*In order to enjoy this exhibit, you will need a Web browser
that understands graphical Fill-Out Forms.
See our list of browsers
for more information.*

**WebPisces**This web-based interface to the Pisces program allows you to compute implicitly defined curves in the plane. You can choose from several pre-defined functions, and can modify their parameters and domains.

**Build a Rainbow**How are rainbows formed? Why do they only occur when the sun is behind the observer? If the sun is low on the horizon, at what angle in the sky should we expect to see a rainbow? This laboratory, developed as part of the University of Minnesota Calculus Initiative, helps to answer these and other questions by examining a mathematical model of light passing through a water droplet.

**QuasiTiler**Generate the famous Penrose tilings, or design your own nonperiodic tilings of the plane. In the process, you can select and visualize plane cross-sections of a lattice in anywhere from 3 up to 13 dimensions!

#### For more about tilings, go to ScienceU

**Kali****Kali-Jot***(with free-hand drawing, for X Mosaic only)*Kali is an interactive editor for symmetric patterns of the plane, as seen in some of the woodcuts of M.C. Escher. It's also a fun way to learn about the 17 crystallographic symmetry groups of the plane.

#### For more about tilings, go to ScienceU

**Cyberview-X**,*(Version 2.0 -- now with smooth shading!)*An interactive 3D viewer that works with any HTML 2.0 compatible Web browser. You can pick an object out of our predefined library, or you can learn about the OOGL format and define your own 3D objects. (You are free to choose either version of Cyberview; the only difference is the rendering system used by the server.)

**Projective Conics**This discussion of Pascal's theorem in terms of projective geometry includes an interactive application that lets you specify points on a conic and see how the theorem applies to them.

**Orbifold Pinball**Explore the effects of negatively curved space in this pinball-style game. The game board is not only curved, but also contains singularities which serve as ``bumpers'' off which the ball can bounce.

**Teichmuller Navigator**Explore Teichmuller space, the space of all different angle geometries on a genus two surface. Moving through this space is accomplished by shifting the vertices of a tiling of the hyperbolic plane.

**Integrator**Experiment with numerical integration of data sets. Enter your own data set, choose a model function, and interpret both numerical and graphical results. This module, developed as part of the University of Minnesota Calculus Initiative, introduces the key ideas of modeling discrete data, as well as computing the total change in a quantity from data about the rate at which it is changing.

**Unifweb**Discover and visualize families of Riemann surfaces with a specified group of symmetries. The presentation you choose for your symmetry group corresponds geometrically to a construction of the surface as a covering of a particular orbifold.

**Lafite**Work with any discrete symmetry group of the hyperbolic plane. Lafite will calculate the fundamental region and generators of the group you chose. The program then creates Escher-like patterns by replicating a motif through the action of that group.

Most of the programs presented here were written using the W3Kit library developed at the Geometry Center. This is an object-oriented toolkit for building interactive World-Wide Web applications.

Comments to:
webmaster@geom.umn.edu

Created: Late 1993? ---
Last modified: Mon Feb 3 10:55:22 1997

Copyright © 1993-1996 by
The Geometry Center
All rights reserved.