毛玻璃GeoGebra 快速入门(英文版)

2021年1月16日发(作者：毛江森)
GeoGebra Quickstart
A quick reference guide for GeoGebra

GeoGebra is free educational mathematics software that joins dynamic geometry,
algebra and calculus.
In the most simple manner, you can do constructions including points, vectors, seg-
ments, lines, and conic sections as well as functions, which can be altered dynami-
cally by mouse afterwards. On the other hand, also the direct input in school-notation
like
g: 3x + 4y = 7 or c: (x – 2)
2
+ (y – 3)
2
= 25 is possible, and a range of commands in-
cluding differentiation and integration are at your disposal. The most remarkable fea-
ture of GeoGebra is the dual view of objects: every expression in the algebra window
corresponds to an object in the geometry window and vice versa.

In the following, you will get acquainted to GeoGebra by examining three examples.
You should work them out one after the other and not forget to try out the given tips,
too.

Example 1: Circumcircle of a triangle
Example 2: Tangents to a circle
Example 3: Derivative and tangent of a function

After starting GeoGebra, the window depicted below appears. By means of the con-
struction tools (modes) in the toolbar you can do constructions on the drawing pad by
mouse. At the same time the corresponding coordinates and equations are displayed
in the algebra window. The input text field is used to enter coordinates, equations,
commands and functions directly; these are displayed at the drawing pad immedi-
ately after pressing the enter key. Geometry and algebra side by side:

Algebra
Window

Toolbar
Undo/Redo
Drawing Pad
Input Field

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Input Options

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Example 1: Circumcircle of a triangle
Task: Plot a triangle A, B, C and construct its circumcircle using GeoGebra.

Construction using the mouse



Choose the mode “Polygon” from the toolbar (click on the small arrow at the
third icon from the left). Now click on the drawing pad three times to create the
vertices A, B, and C. Close the triangle by clicking on A again.
Next, choose the mode “Line bisector” and construct two line bisectors by
clicking on two sides of the triangle.
In the mode “Intersect two objects” you can click on the intersection of both
line bisectors to get the center of your triangle’s circumcircle. To name it “M”,
click on it with the right mouse button (Mac OS: ctrl-click) and choose “Re-
name” from the appearing menu.
To finish the construction, you have to choose the mode “Circle with center
through point” and to click first at the center, then at any vertex of the triangle.
Now choose the mode “Move” and use the mouse to change the position of
any of the vertices – you will experience the meaning of “dynamic geometry”.


Some tips

Try the “Undo” button on the right side of the toolbar.

To hide an object, right click on it (Mac OS: ctrl-click) and uncheck “Show object”.

The appearance of objects (color, type of line, ...) can be changed easily: just use
the right mouse button (Mac OS: ctrl- click) again to click on the object and choose
“Properties” from the appearing context menu.

In the menu “View” algebra window, axes, and grid can be hidden or shown.
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In order to change the position of the drawing pad, choose the mode “Move draw-
ing pad” and simply use the mouse to drag it.

The menu “View – Construction Protocol“ provides a table listing all the steps you
took while doing your construction. This allows you to redo the construction step
by step by the use of the arrow keys, and also to modify the order of various steps
afterwards (see menu “Help” of the construction protocol). Moreover, you are able
to use the menu “View” to hide or show unwanted columns.

Further information on constructions by mouse can be found in menu “Help“, sec-
tion “Geometric input”.
Construction using the input text field
We are now going to do the same construction as above using the input text field, so
you will need a new drawing pad (menu “File – New”). Then, type the following com-
mands into the input text field at the bottom of the screen and press the enter key
after every line.
A = (2, 1)
B = (12, 5)
C = (8, 11)
Polygon[A, B, C]
l_a = LineBisector[a]
l_b = LineBisector[b]
M = Intersect[l_a, l_b]
Circle[M, A]
Some tips

Automatic completion of commands: after entering the first two letters of a com-



mand, it will be displayed automatically. If you want to adopt the suggestion, press
the enter key, otherwise just continue typing.

It is not necessary to key in every command, you can also choose it from the list
of commands that is found at the right next to the input text field.

Clicking at the icon “Input“ (bottom left) activates the mode “Input field”. In this
mode you can click on an object from the algebra window or drawing pad to copy
its name into the input text field.

For more tips concerning the input text field click on the question mark in the bot-
tom left corner.
You will obtain especially good results from your work with GeoGebra by combining
the advantages of both input forms, mouse and input text field.
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