Receiving Helpdesk

what is the space inside a 2 dimensional figure called

by Guadalupe Lebsack Published 2 years ago Updated 2 years ago

Area is the space inside the shape. It's a measure of 2-D space, and the units for area are squared ("length squared").

What is the inside part of a two dimensional figure called?

A two-dimensional figure, also called a plane or planar figure, is a set of line segments or sides and curve segments or arcs, all lying in a single plane. The sides and arcs are called the edges of the figure. The inside part is called the region enclosed by the figure. Click to see full answer.

What is the area of a two dimensional shape?

The area of a 2D shape is the space inside the shape. Also, what is a two dimensional plane? In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

What is an example of a two-dimensional shape?

For example, a sheet of paper is two-dimensional in shape. It consists of a length and a width but does not have any depth or height. Some common 2D shapes are square, rectangle, triangle, circle, and hexagon.

Is our space really four dimensional?

I am NOT saying that our space is really four dimensional. It is not. It has only three spatial dimensions. I AM merely trying to show that we can understand what it would be like if space did happen to have four dimensions.

What is the space inside of a 3D object called?

As discussed, all 3 Dimensional shapes have a surface area and volume. The surface area is the area covered by the 3D shape at the bottom, top, and all the faces including the curved surfaces, if any. Volume is defined as the amount of space occupied by a 3D shape.

What is the name space inside of a plane figure?

In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure. The area is measured in square units such as square centimeters, square feet, square inches, etc.

What is a two-dimensional figure called?

A plane figure or two-dimensional figure is a figure that lies completely in one plane.

What is the amount of space taken by 2 dimensional shape or figure?

In math, the area of a two-dimensional figure is the quantity of surface delimited by the perimeter of a figure in a plane. In other words, the area in 2D is the space inside the lines we use to draw a figure. We use square units to describe area, like square meters (m2) or square feet (ft2).

What is area of a plane figure?

The area (A) of a closed plane figure is the region of the plane enclosed by the figure's boundary. Area is measured in square units of length such as square centimetre (cm2) and square metre (m2).

Is the space that covers the plane figure?

In mathematics the area of a plane figure refers to the number of square units the figure covers. The area is the inside shape or space measured in square units.

What is a 2D surface?

Definition of two-dimensional adjective. having the dimensions of height and width only: a two-dimensional surface. (of a work of art) having its elements organized in terms of a flat surface, especially emphasizing the vertical and horizontal character of the picture plane: the two-dimensional structure of a painting.

What is a 2-dimensional object?

Two Dimensions: A flat plane or shape is two-dimensional. Its two dimensions are length and width. Polygons, such as squares and rectangles, are examples of two-dimensional objects. Two-dimensional objects can be rotated in a plane.

What are the properties of 2-dimensional shapes?

A 2D (two-dimensional) shape can be defined as a plane figure that can be drawn on a flat surface. It has only two dimensions – length and width, with no thickness or depth. Some of the basic 2D shapes are rectangle, pentagon, quadrilateral, circle, triangles, square, octagon, and hexagon.

What is the area inside the shape?

Area is the space inside the shape. It's a measure of 2-D space, and the units for area are squared ("length squared"). Congruent shapes have the same area.

Is area a 2-dimensional measurement?

To find the area of a rectangle, you multiply the length by the width. Although area is a two-dimensional measurement, it can also be used with three-dimensional objects. You can find the area of the base (two-dimensional) of a cone (three-dimensional).

Two- and Three-Dimensional Figures: Overview

The simplest way to define two- and three-dimensional figures is that they are shapes. The difference between them is that two-dimensional figures are flat but three-dimensional figures are not. A two-dimensional figure is built from one-dimensional figures. A line segment is an example of a one-dimensional figure.

What is a Two-Dimensional Figure?

Two-dimensional figures are shapes that can be measured in two directions. Two characteristics of two-dimensional figures are that they have area and also perimeter. Two-dimensional figures are shapes like squares and rectangles. They can be used to describe the shape of things like windows, tables, or tennis courts.

What is a Three-Dimensional Figure?

After defining two-dimensional figures, the next question of course is what is a three-dimensional figure? Just as a two-dimensional figure can be measured in three directions, a three-dimensional figure can be measured in three directions. In fact, a three-dimensional figure can be formed by joining two-dimensional figures together.

