' ) ) {
				continue;
			}

			list( $type, $attr_parts ) = explode( ';', $value, 2 );

			$attr_parts = explode( ';', $attr_parts );
			$attributes = array();

			foreach ( $attr_parts as $part ) {
				if ( ! str_contains( $part, '=' ) ) {
					continue;
				}

				list( $key, $value ) = explode( '=', $part, 2 );

				$attributes[ trim( $key ) ] = trim( $value );
			}

			if ( empty( $attributes['filename'] ) ) {
				continue;
			}

			$filename = trim( $attributes['filename'] );

			// Unquote quoted filename, but after trimming.
			if ( str_starts_with( $filename, '"' ) && str_ends_with( $filename, '"' ) ) {
				$filename = substr( $filename, 1, -1 );
			}
		}

		return $filename;
	}

	/**
	 * Retrieves the query params for collections of attachments.
	 *
	 * @since 4.7.0
	 *
	 * @return array Query parameters for the attachment collection as an array.
	 */
	public function get_collection_params() {
		$params                            = parent::get_collection_params();
		$params['status']['default']       = 'inherit';
		$params['status']['items']['enum'] = array( 'inherit', 'private', 'trash' );
		$media_types                       = $this->get_media_types();

		$params['media_type'] = array(
			'default'     => null,
			'description' => __( 'Limit result set to attachments of a particular media type.' ),
			'type'        => 'string',
			'enum'        => array_keys( $media_types ),
		);

		$params['mime_type'] = array(
			'default'     => null,
			'description' => __( 'Limit result set to attachments of a particular MIME type.' ),
			'type'        => 'string',
		);

		return $params;
	}

	/**
	 * Handles an upload via multipart/form-data ($_FILES).
	 *
	 * @since 4.7.0
	 * @since 6.6.0 Added the `$time` parameter.
	 *
	 * @param array       $files   Data from the `$_FILES` superglobal.
	 * @param array       $headers HTTP headers from the request.
	 * @param string|null $time    Optional. Time formatted in 'yyyy/mm'. Default null.
	 * @return array|WP_Error Data from wp_handle_upload().
	 */
	protected function upload_from_file( $files, $headers, $time = null ) {
		if ( empty( $files ) ) {
			return new WP_Error(
				'rest_upload_no_data',
				__( 'No data supplied.' ),
				array( 'status' => 400 )
			);
		}

		// Verify hash, if given.
		if ( ! empty( $headers['content_md5'] ) ) {
			$content_md5 = array_shift( $headers['content_md5'] );
			$expected    = trim( $content_md5 );
			$actual      = md5_file( $files['file']['tmp_name'] );

			if ( $expected !== $actual ) {
				return new WP_Error(
					'rest_upload_hash_mismatch',
					__( 'Content hash did not match expected.' ),
					array( 'status' => 412 )
				);
			}
		}

		// Pass off to WP to handle the actual upload.
		$overrides = array(
			'test_form' => false,
		);

		// Bypasses is_uploaded_file() when running unit tests.
		if ( defined( 'DIR_TESTDATA' ) && DIR_TESTDATA ) {
			$overrides['action'] = 'wp_handle_mock_upload';
		}

		$size_check = self::check_upload_size( $files['file'] );
		if ( is_wp_error( $size_check ) ) {
			return $size_check;
		}

		// Include filesystem functions to get access to wp_handle_upload().
		require_once ABSPATH . 'wp-admin/includes/file.php';

		$file = wp_handle_upload( $files['file'], $overrides, $time );

		if ( isset( $file['error'] ) ) {
			return new WP_Error(
				'rest_upload_unknown_error',
				$file['error'],
				array( 'status' => 500 )
			);
		}

		return $file;
	}

	/**
	 * Retrieves the supported media types.
	 *
	 * Media types are considered the MIME type category.
	 *
	 * @since 4.7.0
	 *
	 * @return array Array of supported media types.
	 */
	protected function get_media_types() {
		$media_types = array();

		foreach ( get_allowed_mime_types() as $mime_type ) {
			$parts = explode( '/', $mime_type );

			if ( ! isset( $media_types[ $parts[0] ] ) ) {
				$media_types[ $parts[0] ] = array();
			}

			$media_types[ $parts[0] ][] = $mime_type;
		}

		return $media_types;
	}

	/**
	 * Determine if uploaded file exceeds space quota on multisite.
	 *
	 * Replicates check_upload_size().
	 *
	 * @since 4.9.8
	 *
	 * @param array $file $_FILES array for a given file.
	 * @return true|WP_Error True if can upload, error for errors.
	 */
	protected function check_upload_size( $file ) {
		if ( ! is_multisite() ) {
			return true;
		}

		if ( get_site_option( 'upload_space_check_disabled' ) ) {
			return true;
		}

		$space_left = get_upload_space_available();

		$file_size = filesize( $file['tmp_name'] );

		if ( $space_left < $file_size ) {
			return new WP_Error(
				'rest_upload_limited_space',
				/* translators: %s: Required disk space in kilobytes. */
				sprintf( __( 'Not enough space to upload. %s KB needed.' ), number_format( ( $file_size - $space_left ) / KB_IN_BYTES ) ),
				array( 'status' => 400 )
			);
		}

		if ( $file_size > ( KB_IN_BYTES * get_site_option( 'fileupload_maxk', 1500 ) ) ) {
			return new WP_Error(
				'rest_upload_file_too_big',
				/* translators: %s: Maximum allowed file size in kilobytes. */
				sprintf( __( 'This file is too big. Files must be less than %s KB in size.' ), get_site_option( 'fileupload_maxk', 1500 ) ),
				array( 'status' => 400 )
			);
		}

