Animated Mathematics

Samuel Dagan, Tel-Aviv University

© 2003

Last Update: 27 May 2003


Introduction

This document is based on a talk at the SVG Open 2003 - Vancouver. It contains graphics written in SVG format and in order to be fully accessible to the reader, it should be viewed by a browser able to display SVG. As an example "Internet Exporer" needs a plugin e.g. "Adobe SVG Viewer" that can be downloaded for free.

The aim of this document is to present to the SVG-developers' community some application of SVG graphics for science education. It aims also the educators of science by showing them applications of the recent SVG graphics technique that undoubtebly could boost the teaching abilities.

About three years ago I decided to work on a teachware project of mathematics intendent for freshmans of science. Beeing physicist myself with teaching experience of more than 30 years, it looked to me very attractive to develop a teaching tool that can be open with a web-browser not only for text and graphics, but also for showing animations and interacting with the user. Animated applets were new at that time, but their teaching potential was immediately recognised and I intended to make an ample use of them.

A year ago I was introduced to SVG and became immediately and unconditionally a fan of it. It has all the necessary properties of what I could dream of for my project. I am still a novice in the subject and the animations I am presenting are lacking for instance interactivity, but even so, I've got so far a very warm and encouraging response from my friends, collegues and students.


Layout

The document contains the following sections:


A curve expressed as a Bezier path

An open source double precision Java program uses the Quadratic Bezier-Casteljau method for convenient expression of two dimensional curves. Details and an example are given at the website http://alzt.tau.ac.il/~dagan/tools/Bezier2/readMe.html.

For seek of completness here are the main points:

Since for many people Java is not their cup of tea, but they use a different program language, here is a detailed presentation of the algorithm used, so they could apply it on a different platform. Each link of the present section that follows leads to an SVG file dispalyed in a separate window. It is recommended to expand the window to a maximum.


Animations

This section contains examples intended to be used in the teachware project. Each one includes animated graphics usind SVG. As known "One picture is worth a thousand words". It is a well known fact that a suitable illustration sometimes can make understandable a very complicated and difficult descriptions. From my experience I would dare say that "One animation is worth a thousand pictures". I hope that the examples given here will illustrate that point.

As in the previous section each link that follows leads to an SVG file dispalyed in a separate window. It is recommended to expand the window to a maximum. Each one of the links is related to a different subject of simple calculus. One have to follow any additional link that appears in a SVG file itself.


Conclusions

My view

SVG is going to revolutionize the education of sciences:


My hope

SVG is here to stay in view of the unprecedent involvement of many software companies in SVG. Even Microsoft is showing interest.


My thanks

My thanks to "Adobe" for enabling us to view and appreciate the beauty of SVG.