Geogebra
Содержание:
- Déplacements d’objets, de la vue
- Интерфейс GeoGebra
- Расширение GeoGebra
- Translation of the Coordinate System
- 3D Graphics View Toolbar
- Client Events
- GeoGebra’s File format
- Miscellaneous
- Création d’objets 3D à l’aide d’outils
- General methods
- Constructions with the Mouse
- Direct Input using the Input Bar
- Barre de style
Déplacements d’objets, de la vue
Translation du repère
En activant le mode Déplacer Graphique et glissant l’arrière-plan de Graphique 3D avec le pointeur de votre souris, avec la possibilité de basculer entre les deux déplacements suivants en cliquant sur l’arrière-plan de Graphique 3D :
- Mode horizontal: La scène est déplacée parallèlement au plan xOy ;
- Mode vertical: La scène est déplacée parallèlement à l’axe des z.
Ou en maintenant enfoncée la touche Maj et glissant l’arrière-plan de Graphique 3D avec le pointeur de votre souris, avec la possibilité de basculer entre les deux déplacements suivants en cliquant sur l’arrière-plan de Graphique 3D :
Note : Revenir à la vue par défaut en cliquant sur Retour à la vue par défaut dans la .
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:
- Полоса меню. Из меню вы можете изменить настройки программы.
- 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.
- 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.
- Кнопки «Отменить» и «Повторить».
- 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.
- 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.
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 .
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 .
Client Events
These events can be observed using the method
| Type | Attributes | Description |
|---|---|---|
| addMacro | : macro name | when new macro is added |
| addPolygon | polygon construction started | |
| addPolygonComplete | : polygon label | polygon construction finished |
| algebraPanelSelected | Graphing / Geometry apps: algebra tab selected in sidebar | |
| deleteGeos | multiple objects deleted | |
| deselect | : object name (for single object) or null (deselect all) | one or all objects removed from selection |
| dragEnd | mouse drag ended | |
| editorKeyTyped | key typed in editor (Algebra view of any app or standalone Evaluator app) | |
| editorStart | object label if editing existing object | user moves focus to the editor (Algebra view of any app or standalone Evaluator app) |
| editorStop | : object label if editing existing object | user (Algebra view of any app or standalone Evaluator app) |
| export | : JSON encoded array including export format | export started |
| mouseDown | : mouse x-coordinate, : mouse y-coordinate | user pressed the mouse button |
| movedGeos | : object labels | multiple objects move ended |
| movingGeos | : object labels | multible objects are being moved |
| openDialog | : dialog ID | dialog is opened (currently just for export dialog) |
| openMenu | : submenu ID | main menu or one of its submenus were open |
| pasteElms | : pasted objects as XML | pasting multiple objects started |
| pasteElmsComplete | pasting multiple objects ended | |
| perspectiveChange | perspective changed (e.g. a view was opened or closed) | |
| redo | redo button pressed | |
| relationTool | : HTML description of the object relation | relation tool used |
| removeMacro | : custom tool name | custom tool removed |
| renameComplete | object renaming complete (in case of chain renames) | |
| renameMacro | : array | custom tool was renamed |
| select | : object label | object added to selection |
| setMode | : mode number (see toolbar reference for details) | app mode changed (e.g. a tool was selected) |
| showNavigationBar | : «true» or «false» | navigation bar visibility changed |
| showStyleBar | : «true» or «false» | style bar visibility changed |
| sidePanelClosed | side panel (where algebra view is in Graphing Calculator) closed | |
| sidePanelOpened | side panel (where algebra view is in Graphing Calculator) opened | |
| tablePanelSelected | table of values panel selected | |
| toolsPanelSelected | tools panel selected | |
| undo | undo pressed | |
| updateStyle | : object label | object style changed |
| viewChanged2D | : horizontal pixel position of point (0,0), : vertical pixel position of point (0,0), : ratio pixels / horizontal units, : ratio pixels / vertical units, : graphics view number (1 or 2) | graphics view dimensions changed by zooming or panning |
| viewChanged3D | similar to 2D, e.g. | 3D view dimensions changed by zooming or panning |
GeoGebra’s File format
With these methods you can set everything in a construction (see XML Reference ).
