An introduction of dynamic mathematical software, GeoGebra

Tatsuyoshi Hamada, Oct 11, 2017

GeoGebra is a dynamic mathematical software. It is developed for learning and teaching mathematics in schools by Markus Hohenwarter and an international team of programmers. GeoGebra supports not only Windows and Mac but also iPhone, iPad and Android devices. GeoGebra is a rapidly expanding community of millions of users located in just about every country. In this talk, we introduce how to use GeoGebra for teaching calculus, curves and surfaces.

Table of Contents

  1. Introduction
    1. KNOPPIX/Math -> MathLibre
    2. Mathematical software is
    3. History of dynamic geometry software
    4. Dynamic mathematical software GeoGebra
    5. How to start GeoGebra?
    6. Some parts of GeoGebra
    7. From "compass and ruler" to computer
    8. Attach and detach
    9. Inputting formula on GeoGebra
    10. How to study materials on the world?
  2. GeoGebra Script
    1. x() and y()
    2. Slider()
    3. Sequence()
    4. List commands
    5. Vectors and matrices
    6. Curve() and Vector()
    7. IF()
    8. SlopeField() and SolveODE()
    9. Surface()
  3. GeoGebra Materials
    1. GeoGebra Materials
    2. Euclidean geometry
    3. TriangleCenter()
    4. Taylor polynomials
    5. Vector field and integral curves
    6. Implicit curves
    7. Fourier series
    8. Spreadsheet
    9. CAS (Computer Algebra System)
    10. Complex function
    11. Complex series
    12. Vector Calculus
    13. Curve of constant width
    14. Undulary
    15. The curve whose curvature is a function
    16. Frenet–Serret frames
    17. 3D graphics view
    18. Quadric surfaces
    19. Shadow of a Sphere
    20. Gradient vector field
    21. Principal Curvatures
    22. Exporting the image with various format
    23. Exporting the image as TeX code
  4. CAS
    1. An introduction of CAS
    2. Shortcut Keys
    3. CAS commands
    4. GroebnerLex(), GroebnerDegRevLex() and GroebnerLexDeg()
  5. How to call Scripts
    1. GeoGebra Script and JavaScript
    2. GeoGebra Script: On Click
    3. GeoGebra Script: On Update
  6. JavaScript
    1. ggbApplet.evalCommand()
    2. ggbApplet.evalCommandCAS()
    3. ggbApplet.setValue() and ggbApplet.getValue()
  7. GeoGebra Graphing Calculator
    1. Android : GeoGebra Graphing Calculator
    2. iPhone : GeoGebra Graphing Calculator
    3. Android : GeoGebra 3D Grapher
    4. iPhone : GeoGebra Augmented Reality
  8. References
    1. References in Japanese

1.

Introduction

  • 1. KNOPPIX/Math -> MathLibre
  • 2. Mathematical software is
  • 3. History of dynamic geometry software
  • 4. Dynamic mathematical software GeoGebra
  • 5. How to start GeoGebra?
  • 6. Some parts of GeoGebra
  • 7. From "compass and ruler" to computer
  • 8. Attach and detach
  • 9. Inputting formula on GeoGebra
  • 10. How to study materials on the world?

1.1.

KNOPPIX/Math -> MathLibre

MathLibre is the direct descendant of KNOPPIX/Math Project.
[url=http://www.mathlibre.org/]http://www.mathlibre.org/[/url][br][br]We started KNOPPIX/Math Project at February 2003, and we restarted this project at March 2012. We focus on mathematical software that is developed in the open source license.[br][br]
– Tatsuyoshi Hamada

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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2.

GeoGebra Script

  • 1. x() and y()
  • 2. Slider()
  • 3. Sequence()
  • 4. List commands
  • 5. Vectors and matrices
  • 6. Curve() and Vector()
  • 7. IF()
  • 8. SlopeField() and SolveODE()
  • 9. Surface()

2.1.

x() and y()

– Tatsuyoshi Hamada

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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3.

