Программа по математике geogebra

Расширение GeoGebra

Создано расширение GeoGebra для браузера Google Chrome

Обратите внимание на количество пользователей расширения: более 2.6 миллиона человек. Немногие расширения из магазина Chrome могут сравниться с такими цифрами

Это свидетельствует о том, что приложение GeoGebra широко используется в мире для образовательных целей.

Для входа в расширение кликните по кнопке «Сервисы» на панели закладок в браузере Google Chrome. После этого будет открыто окно расширения GeoGebra в вашем браузере. На начальном экране вы можете выбрать раздел математики, с которым далее вы будете работать в приложении.

Дополнительные материалы по работе в программе, вы можете найти на сайте производителя приложения, и в интернете.

Translation of the Coordinate System

You may translate the coordinate system by using the Move Graphics View Tool and dragging the background of the 3D Graphics View with your pointing device. Thereby, you can switch between two modes by clicking on the background of the 3D Graphics View:

  • Mode xOy-plane: You may translate the scene parallel to the xOy-plane.
  • Mode z-axis: You may translate the scene parallel to the z-axis.

Alternatively you can hold the Shift key and drag the background of the 3D Graphics View in order to translate the coordinate system. Again, you need to click in order to switch between the two modes while holding the Shift key.

Note: You can go back to the default view by selecting the button Back to Default View in the .

Direct Input using the Input Bar

GeoGebra’s 3D Graphics View supports points, vectors, lines, segments, rays, polygons, and circles in a three-dimensional coordinate system. You may either use the Tools provided in the , or directly enter the algebraic representation of these objects in the Input Bar or Input Field of the Algebra View (GeoGebra Web and Tablet Apps).

Example: Enter into the Input Bar or Input Field of the Algebra View in order to create a point in the three-dimensional coordinate system.

Furthermore, you may now create surfaces, planes, as well as geometric solids (pyramids, prisms, spheres, cylinders, and cones).

Example: Enter in order to create the corresponding surface.

Constructions with the Mouse

Using the construction Tools available in the you can create geometric constructions in the 3D Graphics View with the mouse. Select any construction tool from the 3D Graphics View Toolbar and read the tooltip provided in the 3D Graphics View in order to find out how to use the selected Tool.

Note: Any object you create in the 3D Graphics View also has an algebraic representation in the Algebra View.
Example: Select the Sphere with Center through Point Tool and click in the 3D Graphics View twice. The first click creates the center point while the second click creates a sphere and a point on the sphere.
Hint: In order to create a new point in the 3-dimensional space, you need to…

  • click and hold the mouse key (tap and hold) in order to define it’s x— and y-coordinate, then
  • drag the point up or down in order to change the z-coordinate and
  • release the click (tap) once you reached the desired coordinates.

Translation of the Coordinate System

You may translate the coordinate system by using the Move Graphics View Tool and dragging the background of the 3D Graphics View with your pointing device. Thereby, you can switch between two modes by clicking on the background of the 3D Graphics View:

  • Mode xOy-plane: You may translate the scene parallel to the xOy-plane.
  • Mode z-axis: You may translate the scene parallel to the z-axis.

Alternatively you can hold the Shift key and drag the background of the 3D Graphics View in order to translate the coordinate system. Again, you need to click in order to switch between the two modes while holding the Shift key.

Note: You can go back to the default view by selecting the button Back to Default View in the .

Direct Input using the Input Bar

GeoGebra’s 3D Graphics View supports points, vectors, lines, segments, rays, polygons, and circles in a three-dimensional coordinate system. You may either use the Tools provided in the , or directly enter the algebraic representation of these objects in the Input Bar or Input Field of the Algebra View (GeoGebra Web and Tablet Apps).

Example: Enter into the Input Bar or Input Field of the Algebra View in order to create a point in the three-dimensional coordinate system.

Furthermore, you may now create surfaces, planes, as well as geometric solids (pyramids, prisms, spheres, cylinders, and cones).

Example: Enter in order to create the corresponding surface.

Интерфейс GeoGebra

Интерфейс программы GeoGebra напоминает графический редактор. Программу можно использовать для черчения, но это не основное предназначение приложения.

Давайте рассмотрим основные элементы интерфейса программы GeoGebra:

  1. Полоса меню. Из меню вы можете изменить настройки программы.
  2. Панель инструментов. Здесь находятся инструменты для создания объектов. После щелчка по треугольнику в правом нижнем углу кнопки, будут открыты дополнительные инструменты. Операции, доступные в панели инструментов, можно производить с помощью строки ввода.
  3. Панель объектов. В Панели объектов отображаются введенные переменные и функции. Вместо имен переменных здесь отображаются их значения. Для того, чтобы увидеть формулу в символьном виде, нужно будет кликнуть по ней правой кнопкой мыши.
  4. Кнопки «Отменить» и «Повторить».
  5. Строка ввода. Это основной инструмент при работе в программе GeoGebra. Здесь вводятся команды и формулы, задаются значения переменных. Справа от строки ввода расположена кнопка «Список команд». С помощью дополнительных команд можно будет вводить команды и отсутствующие на клавиатуре символы.
  6. Рабочая область. Все построения в программе производятся в рабочей области. Вы можете изменить масштаб с помощью колесика мыши, перемещать по рабочей области ось координат.

Далее попытаемся выполнить некоторые элементарные действия в программе GeoGebra.

3D Graphics View Toolbar

The 3D Graphics View Toolbar provides a wide range of Tools that can be operated with the mouse and allow you to create the three-dimensional graphical representations of objects directly in the 3D Graphics View.
Every icon in the Toolbar represents a that contains a selection of related construction Tools. In order to open a Toolbox, you need to click on the corresponding default Tool shown in the 3D Graphics View Toolbar (GeoGebra Web and Tablet Apps) or on the small arrow in the lower right corner of the Toolbar icon (GeoGebra Desktop).

Note: The Tools of the 3D Graphics View Toolbar are organized by the nature of resulting objects or the functionality of the Tools. You will find Tools that create different types of planes in the or Tools that allow you to create geometric solids in the .

Constructions with the Mouse

Using the construction Tools available in the you can create geometric constructions in the 3D Graphics View with the mouse. Select any construction tool from the 3D Graphics View Toolbar and read the tooltip provided in the 3D Graphics View in order to find out how to use the selected Tool.

Note: Any object you create in the 3D Graphics View also has an algebraic representation in the Algebra View.
Example: Select the Sphere with Center through Point Tool and click in the 3D Graphics View twice. The first click creates the center point while the second click creates a sphere and a point on the sphere.
Hint: In order to create a new point in the 3-dimensional space, you need to…

  • click and hold the mouse key (tap and hold) in order to define it’s x— and y-coordinate, then
  • drag the point up or down in order to change the z-coordinate and
  • release the click (tap) once you reached the desired coordinates.

3D Graphics View Toolbar

The 3D Graphics View Toolbar provides a wide range of Tools that can be operated with the mouse and allow you to create the three-dimensional graphical representations of objects directly in the 3D Graphics View.
Every icon in the Toolbar represents a that contains a selection of related construction Tools. In order to open a Toolbox, you need to click on the corresponding default Tool shown in the 3D Graphics View Toolbar (GeoGebra Web and Tablet Apps) or on the small arrow in the lower right corner of the Toolbar icon (GeoGebra Desktop).

Note: The Tools of the 3D Graphics View Toolbar are organized by the nature of resulting objects or the functionality of the Tools. You will find Tools that create different types of planes in the or Tools that allow you to create geometric solids in the .

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