| Method Signature | Since | Description |
|---|---|---|
| void evalXML(String xmlString) | 2.7 | Evaluates the given XML string and changes the current construction. Note: the construction is NOT cleared before evaluating the XML string. |
| void setXML(String xmlString) | 2.7 | Evaluates the given XML string and changes the current construction. Note: the construction is cleared before evaluating the XML string. This method could be used to load constructions. |
| String getXML() | 2.7 | Returns the current construction in GeoGebra’s XML format. This method could be used to save constructions. |
| String getXML(String objName) | 3.2 | Returns the GeoGebra XML string for the given object, i.e. only the <element> tag is returned. |
| String getAlgorithmXML(String objName) | 3.2 | For a dependent GeoElement objName the XML string of the parent algorithm and all its output objects is returned. For a free GeoElement objName «» is returned. |
| String getFileJSON() | 5.0 | Gets the current construction as JSON object including the XML and images |
| String setFileJSON(Object content) | 5.0 | Sets the current construction from a JSON (object or string) that includes XML and images (try getFileJSON for the precise format) |
| String getBase64() | Gets the current construction as a base64-encoded .ggb file | |
| String getBase64(function callback) | 4.2 | Gets the current construction as a base64-encoded .ggb file asynchronously, passes as parameter to the callback function when ready. The callback function should take one parameter (the base64 string). |
| void setBase64(String ) | 4.0 | Sets the current construction from a base64-encoded .ggb file. If callback function is specified, it is called after the file is loaded. |
Miscellaneous
| Method Signature | Since | Description |
|---|---|---|
| void debug(String string) | 3.2 | Prints the string to the Java Console |
| String getVersion() | 5.0 | Returns the version of GeoGebra |
Création d’objets 3D à l’aide d’outils
En utilisant les outils de construction disponibles dans la Barre_d’outils vous pouvez faire, avec la souris, des constructions géométriques dans la vue Graphique 3D. Choisissez un outil de construction quelconque dans la Barre d’outils et lisez l’Aide Barre d’outils pour trouver comment utiliser l’outil choisi. Tout objet que vous créez dans la vue Graphique 3D a aussi une représentation algébrique dans la Fenêtre Algèbre, si de plus vous lui donnez (Renommer) un nom de cellule ( par ex. A1) sa valeur sera portée dans la cellule correspondante du Tableur.
Création, gestion d’un point 3D
En mode Point il vous faut promener votre pointeur de souris sur la partie (affichée ou non) du plan xOy afin qu’il prenne l’aspect d’une Croix ;
Un clic à l’endroit voulu va créer un Point3D du plan xOy.
Maintenant tout en restant en mode Point, ou en passant en mode Déplacer, tout clic sur le point va autoriser
- par le déplacement du point dans un plan horizontal, ou par sur une droite verticale.
Quelque soit le type de déplacement d’un Point3D, vous verrez apparaître sa projetante verticale pendant le déplacement
Note : En mode Déplacer, vous pouvez bouger des objets à l’aide de la souris dans la vue Graphique 3D. Simultanément, leurs représentations algébriques (et dans le Tableur) sont dynamiquement actualisées dans la Fenêtre Algèbre (et dans le Tableur).
Chaque icône dans la barre d’outils représente une boîte à outils contenant une sélection d’outils de construction analogues. Pour ouvrir une boîte à outils, vous devez cliquer sur la petite flèche dans le coin inférieur droit de l’icône affichée.
Note : Les outils de construction sont organisés en fonction de la nature des objets produits.Par exemple, vous trouverez les outils créant différents types de points dans la Boîte à outils Points (icône par défaut ) et les outils permettant d’utiliser des transformations géométriques dans la Boîte à outils Transformations (icône par défaut ).