GeoGebra Materials

  • 1. GeoGebra Materials
  • 2. Euclidean geometry
  • 3. TriangleCenter()
  • 4. Taylor polynomials
  • 5. Vector field and integral curves
  • 6. Implicit curves
  • 7. Fourier series
  • 8. Spreadsheet
  • 9. CAS (Computer Algebra System)
  • 10. Complex function
  • 11. Complex series
  • 12. Vector Calculus
  • 13. Curve of constant width
  • 14. Undulary
  • 15. The curve whose curvature is a function
  • 16. Frenet–Serret frames
  • 17. 3D graphics view
  • 18. Quadric surfaces
  • 19. Shadow of a Sphere
  • 20. Gradient vector field
  • 21. Principal Curvatures
  • 22. Exporting the image with various format
  • 23. Exporting the image as TeX code

3.1.

GeoGebra Materials

[url=https://www.geogebra.org/materials]https://www.geogebra.org/materials[/url][br][br][list][*]It will be 1 million of materials, soon.[/*][*]CC-BY-SA, GeoGebra Terms of Use[/*][/list]
– Tatsuyoshi Hamada

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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3.16.

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3.17.

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3.18.

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3.19.

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3.20.

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3.21.

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3.22.

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3.23.

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4.

CAS

  • 1. An introduction of CAS
  • 2. Shortcut Keys
  • 3. CAS commands
  • 4. GroebnerLex(), GroebnerDegRevLex() and GroebnerLexDeg()

4.1.

An introduction of CAS

[code]a:=1/2[/code] --- Assignment of variable[br][br][code]Delete[a][/code] --- Deletion of variable[br][br]x+y=1 --- Assignment of equation[br]LeftSide[x+y=1] -> x+y[br]RightSide[x+y=1] -> 1[br][br][code]#[/code] --- Copies the previous output.[br][code]#2[/code] --- Copies the output of row 2.[br][code]$[/code] --- Inserts a reference to the previous output.[br][code]$2[/code] --- nserts a reference to the output of row 2.
– Tatsuyoshi Hamada

4.2.

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4.3.

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4.4.

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5.

How to call Scripts

  • 1. GeoGebra Script and JavaScript
  • 2. GeoGebra Script: On Click
  • 3. GeoGebra Script: On Update

5.1.

GeoGebra Script and JavaScript

We can use GeoGebra Script and JavaScript.[br][br]GeoGebra Script[br][list][*]Same commands with Input bar.[br][/*][*]1 command for 1 line.[/*][*]It support IF command, but no "for" and "while" loop, use "Sequence()".[/*][*]You can find "Create New Tool" and "Manage Tools" in main menu.[/*][*]It's not supporting recursive programming.[/*][*]It's an original language, is easy to learn for users of GeoGebra.[/*][*]Basically, it's an script attached to some object.[/*][/list]JavaScript[br][list][*]It is a general (and popular) programming language.[/*][*]It's supporting statements: "[code]if[/code]", "[code]for[/code]" and "[code]while[/code]", ...[/*][*]Declares a variable x with [code]"[/code][code]var x;"[/code][/*][*]It's supporting array data structure.[/*][*]2 kinds of scripts, one is attached to some object, the other is global script.[/*][/list][br]Script attached to some objects[br][list][*]On Click[br][/*][*]On Update[/*][/list]Global JavaScript[br][list][*]Defining functions (not variables) which will be available from the other scripts.[/*][/list]
– Tatsuyoshi Hamada

5.2.

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5.3.

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6.

JavaScript

  • 1. ggbApplet.evalCommand()
  • 2. ggbApplet.evalCommandCAS()
  • 3. ggbApplet.setValue() and ggbApplet.getValue()

6.1.

ggbApplet.evalCommand()

Example
[code]for (var i=0; i<10; i++) {[br] ggbApplet.evalCommand("A_" + i + "=(random()*10, random()*10)");[br]}[br][br][/code]
– Tatsuyoshi Hamada

6.2.

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6.3.

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7.