		// Include multisite admin functions to get access to upload_is_user_over_quota().
		require_once ABSPATH . 'wp-admin/includes/ms.php';

		if ( upload_is_user_over_quota( false ) ) {
			return new WP_Error(
				'rest_upload_user_quota_exceeded',
				__( 'You have used your space quota. Please delete files before uploading.' ),
				array( 'status' => 400 )
			);
		}

		return true;
	}

	/**
	 * Gets the request args for the edit item route.
	 *
	 * @since 5.5.0
	 *
	 * @return array
	 */
	protected function get_edit_media_item_args() {
		return array(
			'src'       => array(
				'description' => __( 'URL to the edited image file.' ),
				'type'        => 'string',
				'format'      => 'uri',
				'required'    => true,
			),
			'modifiers' => array(
				'description' => __( 'Array of image edits.' ),
				'type'        => 'array',
				'minItems'    => 1,
				'items'       => array(
					'description' => __( 'Image edit.' ),
					'type'        => 'object',
					'required'    => array(
						'type',
						'args',
					),
					'oneOf'       => array(
						array(
							'title'      => __( 'Rotation' ),
							'properties' => array(
								'type' => array(
									'description' => __( 'Rotation type.' ),
									'type'        => 'string',
									'enum'        => array( 'rotate' ),
								),
								'args' => array(
									'description' => __( 'Rotation arguments.' ),
									'type'        => 'object',
									'required'    => array(
										'angle',
									),
									'properties'  => array(
										'angle' => array(
											'description' => __( 'Angle to rotate clockwise in degrees.' ),
											'type'        => 'number',
										),
									),
								),
							),
						),
						array(
							'title'      => __( 'Crop' ),
							'properties' => array(
								'type' => array(
									'description' => __( 'Crop type.' ),
									'type'        => 'string',
									'enum'        => array( 'crop' ),
								),
								'args' => array(
									'description' => __( 'Crop arguments.' ),
									'type'        => 'object',
									'required'    => array(
										'left',
										'top',
										'width',
										'height',
									),
									'properties'  => array(
										'left'   => array(
											'description' => __( 'Horizontal position from the left to begin the crop as a percentage of the image width.' ),
											'type'        => 'number',
										),
										'top'    => array(
											'description' => __( 'Vertical position from the top to begin the crop as a percentage of the image height.' ),
											'type'        => 'number',
										),
										'width'  => array(
											'description' => __( 'Width of the crop as a percentage of the image width.' ),
											'type'        => 'number',
										),
										'height' => array(
											'description' => __( 'Height of the crop as a percentage of the image height.' ),
											'type'        => 'number',
										),
									),
								),
							),
						),
					),
				),
			),
			'rotation'  => array(
				'description'      => __( 'The amount to rotate the image clockwise in degrees. DEPRECATED: Use `modifiers` instead.' ),
				'type'             => 'integer',
				'minimum'          => 0,
				'exclusiveMinimum' => true,
				'maximum'          => 360,
				'exclusiveMaximum' => true,
			),
			'x'         => array(
				'description' => __( 'As a percentage of the image, the x position to start the crop from. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
			'y'         => array(
				'description' => __( 'As a percentage of the image, the y position to start the crop from. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
			'width'     => array(
				'description' => __( 'As a percentage of the image, the width to crop the image to. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
			'height'    => array(
				'description' => __( 'As a percentage of the image, the height to crop the image to. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
		);
	}
}<!doctype html>
<html lang="en-US">
<head>
	<script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-7744495812468961"
     crossorigin="anonymous"></script>
	
	<script async custom-element="amp-auto-ads"
        src="https://cdn.ampproject.org/v0/amp-auto-ads-0.1.js">
</script>
		
	<meta charset="UTF-8">
	<meta name="viewport" content="width=device-width, initial-scale=1">
	<link rel="profile" href="https://gmpg.org/xfn/11">

	<title>Curious Mathematics Points and you will Interesting Functions &#8211; Sanathan Dharm Veda</title>
<meta name='robots' content='max-image-preview:large' />
<link rel="alternate" type="application/rss+xml" title="Sanathan Dharm Veda &raquo; Feed" href="https://sanatandharmveda.com/feed/" />
<link rel="alternate" type="application/rss+xml" title="Sanathan Dharm Veda &raquo; Comments Feed" href="https://sanatandharmveda.com/comments/feed/" />
<link rel="alternate" type="application/rss+xml" title="Sanathan Dharm Veda &raquo; Curious Mathematics Points and you will Interesting Functions Comments Feed" href="https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/feed/" />
<script type="text/javascript">
/* <![CDATA[ */
window._wpemojiSettings = {"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.0.3\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.0.3\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/sanatandharmveda.com\/wp-includes\/js\/wp-emoji-release.min.js?ver=6.6.7"}};
/*! This file is auto-generated */
!function(i,n){var o,s,e;function c(e){try{var t={supportTests:e,timestamp:(new Date).valueOf()};sessionStorage.setItem(o,JSON.stringify(t))}catch(e){}}function p(e,t,n){e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(t,0,0);var t=new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data),r=(e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(n,0,0),new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data));return t.every(function(e,t){return e===r[t]})}function u(e,t,n){switch(t){case"flag":return n(e,"\ud83c\udff3\ufe0f\u200d\u26a7\ufe0f","\ud83c\udff3\ufe0f\u200b\u26a7\ufe0f")?!1:!n(e,"\ud83c\uddfa\ud83c\uddf3","\ud83c\uddfa\u200b\ud83c\uddf3")&&!n(e,"\ud83c\udff4\udb40\udc67\udb40\udc62\udb40\udc65\udb40\udc6e\udb40\udc67\udb40\udc7f","\ud83c\udff4\u200b\udb40\udc67\u200b\udb40\udc62\u200b\udb40\udc65\u200b\udb40\udc6e\u200b\udb40\udc67\u200b\udb40\udc7f");case"emoji":return!n(e,"\ud83d\udc26\u200d\u2b1b","\ud83d\udc26\u200b\u2b1b")}return!1}function f(e,t,n){var r="undefined"!=typeof WorkerGlobalScope&&self instanceof WorkerGlobalScope?new OffscreenCanvas(300,150):i.createElement("canvas"),a=r.getContext("2d",{willReadFrequently:!0}),o=(a.textBaseline="top",a.font="600 32px Arial",{});return e.forEach(function(e){o[e]=t(a,e,n)}),o}function t(e){var t=i.createElement("script");t.src=e,t.defer=!0,i.head.appendChild(t)}"undefined"!=typeof Promise&&(o="wpEmojiSettingsSupports",s=["flag","emoji"],n.supports={everything:!0,everythingExceptFlag:!0},e=new Promise(function(e){i.addEventListener("DOMContentLoaded",e,{once:!0})}),new Promise(function(t){var n=function(){try{var e=JSON.parse(sessionStorage.getItem(o));if("object"==typeof e&&"number"==typeof e.timestamp&&(new Date).valueOf()<e.timestamp+604800&&"object"==typeof e.supportTests)return e.supportTests}catch(e){}return null}();if(!n){if("undefined"!=typeof Worker&&"undefined"!=typeof OffscreenCanvas&&"undefined"!=typeof URL&&URL.createObjectURL&&"undefined"!=typeof Blob)try{var e="postMessage("+f.toString()+"("+[JSON.stringify(s),u.toString(),p.toString()].join(",")+"));",r=new Blob([e],{type:"text/javascript"}),a=new Worker(URL.createObjectURL(r),{name:"wpTestEmojiSupports"});return void(a.onmessage=function(e){c(n=e.data),a.terminate(),t(n)})}catch(e){}c(n=f(s,u,p))}t(n)}).then(function(e){for(var t in e)n.supports[t]=e[t],n.supports.everything=n.supports.everything&&n.supports[t],"flag"!==t&&(n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&n.supports[t]);n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&!n.supports.flag,n.DOMReady=!1,n.readyCallback=function(){n.DOMReady=!0}}).then(function(){return e}).then(function(){var e;n.supports.everything||(n.readyCallback(),(e=n.source||{}).concatemoji?t(e.concatemoji):e.wpemoji&&e.twemoji&&(t(e.twemoji),t(e.wpemoji)))}))}((window,document),window._wpemojiSettings);
/* ]]> */
</script>
<style id='wp-emoji-styles-inline-css' type='text/css'>

