GeoGebra for Geometers
GeoGebra is a dynamic mathematical software. It is developed for learning and teaching mathematics in schools by Markus Hohenwarter and the 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
- Introduction
- Mathematical software is
- History of dynamic geometry software
- Dynamic mathematical software GeoGebra
- How to start GeoGebra?
- Some parts of GeoGebra
- From "compass and ruler" to computer
- Attach and detach
- Inputting formula on GeoGebra
- How to study materials on the world?
- GeoGebra Script
- x() and y()
- Slider()
- Sequence()
- List commands
- Vectors and matrices
- Curve() and Vector()
- IF()
- SlopeField() and SolveODE()
- Surface()
- GeoGebra Materials
- GeoGebra Materials
- Euclidean geometry
- TriangleCenter()
- Taylor polynomials
- Vector field and integral curves
- Implicit curves
- Fourier series
- Spreadsheet
- CAS (Computer Algebra System)
- Complex function
- Complex series
- Vector Calculus
- Curve of constant width
- Undulary
- The curve whose curvature is a function
- Frenet–Serret frames
- 3D graphics view
- Quadric surfaces
- Shadow of a Sphere
- Gradient vector field
- Principal Curvatures
- Exporting the image with various format
- Exporting the image as TeX code
- CAS
- An introduction of CAS
- Shortcut Keys
- CAS commands
- GroebnerLex(), GroebnerDegRevLex() and GroebnerLexDeg()
- How to call Scripts
- GeoGebra Script and JavaScript
- GeoGebra Script: On Click
- GeoGebra Script: On Update
- JavaScript
- ggbApplet.evalCommand()
- ggbApplet.evalCommandCAS()
- ggbApplet.setValue() and ggbApplet.getValue()
- GeoGebra Graphing Calculator
- Android : GeoGebra Graphing Calculator
- iPhone : GeoGebra Graphing Calculator
- Android : GeoGebra 3D Grapher
- iPhone : GeoGebra Augmented Reality
- References
- References in Japanese
Mathematical software is
[size=100]a software for "mathematics". It contains various systems.[br][br]CAS, Computer Algebra System is one of them.[br]For example, we calculate quotient numbers with CAS.[br][br][math]\frac{1}{2}+\frac{1}{3}=\frac{5}{6}[/math][br] [br]CAS is supporting polynomials, factorization, derivatives, integrals, group and algebra, etc.[br][br]General purpose sytems:[br][list][*][color=#ff0000]Mathematica, Maple[/color], [color=#0000ff]Maxima, Reduce, Sage, Giac/XCAS[/color], ...[/*][/list]CAS for research:[br][list][*][color=#0000ff]GAP, PARI/GP, [/color][/*][*][color=#0000ff]CoCoA, JAS, Macaulay2, Risa/Asir, Singular, ...[/color][/*][*][color=#0000ff]Cadabra, Polymake, Regina, Snappy, Surf families, ...[/color][/*][/list]Numerical systems:[br][list][*][color=#ff0000]Matlab[/color], [color=#0000ff]Octave, Scilab, BLAS, Julia[/color], ...[/*][/list]Publishing systems is a mathematical software:[br][list][*][color=#0000ff]TeX, LaTeX, (Beamer, a0poster, TikZ)[/color][br][/*][/list]Statistical software:[br][list][*][color=#0000ff]R[/color], Fathom, ...[br][/*][/list]Dynamic geometry software:[br][list][*][color=#ff0000]Cabri, Geometer's Sketchpad[/color], Cinderella, [color=#0000ff]GeoGebra[/color], ...[br][/*][/list][br]Developing mathematical software is a research area for mathematics.[br][list][*][url=http://www.swmath.org/]http://www.swmath.org/[/url][/*][/list][br][/size]
x() and y()
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]
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.
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]
ggbApplet.evalCommand()
Example
[code]for (var i=0; i<10; i++) {[br] ggbApplet.evalCommand("A_" + i + "=(random()*10, random()*10)");[br]}[br][br][/code]
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
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]