Measuring Two- and Three-Dimensional Figures

There are three main ways to measure figures. These are by finding the distance, area, and volume.

The one dimensional interval

The one dimensional analog of a cube is an interval. It is formed by taking a dimensionless point and dragging it through a distance. That distance could be 2 inches or 3 feet or anything. Let us call the distance "L".

The two dimensional square

The two dimensional analog of a cube is a square. It is formed by dragging the one dimensional interval through a distance L in the second dimension.

The three dimensional cube

To form a cube, we take the square and drag it a distance L in the third dimension.

The four dimensional cube: the tesseract

So far I hope you have found our constructions entirely unchallenging. The next step into four dimensions can be done equally mechanically. We just systematically repeat every step above. The only difference is that this time we cannot readily form a mental picture of what we are building. But we can know all its properties!

Stereovision

The "drawings" of the tesseract are hard to see clearly. That is because they are really supposed to be three dimensional models in a three dimensional space. So what we have above are two dimensional drawings of three dimensional models of a four dimensional tesseract. No wonder it is getting messy!

Summary table

We can summarize the development of the properties of a tesseract as follows:

A roomy challenge

If you were to live in a tesseract, you might choose to live in its three dimensional surface, much as a two dimensional person might choose live in the 6 square rooms that form the two dimensional surface of a cube. So your house would be the eight cubes that form the surface of the tesseract.