	img.wp-smiley, img.emoji {
		display: inline !important;
		border: none !important;
		box-shadow: none !important;
		height: 1em !important;
		width: 1em !important;
		margin: 0 0.07em !important;
		vertical-align: -0.1em !important;
		background: none !important;
		padding: 0 !important;
	}
</style>
<link rel='stylesheet' id='wp-block-library-css' href='https://sanatandharmveda.com/wp-includes/css/dist/block-library/style.min.css?ver=6.6.7' type='text/css' media='all' />
<link rel='stylesheet' id='hostinger-affiliate-plugin-block-frontend-css' href='https://sanatandharmveda.com/wp-content/plugins/hostinger-affiliate-plugin/assets/dist/frontend.css?ver=1787240739' type='text/css' media='all' />
<style id='classic-theme-styles-inline-css' type='text/css'>
/*! This file is auto-generated */
.wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
</style>
<style id='global-styles-inline-css' type='text/css'>
:root{--wp--preset--aspect-ratio--square: 1;--wp--preset--aspect-ratio--4-3: 4/3;--wp--preset--aspect-ratio--3-4: 3/4;--wp--preset--aspect-ratio--3-2: 3/2;--wp--preset--aspect-ratio--2-3: 2/3;--wp--preset--aspect-ratio--16-9: 16/9;--wp--preset--aspect-ratio--9-16: 9/16;--wp--preset--color--black: #000000;--wp--preset--color--cyan-bluish-gray: #abb8c3;--wp--preset--color--white: #ffffff;--wp--preset--color--pale-pink: #f78da7;--wp--preset--color--vivid-red: #cf2e2e;--wp--preset--color--luminous-vivid-orange: #ff6900;--wp--preset--color--luminous-vivid-amber: #fcb900;--wp--preset--color--light-green-cyan: #7bdcb5;--wp--preset--color--vivid-green-cyan: #00d084;--wp--preset--color--pale-cyan-blue: #8ed1fc;--wp--preset--color--vivid-cyan-blue: #0693e3;--wp--preset--color--vivid-purple: #9b51e0;--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple: linear-gradient(135deg,rgba(6,147,227,1) 0%,rgb(155,81,224) 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan: linear-gradient(135deg,rgb(122,220,180) 0%,rgb(0,208,130) 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange: linear-gradient(135deg,rgba(252,185,0,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red: linear-gradient(135deg,rgba(255,105,0,1) 0%,rgb(207,46,46) 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray: linear-gradient(135deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%);--wp--preset--gradient--cool-to-warm-spectrum: linear-gradient(135deg,rgb(74,234,220) 0%,rgb(151,120,209) 20%,rgb(207,42,186) 40%,rgb(238,44,130) 60%,rgb(251,105,98) 80%,rgb(254,248,76) 100%);--wp--preset--gradient--blush-light-purple: linear-gradient(135deg,rgb(255,206,236) 0%,rgb(152,150,240) 100%);--wp--preset--gradient--blush-bordeaux: linear-gradient(135deg,rgb(254,205,165) 0%,rgb(254,45,45) 50%,rgb(107,0,62) 100%);--wp--preset--gradient--luminous-dusk: linear-gradient(135deg,rgb(255,203,112) 0%,rgb(199,81,192) 50%,rgb(65,88,208) 100%);--wp--preset--gradient--pale-ocean: linear-gradient(135deg,rgb(255,245,203) 0%,rgb(182,227,212) 50%,rgb(51,167,181) 100%);--wp--preset--gradient--electric-grass: linear-gradient(135deg,rgb(202,248,128) 0%,rgb(113,206,126) 100%);--wp--preset--gradient--midnight: linear-gradient(135deg,rgb(2,3,129) 0%,rgb(40,116,252) 100%);--wp--preset--font-size--small: 13px;--wp--preset--font-size--medium: 20px;--wp--preset--font-size--large: 36px;--wp--preset--font-size--x-large: 42px;--wp--preset--spacing--20: 0.44rem;--wp--preset--spacing--30: 0.67rem;--wp--preset--spacing--40: 1rem;--wp--preset--spacing--50: 1.5rem;--wp--preset--spacing--60: 2.25rem;--wp--preset--spacing--70: 3.38rem;--wp--preset--spacing--80: 5.06rem;--wp--preset--shadow--natural: 6px 6px 9px rgba(0, 0, 0, 0.2);--wp--preset--shadow--deep: 12px 12px 50px rgba(0, 0, 0, 0.4);--wp--preset--shadow--sharp: 6px 6px 0px rgba(0, 0, 0, 0.2);--wp--preset--shadow--outlined: 6px 6px 0px -3px rgba(255, 255, 255, 1), 6px 6px rgba(0, 0, 0, 1);--wp--preset--shadow--crisp: 6px 6px 0px rgba(0, 0, 0, 1);}:where(.is-layout-flex){gap: 0.5em;}:where(.is-layout-grid){gap: 0.5em;}body .is-layout-flex{display: flex;}.is-layout-flex{flex-wrap: wrap;align-items: center;}.is-layout-flex > :is(*, div){margin: 0;}body .is-layout-grid{display: grid;}.is-layout-grid > :is(*, div){margin: 0;}:where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;}:where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;}.has-black-color{color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-color{color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-color{color: var(--wp--preset--color--white) !important;}.has-pale-pink-color{color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-color{color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-color{color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-color{color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-color{color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-color{color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-color{color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-color{color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-color{color: var(--wp--preset--color--vivid-purple) !important;}.has-black-background-color{background-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-background-color{background-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-background-color{background-color: var(--wp--preset--color--white) !important;}.has-pale-pink-background-color{background-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-background-color{background-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-background-color{background-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-background-color{background-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-background-color{background-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-background-color{background-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-background-color{background-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-background-color{background-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-background-color{background-color: var(--wp--preset--color--vivid-purple) !important;}.has-black-border-color{border-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-border-color{border-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-border-color{border-color: var(--wp--preset--color--white) !important;}.has-pale-pink-border-color{border-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-border-color{border-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-border-color{border-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-border-color{border-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-border-color{border-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-border-color{border-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-border-color{border-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-border-color{border-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-border-color{border-color: var(--wp--preset--color--vivid-purple) !important;}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background: var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple) !important;}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background: var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan) !important;}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange) !important;}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red) !important;}.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background: var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray) !important;}.has-cool-to-warm-spectrum-gradient-background{background: var(--wp--preset--gradient--cool-to-warm-spectrum) !important;}.has-blush-light-purple-gradient-background{background: var(--wp--preset--gradient--blush-light-purple) !important;}.has-blush-bordeaux-gradient-background{background: var(--wp--preset--gradient--blush-bordeaux) !important;}.has-luminous-dusk-gradient-background{background: var(--wp--preset--gradient--luminous-dusk) !important;}.has-pale-ocean-gradient-background{background: var(--wp--preset--gradient--pale-ocean) !important;}.has-electric-grass-gradient-background{background: var(--wp--preset--gradient--electric-grass) !important;}.has-midnight-gradient-background{background: var(--wp--preset--gradient--midnight) !important;}.has-small-font-size{font-size: var(--wp--preset--font-size--small) !important;}.has-medium-font-size{font-size: var(--wp--preset--font-size--medium) !important;}.has-large-font-size{font-size: var(--wp--preset--font-size--large) !important;}.has-x-large-font-size{font-size: var(--wp--preset--font-size--x-large) !important;}
:where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;}
:where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;}
:root :where(.wp-block-pullquote){font-size: 1.5em;line-height: 1.6;}
</style>
<link rel='stylesheet' id='bootstrap-css' href='https://sanatandharmveda.com/wp-content/themes/religion-twp/css/bootstrap.css?ver=4.0' type='text/css' media='all' />
<link rel='stylesheet' id='logitech-flaticon-css' href='https://sanatandharmveda.com/wp-content/themes/religion-twp/css/flaticon.css?ver=6.6.7' type='text/css' media='all' />
<link rel='stylesheet' id='owl-slider-css' href='https://sanatandharmveda.com/wp-content/themes/religion-twp/css/owl.carousel.min.css?ver=6.6.7' type='text/css' media='all' />
<link rel='stylesheet' id='lightgallery-css' href='https://sanatandharmveda.com/wp-content/themes/religion-twp/css/lightgallery.css?ver=6.6.7' type='text/css' media='all' />
<link rel='stylesheet' id='logitech-style-css' href='https://sanatandharmveda.com/wp-content/themes/religion-twp/style.css?ver=6.6.7' type='text/css' media='all' />
<link rel='stylesheet' id='logitech-preload-css' href='https://sanatandharmveda.com/wp-content/themes/religion-twp/css/royal-preload.css?ver=6.6.7' type='text/css' media='all' />
<script type="text/javascript" src="https://sanatandharmveda.com/wp-includes/js/jquery/jquery.min.js?ver=3.7.1" id="jquery-core-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-includes/js/jquery/jquery-migrate.min.js?ver=3.4.1" id="jquery-migrate-js"></script>
<script type="text/javascript" id="logitech_scripts-js-extra">
/* <![CDATA[ */
var logitech_loadmore_params = {"ajaxurl":"https:\/\/sanatandharmveda.com\/wp-admin\/admin-ajax.php"};
/* ]]> */
</script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/myloadmore.js?ver=1787661493" id="logitech_scripts-js"></script>
<link rel="https://api.w.org/" href="https://sanatandharmveda.com/wp-json/" /><link rel="alternate" title="JSON" type="application/json" href="https://sanatandharmveda.com/wp-json/wp/v2/posts/173810" /><link rel="EditURI" type="application/rsd+xml" title="RSD" href="https://sanatandharmveda.com/xmlrpc.php?rsd" />
<meta name="generator" content="WordPress 6.6.7" />
<link rel="canonical" href="https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/" />
<link rel='shortlink' href='https://sanatandharmveda.com/?p=173810' />
<link rel="alternate" title="oEmbed (JSON)" type="application/json+oembed" href="https://sanatandharmveda.com/wp-json/oembed/1.0/embed?url=https%3A%2F%2Fsanatandharmveda.com%2Fcurious-mathematics-points-and-you-will-interesting-functions%2F" />
<link rel="alternate" title="oEmbed (XML)" type="text/xml+oembed" href="https://sanatandharmveda.com/wp-json/oembed/1.0/embed?url=https%3A%2F%2Fsanatandharmveda.com%2Fcurious-mathematics-points-and-you-will-interesting-functions%2F&#038;format=xml" />
<link rel="pingback" href="https://sanatandharmveda.com/xmlrpc.php"><style type="text/css">
		  	/****Main Color****/

