Interactive and animated Geometric Algebra with Cinderella

L'on voit que Jésus-Christ, achevant ce que Moïse avait commencé, a voulu que la divinité fût l'objet, non seulement de notre crainte et de notre vénération, mais encore de notre amour et de notre tendresse.

Essai de théodicée - Préface et abrégé, Gottfried Wilhelm Leibnitz (1646-1716)


I originally learned about Cinderella from Leo Dorst (Amsterdam). He also used it to do some Geometric Algebra illustrations. Here I have elaborated his approach, producing a variety of online JAVA applets, part of them animated and part of them interactive. Especially the interactive applets invite you to explore the full meaning of geometric relationships in a visual way. I have freely drawn on the material of David Hestenes, New Foundations for Classical Mechanics, Kluwer 1999, 2nd ed. You can tour the applets without using the book. But if you have it, it might increase the fun of reading it. Another important source is Dorst, Mann and Bouma's geometric algebra MATLAB tutorial GABLE.

Particularly in the section on conics I have compiled an instructive variety of ways to obtain conics (points, pairs of intersection lines, circles, ellipses, hyperbolas and parabolas).

Finally, W.K. Clifford's circle chain theorem in the ordinary Euclidean plane refers to a "chain of theorems" of increasing complexity. Every one of this infinite sequence of theorems must be true for the whole to be true. You will find the illustrations for n=2 to n=8 circles through one point O.

The applets work with Netscape 6.2, Explorers 5 and 6, but not with Netscape 4.7. In each group the first applet may take some time, because your browser has to load the 412k cindyrun.jar file. Later on some of the more involved applets may also take a few minutes to appear on your screen. If the applets do not display properly, please try the page with support for Java 1.4.1 and older.

Latest additions: 1) Luca Redaelli (Milan) illustrates how to visualize the structural mechanics of a simply supported beam in terms of Geometric Algebra. 2) Point groups in two dimensions (E. Hitzer)

Please send any suggestions+corrections+improvements to Eckhard Hitzer. Especially if you detect any geometric errors in the constructions!

[ vectors | bivectors | outer prod. | triangle | rotations | oscillations | circ. pol. waves | conics | circle chain | struc. mechanics | 2D point groups ]

Vectors

Bivectors

Outer product

Triangle

Rotations

Oscillations

Circular polarized waves

Conics

Clifford's circle chain theorem

Simple structural mechanics computations by Luca Redaelli (Milan)

Point groups in two dimensions

2D lattice symmetries

[ vectors | bivectors | outer prod. | triangle | rotations | oscillations | circ. pol. waves | conics | circle chain | struc. mechanics | 2D point groups ]

Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).
Last Modified 11 Jun 2004
EMS Hitzer is not responsible for the content of external internet sites.