Animated Mathematics

Keywords: instructional software, scientific graphics, animation

Samuel Dagan, Prof. of physics
Tel-Aviv University
Tel-Aviv
Israel
dagan@post.tau.ac.il
http://alzt.tau.ac.il/~dagan/

Biography

Samuel Dagan got his PhD degree of physics in 1964. On 1967 he was appointed at the Tel-Aviv University as member of the academic staff, where he spent most of his time in research as high-energy physics experimentalist and in teaching undergraduate students. On 1999 he became professor emeritus and decided to make use of his long experience in teaching for developing new educational tools for sciences. He is involved at present in a project of a teachware for learning mathematics. Web site: "http://alzt.tau.ac.il/~dagan/". Email: "dagan@post.tau.ac.il".


Abstract


This document is based on a talk given at the SVG Open 2003 - Vancouver (http://www.svgopen.org/).

The talk is based on a teachware project of mathematics for science and engineering students of the first year. Teachware means a teaching aid to be open with a web browser. This presentation includes animated SVG graphics from very basic calculus and therefore it aims also the general audience without any mathematical orientation.

The first part of the talk deals with the parametrization of any mathematical curve for use with SVG. An open source java program uses the quadratic Bezier-Casteljau method ( e.g. http://graphics.cs.ucdavis.edu/GraphicsNotes/Bezier-Curves/Bezier-Curves.html ) for convenient expression of two dimensional curves. A finite curve provided by the user is approximated in number of intervals as quadratic expressions. The number of intervals is automatically obtained by the required error limit. The algorithm is described and an example is shown. More details are available on the web site of the program ( http://alzt.tau.ac.il/~dagan/tools/Bezier2/readMe.html ).

The second part is the core of the presentation with animated graphics. Since they are written with the purpose of teaching, each one of them consists of two parts presented in parallel and modified consecutively: text with the written explanation about the next stage and the graphics changing appearance and animated.


Table of Contents


Introduction
A curve expressed as a Bezier path
Animations
Conclusions
     My view
     My hope
     My thanks

Introduction

This document is based on a talk given at the SVG Open 2003 - Vancouver (http://www.svgopen.org/). 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" (http://www.adobe.com/products/main.html) 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 friends, collegues and students.

A curve expressed as a Bezier path

An open source double precision Java program uses the Quadratic Bezier-Casteljau method (see e.g. http://graphics.cs.ucdavis.edu/GraphicsNotes/Bezier-Curves/Bezier-Curves.html) 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 belongs to a SVG file. 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 belongs to a SVG file. It is recommended to expand the windows 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.

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