## Kali

This week we explore planar patterns, using a brand new geometry center program,

##### kali

If you're reading this from the Outside World, you can download a copy of the program; if you're at a Mac here in the Geometry Center, you can look under the

. . . Math Apps
. . . .-> Kali

Check it out! Draw some patterns!
Have Some Fun!!

### A couple of things

Using the pencil:
A single click marks a point; kali draws lines or curves between successive points. A double click "picks up" the pencil-- that is, lets you stops drawing. The next click starts you up anew.

But-- sometimes you can get off in the number of times you click, especially if you start clicking wildly in frustration. The DELETE command under the EDIT menu picks up the pencil. The UNDO CLICK does just that. And CLEAR lets you start all over.

Different Symmetries
You can get different symmetries with the buttons on the PALETTES. The palettes allow you to make every possible planar symmetry. This is a quality establishment, after all! There are seven linear patterns (the frieze patterns), seventeen patterns with finite motifs, and an infinite number of circular patterns. (Okay, so not every circular pattern is represented.)

You can select pen colors with the color palette. A double click on a color allows you to change it; you can change the background from the OPTIONS menu.

Check out some of the other options! What does SMOOTHING do? How about SHOW SINGULARITIES?

Q1: Make something really neat! Print out four copies-- one for each group in the class. These will come in handy later.

Q2: Why do you think some patterns can be stretched, but others not? Can all the patterns be rotated and zoomed? Can any patterns be skewed? What makes the difference-- why are these options available for some patterns and not others?

##### But

why are these the only symmetries possible?
And what on earth could those names mean?

Kali has been here at the Geometry Center for a while. It was first written for the Silicon Graphics workstations by Nina Amenta. Just a few weeks ago (4/95) Jeff Weeks ported the program to the Macs. Lori Thomson has an exposition and exercises on the frieze groups.

Next
to outline

```
Chaim Goodman-Strauss
Dept. Mathematics
Univ. Arkansas
Fayetteville, AR 72701
strauss@comp.uark.edu
501-575-6332```