image
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version900msRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[13:26:16] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[13:26:16] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[13:26:16] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[13:26:16] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[13:26:16] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[13:26:16] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[13:26:16] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[13:26:16] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[13:26:16] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[13:26:16] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[13:26:16] LOG.warning: explode(): Passing null to parameter #2 ($string) of type string is deprecat...
  • Booting (10.19ms)
  • Application (889ms)
  • 1 x Application (98.83%)
    889.34ms
    1 x Booting (1.13%)
    10.19ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed872ms
    • select * from `posts` where `published_at` <= '2025-06-21 13:26:16' and `slug` = 'what-is-the-space-inside-a-2-dimensional-figure-called' and `posts`.`deleted_at` is null limit 1
      2.55ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-21 13:26:16
      • 1. what-is-the-space-inside-a-2-dimensional-figure-called
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 207884 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      11.56msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 207884
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      820μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      350μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      290μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      856ms/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 93 limit 1
      590μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 93
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        mkdUMTxcnTJsWAhuoIDG7e51B9nHB8Gf3uqdpOoy
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-is-the-space-inside-a-2-dimensional-fig...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /what-is-the-space-inside-a-2-dimensional-figure-called
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:25 [ "cookie" => array:1 [ 0 => "_pk_id.64.7c30=20d463f20a15d8e4.1750492557.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImI0aUxHZ296NUNKcy9NdGN6YS9sSlE9PSIsInZhbHVlIjoieVNub3QxalV3MU1GdnZGemtiZkZOQ3RGKzB3Qlg2eDZaZmhjNXl1MUVlNUhBREg0V2NDQlV6Z3B6elhESWhacnlNbk1rbHRSbjNqTjNOa2tlTGZ6MTM2M2I1STMvZ1RZYVA5ck9YRUdERFVoNDV5eWlxZHAvWGJEbTFIaldOWmUiLCJtYWMiOiIxNjc2NWVkODZmY2RkOWU1ZWJmMzM4MjhmNmJhYjRkZDg2ZTNhYzE2MTIxZTczNmNkMGFhNDRjZDBiODY0NTQ3IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IjNvZjhvTTJ4WnpXUlNVbHkvZWM4ZEE9PSIsInZhbHVlIjoiVCtUYXBubndZY3dWUkZ4OUQ4VjhMY2Uzakt5dEFKT21UbGtyWHJ1blQzSHFOejVmVSt5Vmx3TkJubFJrenpJbFNzbjRsUUxrV3ZlL1JtLzNDTlJUbHdoZDRZM2FEck5LdGRadEF6dWxsdUFmYlVLRCtuZGFhR1FmSVdOeE1DTHoiLCJtYWMiOiI3MzdkZWZhM2U0ZmIxZWVlMTU4Y2Q5NWU5ZWZmMzliYTBjZDA0MzA3MDQ5NTZiY2Q4ZDU3NTc0NzUzMGU3YzhkIiwidGFnIjoiIn0%3D_pk_id.64.7c30=20d463f20a15d8e4.1750492557.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImI0aUxHZ296NUNKcy9NdGN6YS9sSlE9PSIsInZhbHVlIjoieVNub3QxalV3MU1GdnZGemtiZkZOQ" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.243" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "9531f2cbdff2eaf5-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.243, 172.71.255.104" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/what-is-the-space-inside-a-2-dimensional-figure-called" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/what-is-the-space-inside-a-2-dimensional-figure-called" "REMOTE_PORT" => "53358" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.71.255.104" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "_pk_id.64.7c30=20d463f20a15d8e4.1750492557.