			/*Background Color*/
			.bg-primary,
			.list-primary li:before,
			.btn-details:hover,
			.owl-carousel .owl-dots button.owl-dot.active span,
			.owl-carousel .owl-dots button.owl-dot:hover span,
			.owl-carousel .owl-nav button.owl-prev:hover,.owl-carousel .owl-nav button.owl-next:hover,
			.octf-btn,
			.octf-btn-dark:hover, .octf-btn-dark:focus,
			.octf-btn-light:hover, .octf-btn-light:focus,
			.octf-btn.octf-btn-border:hover, .octf-btn.octf-btn-border:focus,
			.main-navigation > ul > li:before,
			.post-box .post-cat a,
			.post-box .btn-play:hover i,
			.page-pagination li span, .page-pagination li a:hover,
			.blog-post .share-post a,
			.post-nav > div .thumb-post:before,
			.post-nav .post-prev.not-thumb a:hover .thumb-post:before,
			.post-nav .post-next.not-thumb a:hover .thumb-post:before,
			.widget-area .widget .widget-title:before,
			.widget-area .widget_categories ul li a:before,.widget-area .widget_product_categories ul li a:before,.widget-area .widget_archive ul li a:before,
			.search-form .search-submit,
			.author-widget_social a:hover,
			.bline-yes .icon-box-1:after,
			.bline-yes .icon-box-2 .content-box:after,
			.box-s2.icon-right .icon-main,
			.ot-image-box:hover .link-box,
			.line-progress .progress-bar,
			.ot-pricing-table.is-featured .inner-table .title-table span,
			.ot-pricing-table.is-featured .octf-btn,
			.circle-social .team-social a:hover,
			.ot-accordions .acc-item.current .acc-toggle,
			.ot-testimonials .tphoto:after,
			.ot-message-box .icon-main,
			.ot-minicart .count,
			.ot-heading > span.is_line:before,
			.mc4wp-form-fields .subscribe-inner-form .subscribe-btn-icon:hover,
			#back-to-top,
			.error-404 .page-content form button:hover,
			.woocommerce ul.products li.product .added_to_cart, .woocommerce ul.products li.product .product_type_grouped, .woocommerce-page ul.products li.product .added_to_cart, .woocommerce-page ul.products li.product .product_type_grouped,
			.woocommerce #respond input#submit.alt, .woocommerce a.button.alt,.woocommerce button.button.alt, .woocommerce input.button.alt,.woocommerce #respond input#submit, .woocommerce a.button,.woocommerce input.button, .woocommerce button.button.alt.disabled,
			.woocommerce button.button,
			.woocommerce-mini-cart__buttons a.button.wc-forward,
			.woocommerce-mini-cart__buttons a.button.wc-forward:hover{ background: #ef7008; }
			.post-box .entry-meta .btn-details:hover, 
			.widget .tagcloud a:hover,
			.ot-heading > span.is_highlight,
			.icon-box-1 .icon-main{background: rgba(239,112,8,0.1);}
			.team-3 .team-thumb a:before{background: rgba(239,112,8,0.8);}
			.projects-grid .projects-box .portfolio-info,
			.projects-grid.style-3 .projects-thumbnail .overlay{background: rgba(239,112,8,0.9);}