GeoGebra Graphing Calculator

  • 1. Android : GeoGebra Graphing Calculator
  • 2. iPhone : GeoGebra Graphing Calculator
  • 3. Android : GeoGebra 3D Grapher
  • 4. iPhone : GeoGebra Augmented Reality

7.1.

Android : GeoGebra Graphing Calculator

Android[br][list][*][url=https://play.google.com/store/apps/details?id=org.geogebra.android&hl=ja]https://play.google.com/store/apps/details?id=org.geogebra.android&hl=ja[/url][/*][/list]
Google Play
– Tatsuyoshi Hamada

7.2.

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7.3.

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7.4.

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8.

References

  • 1. References in Japanese

8.1.

References in Japanese

[list][*][url=http://amogha.jp/GeoGebra/index-2017.html]29-共研-5008 動的幾何学ソフトウェアGeoGebraの整備と普及[/url](共同研究リポートNo.396([url=http://amogha.jp/GeoGebra/report396.pdf]B5版[/url]、[url=http://amogha.jp/GeoGebra/geogebra-2017.pdf]A4版[/url]))[/*][*][url=http://amogha.jp/GeoGebra/index-2016.html]28-共研-5008 動的幾何学ソフトウェアGeoGebraの整備と普及[/url](共同研究リポートNo.391([url=http://amogha.jp/GeoGebra/report391.pdf]B5版[/url]、[url=http://amogha.jp/GeoGebra/geogebra-2016.pdf]A4版[/url]))[/*][*][url=http://amogha.jp/GeoGebra/program-2015.pdf]27-共研-5007 動的幾何学ソフトウェアGeoGebraの整備と普及[/url](共同研究リポートNo.370([url=http://amogha.jp/GeoGebra/report370.pdf]B5版[/url]、[url=http://amogha.jp/GeoGebra/geogebra-2015.pdf]A4版[/url]))[/*][*]25-共研-5009 GeoGebraの数学、数学教育、および統計教育での利用(共同研究リポートNo.326([url=http://amogha.jp/GeoGebra/report326.pdf]B5版[/url]、[url=http://amogha.jp/GeoGebra/geogebra-2013.pdf]A4版[/url]))[/*][*]2018年は11月12日（月）ー13日（火）に統計数理研究所で開催する可能性？[/*][*][url=https://nyoho.github.io/GeoGebraWebExamples/]GeoGebra web Examples[/url] by Yukinori Kitadai[br][/*][*][url=https://sites.google.com/site/geogebrajp/]GeoGebra日本[/url][/*][*][url=https://wiki.geogebra.orgen/CAS_Specific_Commands]GeoGebra : CAS Specific Commands[/url][/*][*][url=https://wiki.geogebra.orgen/Reference:JavaScript]GeoGebra : Reference:JavaScript[/url][/*][*][url=https://developer.mozilla.org/ja/docs/Web/JavaScript]MDN : JavaScript[/url][/*][*][url=https://ja.wikipedia.org/wiki/%E5%8B%95%E7%9A%84%E5%B9%BE%E4%BD%95%E5%AD%A6%E3%82%BD%E3%83%95%E3%83%88%E3%82%A6%E3%82%A8%E3%82%A2]動的幾何学ソフトウエア（Wikipedia)[/url][/*][*][url=http://www.kyoritsu-pub.co.jp/bookdetail/9784320019768]グレブナー道場（共立出版）[/url] [/*][*][url=http://www.kyoritsu-pub.co.jp/bookdetail/9784320019072]曲線の事典（共立出版）[/url][br][/*][*][url=https://www.cambridge.org/core/books/book-of-curves/F08B52C8FB0563B2F9866DA186FC87F1]A Book of Curves (Cambridge University Press)[/url][/*][*][url=https://www.crcpress.com/Modern-Differential-Geometry-of-Curves-and-Surfaces-with-Mathematica-Third/Abbena-Salamon-Gray/p/book/9781584884484]Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (CRC Press)[/url][/*][/list]
– Tatsuyoshi Hamada

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