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImI0aUxHZ296NUNKcy9NdGN6YS9sSlE9PSIsInZhbHVlIjoieVNub3QxalV3MU1GdnZGemtiZkZOQ3RGKzB3Qlg2eDZaZmhjNXl1MUVlNUhBREg0V2NDQlV6Z3B6elhESWhacnlNbk1rbHRSbjNqTjNOa2tlTGZ6MTM2M2I1STMvZ1RZYVA5ck9YRUdERFVoNDV5eWlxZHAvWGJEbTFIaldOWmUiLCJtYWMiOiIxNjc2NWVkODZmY2RkOWU1ZWJmMzM4MjhmNmJhYjRkZDg2ZTNhYzE2MTIxZTczNmNkMGFhNDRjZDBiODY0NTQ3IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IjNvZjhvTTJ4WnpXUlNVbHkvZWM4ZEE9PSIsInZhbHVlIjoiVCtUYXBubndZY3dWUkZ4OUQ4VjhMY2Uzakt5dEFKT21UbGtyWHJ1blQzSHFOejVmVSt5Vmx3TkJubFJrenpJbFNzbjRsUUxrV3ZlL1JtLzNDTlJUbHdoZDRZM2FEck5LdGRadEF6dWxsdUFmYlVLRCtuZGFhR1FmSVdOeE1DTHoiLCJtYWMiOiI3MzdkZWZhM2U0ZmIxZWVlMTU4Y2Q5NWU5ZWZmMzliYTBjZDA0MzA3MDQ5NTZiY2Q4ZDU3NTc0NzUzMGU3YzhkIiwidGFnIjoiIn0%3D_pk_id.64.7c30=20d463f20a15d8e4.1750492557.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImI0aUxHZ296NUNKcy9NdGN6YS9sSlE9PSIsInZhbHVlIjoieVNub3QxalV3MU1GdnZGemtiZkZOQ" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.243" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "9531f2cbdff2eaf5-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.243, 172.71.255.104" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1750492576.6317 "REQUEST_TIME" => 1750492576 ]
        request_cookies
        0 of 0
        array:4 [ "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null "XSRF-TOKEN" => "mkdUMTxcnTJsWAhuoIDG7e51B9nHB8Gf3uqdpOoy" "askhelpdesk_session" => "BTvZ1TQH4DXaVQtdKSFvDBNbw1gg1FBJef0CkTHz" ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Sat, 21 Jun 2025 07:56:16 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ii9iKzZBZTZ3QTVzL3o0MGJrbUpORVE9PSIsInZhbHVlIjoiVWtYZWRTL2dJOUJLZXQwQXRCalh3dDRXU0NXVGd2Qy9rWlJ4Y1dBWG90NDJ3MUkxTk90Q0NIS0l3KzVDaURWZlhyM3Vyc2NUUTJFQitWMUVGWUorY1ZSajN1R1RvZHovOXUvWlFCTTJWQUJNRHA3VXlyT090b2dGVnhPZlczQVgiLCJtYWMiOiJhZTZmMzlhYjMwNzc3MjgwODVjZjQzNjgwMWE3Y2QxYTk4NDY1N2M2ZmY1MTM3M2ZjNmUxYzI3ZDEwYWIxNGMyIiwidGFnIjoiIn0%3D; expires=Sat, 21-Jun-2025 09:56:17 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6Ii9iKzZBZTZ3QTVzL3o0MGJrbUpORVE9PSIsInZhbHVlIjoiVWtYZWRTL2dJOUJLZXQwQXRCalh3dDRXU0NXVGd2Qy9rWlJ4Y1dBWG90NDJ3MUkxTk90Q0NIS0l3KzVDaURWZlhyM3Vyc" 1 => "askhelpdesk_session=eyJpdiI6InBUZlU5RDJKWE5JOUM5ZjltN2ZqeUE9PSIsInZhbHVlIjoiMG5MSjdsSlJoN1VoMDBGTlRBOVN3ankvZmNzNFhvMi9WeTRkUXc2MUdNbnBsZmZUU2RndXJVTnVHYzB3c09MZ3ljWjRmUVo2YVExWXg3OTN3OVVmYlF0WVJ3V0lXV3hYV0FwUXRWMjZ2NXZtck15V1hXRWlYdnIxQkMwZ1gyWTUiLCJtYWMiOiI5M2U0ZjQ4ZGQ5YTJjYWY4OGVmZjIxYmVmYjAzZmUwZjE2MDJhMGZhZjFjZmM5ZTZmMDkwODE1MmQxZWIwM2U0IiwidGFnIjoiIn0%3D; expires=Sat, 21-Jun-2025 09:56:17 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6InBUZlU5RDJKWE5JOUM5ZjltN2ZqeUE9PSIsInZhbHVlIjoiMG5MSjdsSlJoN1VoMDBGTlRBOVN3ankvZmNzNFhvMi9WeTRkUXc2MUdNbnBsZmZUU2RndXJVTnVHYzB3c09M" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Ii9iKzZBZTZ3QTVzL3o0MGJrbUpORVE9PSIsInZhbHVlIjoiVWtYZWRTL2dJOUJLZXQwQXRCalh3dDRXU0NXVGd2Qy9rWlJ4Y1dBWG90NDJ3MUkxTk90Q0NIS0l3KzVDaURWZlhyM3Vyc2NUUTJFQitWMUVGWUorY1ZSajN1R1RvZHovOXUvWlFCTTJWQUJNRHA3VXlyT090b2dGVnhPZlczQVgiLCJtYWMiOiJhZTZmMzlhYjMwNzc3MjgwODVjZjQzNjgwMWE3Y2QxYTk4NDY1N2M2ZmY1MTM3M2ZjNmUxYzI3ZDEwYWIxNGMyIiwidGFnIjoiIn0%3D; expires=Sat, 21-Jun-2025 09:56:17 GMT; path=/XSRF-TOKEN=eyJpdiI6Ii9iKzZBZTZ3QTVzL3o0MGJrbUpORVE9PSIsInZhbHVlIjoiVWtYZWRTL2dJOUJLZXQwQXRCalh3dDRXU0NXVGd2Qy9rWlJ4Y1dBWG90NDJ3MUkxTk90Q0NIS0l3KzVDaURWZlhyM3Vyc" 1 => "askhelpdesk_session=eyJpdiI6InBUZlU5RDJKWE5JOUM5ZjltN2ZqeUE9PSIsInZhbHVlIjoiMG5MSjdsSlJoN1VoMDBGTlRBOVN3ankvZmNzNFhvMi9WeTRkUXc2MUdNbnBsZmZUU2RndXJVTnVHYzB3c09MZ3ljWjRmUVo2YVExWXg3OTN3OVVmYlF0WVJ3V0lXV3hYV0FwUXRWMjZ2NXZtck15V1hXRWlYdnIxQkMwZ1gyWTUiLCJtYWMiOiI5M2U0ZjQ4ZGQ5YTJjYWY4OGVmZjIxYmVmYjAzZmUwZjE2MDJhMGZhZjFjZmM5ZTZmMDkwODE1MmQxZWIwM2U0IiwidGFnIjoiIn0%3D; expires=Sat, 21-Jun-2025 09:56:17 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6InBUZlU5RDJKWE5JOUM5ZjltN2ZqeUE9PSIsInZhbHVlIjoiMG5MSjdsSlJoN1VoMDBGTlRBOVN3ankvZmNzNFhvMi9WeTRkUXc2MUdNbnBsZmZUU2RndXJVTnVHYzB3c09M" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "mkdUMTxcnTJsWAhuoIDG7e51B9nHB8Gf3uqdpOoy" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-is-the-space-inside-a-2-dimensional-figure-called" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]