			/*Background Image*/
			.author-widget_wrapper:before{ background-image: linear-gradient(230deg, #ef7008 -150%, #fff 80%); }

			/*Border Color*/
			.octf-btn.octf-btn-border,
			.post-box .entry-meta .btn-details:hover,
			.post-box .btn-play:hover i,
			.page-pagination li span, .page-pagination li a:hover,
			.blog-post .tagcloud a:hover,
			.widget .tagcloud a:hover,
			.ot-heading > span.is_highlight,
			.ot-image-box:hover .link-box,
			.ot-accordions .acc-item.current .acc-toggle,
			.ot-tabs .tab-link.current, .ot-tabs .tab-link:hover,
			.ot-video-button a:hover span,
			.woocommerce div.product .woocommerce-tabs ul.tabs li a:hover,
			.woocommerce div.product .woocommerce-tabs ul.tabs li.active a{ border-color: #ef7008; }

			/*Border Top Color*/
			.woocommerce-message,
			.woocommerce-info{ border-top-color: #ef7008; }

			/*Color*/
			blockquote:before,
			blockquote cite,
			.text-primary,
			.link-details,
			.link-details:visited,
			.octf-btn.octf-btn-border,
			.octf-btn.octf-btn-border:visited,
			a:hover, a:focus, a:active,
			.main-navigation > ul > li:hover > a,
			.main-navigation ul li li a:hover,.main-navigation ul ul.sub-menu li.current-menu-item > a,.main-navigation ul ul.sub-menu li.current-menu-ancestor > a,
			.main-navigation ul > li.menu-item-has-children:hover > a,
			.main-navigation ul > li.menu-item-has-children:hover > a:after,
			.main-navigation ul > li.menu-item-has-children > a:hover:after,
			.header_mobile .mobile_nav .mobile_mainmenu li li a:hover,.header_mobile .mobile_nav .mobile_mainmenu ul > li > ul > li.current-menu-ancestor > a,
			.header_mobile .mobile_nav .mobile_mainmenu > li > a:hover, .header_mobile .mobile_nav .mobile_mainmenu > li.current-menu-item > a,.header_mobile .mobile_nav .mobile_mainmenu > li.current-menu-ancestor > a,
			.post-box .entry-meta a:hover,
			.post-box .entry-meta .btn-details:hover,
			.post-box .entry-title a:hover,
			.post-box .link-box a:hover,
			.post-box .link-box i,
			.post-box .quote-box i,
			.post-box .quote-box .quote-text span,
			.blog-post .tagcloud a:hover,
			.blog-post .author-bio .author-info .author-socials a:hover,
			.comments-area .comment-item .comment-meta .comment-reply-link,
			.comment-respond .comment-reply-title small a:hover,
			.comment-form .logged-in-as a:hover,
			.widget .tagcloud a:hover,
			.widget-area .widget ul:not(.recent-news) > li a:hover,
			.widget-area .widget_categories ul li a:hover + span.posts-count,.widget-area .widget_product_categories ul li a:hover + span.posts-count,.widget-area .widget_archive ul li a:hover + span.posts-count,
			.ot-heading > span,
			.icon-box .icon-main,
			.icon-box-grid .icon-box .icon-main,
			.icon-box-grid .icon-box .content-box .title-box a:hover,
			.icon-box-grid .icon-box:hover .icon-main,
			.ot-image-box .link-box,
			.ot-counter span,
			.ot-counter-2 i,
			.ot-countdown li.seperator,
			.ot-pricing-table .inner-table h2,
			.project_filters li a:before,
			.project_filters li a .filter-count,
			.project_filters li a.selected, .project_filters li a:hover,
			.ot-team .team-info span,
			.ot-testimonials .t-head span,
			.woocommerce ul.products li.product .price .woocommerce-Price-amount, .woocommerce-page ul.products li.product .price .woocommerce-Price-amount,
			.woocommerce table.shop_table td.product-price, .woocommerce table.shop_table td.product-subtotal,
			.woocommerce-message:before,
			.woocommerce-info:before,
			.woocommerce .woocommerce-Price-amount,
			.woocommerce .site ul.product_list_widget li a:not(.remove):hover,
			.woocommerce .woocommerce-widget-layered-nav-list li a:hover,
			.woocommerce .widget_price_filter .price_slider_amount button.button,
			.woocommerce div.product p.price,.woocommerce div.product span.price{ color: #ef7008; }

