Last edited May-10, 2003 by pompe@uiuc.edu
Find this document at http://www.ncsa.uiuc.edu/Classes/MATH198/pompe
Alex Pompe: Math 198 Hypergraphics at the University of Illinois in Urbana-Champaign.
Project
Math Gallery:
A Graphical Exploration of Mathematical Beauty.
Abstract- An environment is created allowing the user to explore a virtual math museum and look at various exhibits showcasing mathematical beauty. Using the graphics abilities afforded, the visitor is able to view graphical representations of mathematics at work. The museum functions to educate as well as dazzle. Exhibits are accompanied by tutorials or explanations laying the ground work for understanding the methods used. This project is heavy on content, tends to concentrate on the visualization and education of the mathematics involved.
Documentation-
Shapes:-
-Linked Tori
-Cayley Cubic
-Folium Surface
-Clebsch Diagonal Cubic
-Klein Bottle
-Steiner's Roman Surface
Final Versions:-
-Klein Bottle
-Moebius Band
-Twisted Wire Moebius Band
Architecture:-
-Initial gallery environment.
Narrative:
May 10- Final version of Math Gallery is located in my home directory/public/project. This version includes textured floors, "infinite" expandability, and both the clothed versions of the Klein bottle and Moebius band. It is fully functional in the CAVE. Several of the shapes noted above did not make it into this final version of the gallery as a resuly of time, but my version of the Skel is venerable enough to quickly, (even for the novice,) add in about anything at this point using cut and paste. Demo of this project will be on Wed May 13 at 2:30. We will start out in the REL lab and I plan on moving into the CAVE at some point.
Apr 30- Bonus update from here at Beckman late Wednesday night. I have textures up and running after some help from Professor Francis with make files, and they have made their first appearance into the architecture of the gallery. After this much progress, I figure a screen shot is in order. It is a picture of the corner of the building and yes those are Penrose tilings used to tile the floor. After all this is a math gallery. Next up is getting multiple textures going so the walls and ceiling are better than just blue.
Apr 30- Preliminary exhibits are completed and two of them are 99% final versions and need only move into their new homes in the environment. The environment itself has germinated and serves its purpose and has "infinite" expandability built in by simply adding another floor to the structure. Textures will soon be involved to adorn the environment and will be used to implement the education of the gallery.
Feb 28- Added five more objects that should be fun to work with. Initially I will go for around 10 total and get things running correctly. I'd like to get things into the CAVE quickly if possible for EOH.
Feb 26- Drafted proposal and abstact. Initial plans are to develop a list of shapes to include in the first draft and also to explore, mainly with DP Graph, other possible mathematics to include. Possibilities are included at bottom of documentation section.
Bibliography:
-Linked Tori shape courtesy of George Francis, Illi-Skel Lectures, Feb. 2003.
-Klein Bottle courtesy of "From Here to Infinity," Ian Stewart, Oxford University Press; Revised Edition 1996.
-Moebius Band courtesy of "From Here to Infinity," Ian Stewart, Oxford University Press; Revised Edition 1996.
Project Documentation.
**Disclaimer: This site is not the same as my final write-up for the Math Gallery**
Follow the White Rabbit.