General methods
| Method Signature | Since | Description |
|---|---|---|
| void deleteObject(String objName) | 2.7 | Deletes the object with the given name. |
| void setAuxiliary(geo, true/false) | 5.0 | Affects or not the status of «auxiliary object» to object geo. |
| void setValue(String objName, double value) | 3.2 | Sets the double value of the object with the given name. Note: if the specified object is boolean, use a value of 1 to set it to true and any other value to set it to false. For any other object type, nothing is done. |
| void setTextValue(String objName, String value) | 3.2 | Sets the text value of the object with the given name. For any other object type, nothing is done. |
| void setListValue(String objName, int i, double value) | 5.0 | Sets the value of the list element at position ‘i’ to ‘value’ |
| void setCoords(String objName, double x, double y)void setCoords(String objName, double x, double y, double z) | 3.05.0 | Sets the coordinates of the object with the given name. Note: if the specified object is not a point, vector, line or absolutely positioned object (text, button, checkbox, input box) nothing is done. |
| void setCaption(String objName, String caption) | 5.0 | Sets the caption of object with given name. |
| void setColor(String objName, int red, int green, int blue) |
2.7 | Sets the color of the object with the given name. |
| void setVisible(String objName, boolean visible) | 2.7 | Shows or hides the object with the given name in the graphics window. |
| void setLabelVisible(String objName, boolean visible) | 3.0 | Shows or hides the label of the object with the given name in the graphics window. |
| void setLabelStyle(String objName, int style) | 3.0 | Sets the label style of the object with the given name in the graphics window. Possible label styles are NAME = 0, NAME_VALUE = 1, VALUE = 2 and (from GeoGebra 3.2) CAPTION = 3 |
| void setFixed(String objName, boolean fixed, boolean selectionAllowed) | 3.0 | Sets the «Fixed» and «Selection Allowed» state of the object with the given name. Note: fixed objects cannot be changed. |
| void setTrace(String objName, boolean flag) | 3.0 | Turns the trace of the object with the given name on or off. |
| boolean renameObject(String oldObjName, String newObjName) | 3.2 | Renames oldObjName to newObjName. Returns whether the rename was successful |
| void setLayer(String objName, int layer) | 3.2 | Sets the layer of the object |
| void setLayerVisible(int layer, boolean visible) | 3.2 | Shows or hides the all objects in the given layer |
| void setLineStyle(String objName, int style) | 3.2 | Sets the line style for the object (0 to 4) |
| void setLineThickness(String objName, int thickness) | 3.2 | sets the thickness of the object (1 to 13, -1 for default) |
| void setPointStyle(String objName, int style) | 3.2 | |
| void setPointSize(String objName, int size) | 3.2 | Sets the size of a point (from 1 to 9) |
| void setDisplayStyle(String objName, String style) | 5.0 | Sets the display style of an object. Style should be one of «parametric», «explicit», «implicit», «specific» |
| void setFilling(String objName, double filling) | 3.2 | Sets the filling of an object (from 0 to 1) |
| String getPNGBase64(double exportScale, boolean transparent, double DPI) | 4.0 | Returns the active Graphics View as a base64-encoded Stringeg var str = ggbApplet.getPNGBase64(1, true, 72); The DPI setting is slow, set to if you don’t need it |
| String exportSVG() | 4.0 | Returns the active Graphics View as an SVGeg var svg = ggbApplet.exportSVG(); Returrns if the active view is 3D |
| void getScreenshotBase64(function callback) | 5.0 | Gets the screenshot of the whole applet as PNG and sends it to the callback function as a base64 encoded string. Example: For internal use only, may not work in all browsers |
| boolean writePNGtoFile(String filename, double exportScale, boolean transparent, double DPI) | 4.0 | Exports the active Graphics View to a .PNG file. The DPI setting is slow, set to if you don’t need it eg var success = ggbApplet.writePNGtoFile(«myImage.png», 1, false, 72); |
| boolean isIndependent(String objName) | 4.0 | checks if objName is independent |
| boolean isMoveable(String objName) | 4.0 | checks if objName is is moveable |
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.
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.
Barre de style
GeoGebra pour Ordinateurs :
Cliquez sur le bouton ‘Bascule Barre de style’ à gauche du titre Graphique 3D dans le bandeau supérieur de la fenêtre.
Afficher ou cacher les axes.
-
Afficher ou cacher la grille.
-
Afficher/cacher le plan xOy.
-
Retour à la vue standard.
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Options Capture d’un point : par appui sur , vous affichez les 4 possibilités.
- Démarrer ou arrêter la rotation de la vue autour de l’axe «vertical» de l’espace de travail : par appui sur , vous affichez un curseur vous permettant de régler sens et vitesse de rotation.
-
Idée : L’axe «vertical» de l’espace de travail correspond à
- sauf si vous avez sélectionné l’option axe y’Oy vertical dans les Préférences — Graphique 3D, dans ce cas, à .
- Choix Vue : par appui sur , vous ouvrez un sous-menu.
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Options Capture d’un point : par appui sur , vous affichez les 4 possibilités.
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Retour à la vue standard.
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Afficher/cacher le plan xOy.