			/*Other*/
			.icon-box .icon-main svg,
			.icon-box-grid .icon-box .icon-main svg,
			.ot-counter-2 svg{ fill: #ef7008; }
				</style><style type="text/css">h1, h2, h3, h4, h5, h6,
			blockquote,
			.font-second,
			.link-details,
			.slide-rev-subtitle,
			.octf-btn,
			select,
			.main-navigation ul,
			.page-header,
			.post-box .post-cat a,
			.post-box .entry-meta,
			.post-box .link-box a,
			.post-box .quote-box .quote-text,
			.page-pagination li a, .page-pagination li span,
			.blog-post .tagcloud a,
			.drop-cap,
			.post-nav,
			.comments-area .comment-item .comment-meta .comment-time,
			.comments-area .comment-item .comment-meta .comment-reply-link,
			.comment-form .logged-in-as,
			.widget .tagcloud a,
			.widget table,
			.widget .recent-news .post-on,
			.ot-heading,
			.ot-flip-box .number-title span,
			.ot-counter,
			.ot-counter span,
			.ot-countdown li span,
			.line-progress .percent,
			.project_filters li a,
			.projects-grid .projects-box .portfolio-info .portfolio-cates,
			.project-slider .projects-box .portfolio-info .portfolio-cates,
			.ot-team .team-info span,
			.member-info li span,
			.ot-accordions .acc-item .acc-toggle,
			.ot-tabs .tab-link,
			.ot-testimonials .t-head,
			.features-service-wrapper .features-service-item .features-service-content,
			div.elementor-widget-heading.elementor-widget-heading .elementor-heading-title,
			.elementor-element .elementor-widget-button .elementor-button,
			.elementor-default .elementor-widget-text-editor .elementor-drop-cap,
			.elementor-widget-wp-widget-polylang .lang-item,
			#lang_choice_wp-widget-polylang,
			.mmenu-wrapper .mobile_mainmenu,
			.woocommerce ul.products li.product, .woocommerce-page ul.products li.product,
			.woocommerce ul.products li.product .added_to_cart, .woocommerce ul.products li.product .product_type_grouped, .woocommerce-page ul.products li.product .added_to_cart, .woocommerce-page ul.products li.product .product_type_grouped,
			.woocommerce table.shop_table,
			.woocommerce .quantity .qty,
			.cart_totals h2,
			#add_payment_method .cart-collaterals .cart_totals table td, #add_payment_method .cart-collaterals .cart_totals table th,.woocommerce-cart .cart-collaterals .cart_totals table td, .woocommerce-cart .cart-collaterals .cart_totals table th,.woocommerce-checkout .cart-collaterals .cart_totals table td, .woocommerce-checkout .cart-collaterals .cart_totals table th,
			.woocommerce .site ul.product_list_widget li a:not(.remove),
			.woocommerce .widget_shopping_cart .cart_list .quantity,
			.woocommerce .widget_shopping_cart .total strong,.woocommerce.widget_shopping_cart .total strong,
			.woocommerce .widget_shopping_cart .total .woocommerce-Price-amount,.woocommerce.widget_shopping_cart .total .woocommerce-Price-amount,
			.woocommerce-mini-cart__buttons a.button.wc-forward,
			.woocommerce .woocommerce-widget-layered-nav-list,
			.woocommerce .widget_price_filter .price_slider_amount,
			.woocommerce .widget_price_filter .price_slider_amount button.button,
			.product_meta > span,
			.woocommerce div.product .entry-summary p.price,.woocommerce div.product .entry-summary span.price{ font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif;}
		    </style><link rel="icon" href="https://sanatandharmveda.com/wp-content/uploads/2024/05/cropped-cropped-pexels-himeshmehtaa25-3519190-32x32.jpg" sizes="32x32" />
<link rel="icon" href="https://sanatandharmveda.com/wp-content/uploads/2024/05/cropped-cropped-pexels-himeshmehtaa25-3519190-192x192.jpg" sizes="192x192" />
<link rel="apple-touch-icon" href="https://sanatandharmveda.com/wp-content/uploads/2024/05/cropped-cropped-pexels-himeshmehtaa25-3519190-180x180.jpg" />
<meta name="msapplication-TileImage" content="https://sanatandharmveda.com/wp-content/uploads/2024/05/cropped-cropped-pexels-himeshmehtaa25-3519190-270x270.jpg" />
</head>

<body class="post-template-default single single-post postid-173810 single-format-standard wp-custom-logo royal_preloader logitech-theme-ver-5.0 wordpress-version-6.6.7 footer-fixed">
<div id="royal_preloader" data-width="101" data-height="101" data-url="https://sanatandharmveda.com/wp-content/uploads/2024/10/cropped-Sanathana-Dharma-Veda-Main-1.png" data-color="#0a0f2b" data-bgcolor="#fff"></div><div id="page" class="site">
	
	<amp-auto-ads type="adsense"
        data-ad-client="ca-pub-7744495812468961">
</amp-auto-ads>

<!-- #site-header-open -->
<header id="site-header" class="site-header header-transparent">

    <!-- #header-desktop-open -->
    <div class="header-desktop"></div>    <!-- #header-desktop-close -->

    <!-- #header-mobile-open -->
    <div class="header-mobile"></div>    <!-- #header-mobile-close -->

</header>
<!-- #site-header-close -->
<!-- #side-panel-open -->
<!-- #side-panel-close --><!-- #site-content-open -->
<div id="content" class="site-content">
	        
            <div class="page-header flex-middle" >
                <div class="container">
                    <div class="inner flex-middle">
                                                    <h1 class="page-title">Curious Mathematics Points and you will Interesting Functions</h1>
                        <ul id="breadcrumbs" class="breadcrumbs none-style"><li><a href="https://sanatandharmveda.com">Home</a></li><li><a href="https://sanatandharmveda.com/blog/">Blog</a></li><li class="active">Curious Mathematics Points and you will Interesting Functions</li></ul>    
                            </div>
                </div>
            </div>
        	<div class="entry-content">
		<div class="container">
			<div class="row">
				<div id="primary" class="content-area col-lg-12 col-md-12 col-sm-12 col-xs-12">
					<main id="main" class="site-main">
						
					
 

<article id="post-173810" class="blog-post post-box post-173810 post type-post status-publish format-standard hentry category-blog">
    
    <div class="inner-post no-ptop">
        <div class="post-cat"><div class="posted-in"><a href="https://sanatandharmveda.com/category/blog/" rel="category tag">Blog</a></div></div>        <div class="entry-header">
            <div class="entry-meta">
                            </div>
            
        </div>

        <div class="entry-summary">

            <div class="toc" style="background: #f9f9f9;border: 1px solid #aaa;display: table;margin-bottom: 1em;padding: 1em;width: 350px;">
<p style="font-weight: 700;text-align: center;">Posts</p>
<ul>
<li><a href="#toc-0">Information Extra Fine print</a></li>
</ul>
</div>
<p>Excluding in itself, it offers four best divisors. Altogether, it&#8217;s got six divisors (as well as one to and in itself). When CNN put-out videos corroborating Cassie&apos;s allegation you to Combs punched their, Jackson told the newest Hollywood Reporter &quot;An individual observe you to, whether they have a girl and they would ever guess the girl getting less than those individuals items, you to shit is actually in love. <span id="more-173810"></span> Such as, they assist him pull off they.&quot; Jackson&apos;s feud with Sean &quot;Diddy&quot; Combs began inside 2006, whenever Jackson accused Combs of complicity in the Biggie&apos;s murder inside the diss tune &quot;The new Bomb&quot;. Mayweather rejected the issue and you can insulted Jackson&apos;s strained experience of their boy, offering Jackson one million if the he might post a video out of his kid saying &quot;I like your&quot;. It brought about a public conflict in which the a couple traded insults through online videos.</p>
<p>When the situation escalated, the newest emcees kept a mutual press conference declaring its reconciliation, and you will fans have been unsure if your hip hop artists had staged a hassle stunt to improve sales of their recently put out albums. Inside the an interview in the 2022, fifty Penny stated that inside the a meeting anywhere between him plus the couple in the Los angeles, both hip hop artists were that have a heated argument. The newest conflict resurfaced three-years after January 19, 2018, whenever Ja Signal took in order to Fb, getting in touch with aside fifty Cent for the social network. Ja Signal mentioned that the newest disagreement stemmed out of a great Queens video clips capture, whenever Jackson did not including seeing him &quot;bringing a whole lot like&quot; in the people.</p>
<p>A standout on-line casino in britain <a href="https://mrbetlogin.com/alice-adventure/">mrbetlogin.com visit our web site</a> , Heavens Vegas also provides an user-friendly and modern system that is easy to browse and suitable for each other the fresh and you may knowledgeable players. To get going and you can allege your own Heavens Las vegas 70 100 percent free revolves, all you need to do is sign up for an account that have the working platform, add a fees credit, and then click to &#x2018;opt inside the&#x2019;. The newest Sky Vegas welcome render currently available offers clients 70 100 percent free revolves after they register for the first time! I defense everything you need to learn, in addition to important fine print, tips register and you may claim, the pro review, greatest online game, and much more! Perhaps one of the most accepted labels in the united states, Sky Las vegas, is a household term and a go-so you can online casino attraction. Not consenting otherwise withdrawing agree, could possibly get negatively apply at certain has and functions.</p>
<ul>
<li>He earliest made an effort to promote our home inside the 2007 to own 18.5 million, and you can fell the cost several times in the next 5 years, if it is actually off and on the market industry.</li>
<li>As well as, according to my earlier experience in the fresh Goldrush application, I didn&apos;t features my personal hopes too high for this, because it originates from an identical Goldrush Class.</li>
<li>The statements within comment aren&#8217;t duplicated in the Bravobet selling profiles; when our very own sense failed to fulfill the terms and conditions, we said they.</li>
<li>These types of revolves is valid on the a range of popular Air Vegas video game.</li>
<li>During the 6x the newest maths is certainly beatable &#x2014; instead of the new 30x&#x2013;50x overseas bundles.</li>
<li>No-put 100 percent free revolves try revolves given simply for beginning a free account, with no being qualified put expected.</li>
</ul>
<p>See the list of online casino games you might wager the advantage on the, the newest bets and effective hats, not forgetting, view how frequently you need to choice the benefit. People are provided a while doing the brand new betting conditions and you can enjoy from the bonus. It separate comment &#x2014; checked out and you can confirmed because of the our team in may 2026 &#x2014; talks about all you need to learn before you could sign in. Very first Lay &amp; Buy &#xA3;5 to the Harbors to locate &#xA3;ten Harbors More (40x wagering, chose game), a hundred 100 percent free Revolves (well worth &#xA3;0.10 for every, selected online game).</p>
<p><img decoding="async" src="https://www.casinobonuschecker.com/wp-content/uploads/2023/01/lordpingcasinobonus.jpg" alt="online casino offers" align="left" border="1"></p>
<p>At the years two, Sire modeled for Kidz Safer, a great headphone brand for kids, earning 700,100000. Jackson listed the newest residence for sale in 2007 during the 18.5 million to maneuver nearer to their son, who resided on the A lot of time Isle during the time. 50 percent of the newest legal rights so you can their profile was offered to the British separate tunes publishing business Kobalt Group to own 3 million plus the partner for the next step three million, to your conversion of his records allowing Jackson to possess the brand new legal rights for the grasp tracks while you are using just for shipment. Their Connecticut case of bankruptcy submitting stated that he possessed seven automobiles valued at the more than 500,one hundred thousand, as well as an excellent 2010 Goes-Royce and you will an excellent 1966 Chevrolet Coupe. His possessions was detailed since the ranging from 10 million and fifty million within his personal bankruptcy petition, even if the guy testified under oath that he is worth cuatro.4 million. To the July 17, the new Court given your order making it possible for a creditor so you can proceed that have the newest punitive problems phase from an attempt up against Jackson inside a great Nyc county judge concerning the the new so-called release of a private movies.</p>
<h2 id="toc-0">Information Extra Fine print</h2>
<p>That it implies that 10Bet operates because the an entirely court and you may reliable betting site to own Southern area African people. The best part of your cellular software is that you have a tendency to receive regular announcements of new campaigns from 10Bet, along with all the the new Free Revolves offers which can be only available throughout the chose episodes. It indicates people will enjoy 10Bet&#x2019;s campaigns when, everywhere having complete mobile being compatible.</p>
<p>The fresh players can be check in a great Playbet membership and you may immediately receive R50 inside the incentive fund as well as 50 free revolves immediately, without needing to generate a deposit earliest. And you can really, the current Playbet welcome package is among the far more interesting also provides on the regional business today. No-put free spins are simply just credited to a player&apos;s account just after it&#8217;s been unsealed, with no earliest deposit required.</p>
<p><img decoding="async" src="https://www.bestbingosites.co.uk/gallery/lobby-on-vernons-bingo-full.jpg" alt="no deposit bonus 2" style="padding: 10px;" align="right" border="0"></p>
<p>During the 6x the newest maths try truly beatable &#x2014; unlike the brand new 30x&#x2013;50x overseas packages. The fresh 40-50x wagering requirements make sure the casino has the money. The higher-category of provide is definitely worth a third as much. Begin by the 3 legitimate zero-put also provides &#x2014; clear her or him, find out the systems &#x2014; before putting your own Rands behind the greater bundles. Totally free spin payouts hold their wagering conditions.</p>

        </div>
        <div class="entry-footer clearfix">
            <div class="share-post"><a class="twit" target="_blank" href="https://twitter.com/intent/tweet?text=Curious Mathematics Points and you will Interesting Functions&url=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/" title="Twitter"><i class="fab fa-twitter"></i></a><a class="face" target="_blank" href="https://www.facebook.com/sharer/sharer.php?u=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/" title="Facebook"><i class="fab fa-facebook-f"></i></a><a class="pint" target="_blank" href="https://www.pinterest.com/pin/create/button/?url=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/&description=Curious Mathematics Points and you will Interesting Functions" title="Pinterest"><i class="fab fa-pinterest-p"></i></a><a class="linked" target="_blank" href="https://www.linkedin.com/shareArticle?mini=true&url=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/&title=Curious Mathematics Points and you will Interesting Functions&summary=https://sanatandharmveda.com&source=Sanathan Dharm Veda" title="LinkedIn"><i class="fab fa-linkedin-in"></i></a> <a class="google" target="_blank" href="https://plus.google.com/share?url=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/" title="Google Plus"><i class="fab fa-google-plus-g"></i></a> <a class="tumblr" target="_blank" href="http://www.tumblr.com/share/link?url=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/&name=Curious Mathematics Points and you will Interesting Functions&description=Posts Information Extra Fine print Excluding in itself, it offers four best divisors. Altogether, it&#8217;s got six divisors (as well as one to and in itself). When CNN put-out videos corroborating Cassie&apos;s allegation you to Combs punched their, Jackson told the newest Hollywood Reporter &quot;An individual observe you to, whether they have a girl and [&hellip;]" title="Tumblr"><i class="fab fa-tumblr"></i></a><a class="reddit" href="http://reddit.com/submit?url=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/&title=Curious Mathematics Points and you will Interesting Functions" target="_blank" title="Reddit"><i class="fab fa-reddit-alien" aria-hidden="true"></i></a><a class="vk" href="http://vk.com/share.php?url=https://sanatandharmveda.com/curious-mathematics-points-and-you-will-interesting-functions/" target="_blank" title="VK"><i class="fab fa-vk"></i></a></div>        </div>
                <div class="post-nav clearfix"><div class="post-prev not-thumb"><a href="https://sanatandharmveda.com/evolution-the-new-real-time-gambling-establishment-juggernaut/" rel="prev"><div class="thumb-post"></div><div class="info-post"><h6>Evolution: The new Real time Gambling establishment Juggernaut</h6><span>August 17, 2026</span></div></a></div><div class="post-next not-thumb"><a href="https://sanatandharmveda.com/free-online-games-2/" rel="next"><div class="thumb-post"></div><div class="info-post"><h6>Free online games</h6><span>August 17, 2026</span></div></a></div></div>        <div class="related-posts"><h4>Related Posts</h4><div class="row">    
    <div class="col-sm-6">
        <div class="post-box post-item">
            <div class="post-inner">
                                <div class="inner-post">
                    <div class="post-cat"><div class="posted-in"><a href="https://sanatandharmveda.com/category/blog/" rel="category tag">Blog</a></div></div>                    <div class="entry-header">
                        <h5 class="entry-title"><a class="title-link" href="https://sanatandharmveda.com/blackjack-victoria-the-local-guide-to-table-games/" rel="bookmark">Blackjack Victoria The Local Guide To Table Games</a></h5>                    </div>
                </div>
                <div class="entry-meta">
                                        <a href="https://sanatandharmveda.com/blackjack-victoria-the-local-guide-to-table-games/" class="btn-details"><i class="ot-flaticon-trajectory"></i></a>
                </div>
            </div>
        </div>
    </div>

        
    <div class="col-sm-6">
        <div class="post-box post-item">
            <div class="post-inner">
                                <div class="inner-post">
                    <div class="post-cat"><div class="posted-in"><a href="https://sanatandharmveda.com/category/blog/" rel="category tag">Blog</a></div></div>                    <div class="entry-header">
                        <h5 class="entry-title"><a class="title-link" href="https://sanatandharmveda.com/ja-naka-ra-pa-ra-nae-tha-shha-ta-ka-nae-sa-chicken-road-ka-va/" rel="bookmark">ज_नक_र_प_र_ण_द_ष_ट_क_ण_स_chicken_road_क_व_श_ल-44491282</a></h5>                    </div>
                </div>
                <div class="entry-meta">
                                        <a href="https://sanatandharmveda.com/ja-naka-ra-pa-ra-nae-tha-shha-ta-ka-nae-sa-chicken-road-ka-va/" class="btn-details"><i class="ot-flaticon-trajectory"></i></a>
                </div>
            </div>
        </div>
    </div>

    </div></div>    </div>

</article>

					</main><!-- #main -->
				</div><!-- #primary -->
				
							</div>
		</div>	
	</div>

	</div><!-- #content -->
	<footer id="site-footer" class="site-footer" itemscope="itemscope" itemtype="http://schema.org/WPFooter"></footer></div><!-- #page -->
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/royal_preloader.min.js?ver=20200716" id="royal-preloader-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-includes/js/imagesloaded.min.js?ver=5.0.0" id="imagesloaded-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/jquery.isotope.min.js?ver=20200716" id="isotope-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/lightgallery-all.min.js?ver=20200716" id="lightgallery-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/owl.carousel.min.js?ver=20200716" id="owl-slider-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/easypiechart.min.js?ver=20200716" id="easypiechart-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/jquery.countdown.min.js?ver=20180910" id="countdown-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/elementor.js?ver=20200716" id="logitech-elementor-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/elementor-header.js?ver=20200716" id="logitech-elementor-header-js"></script>
<script type="text/javascript" src="https://sanatandharmveda.com/wp-content/themes/religion-twp/js/scripts.js?ver=20200716" id="logitech-scripts-js"></script>

</body>
</html>