# Geometry Expressions

## Activities

We present a number of student activities. Many more classroom activities may be found in our books.

### String Art

How do you create string art on a computer? In this lesson sequence, suitable for students at all levels of high school, we learn to create some beautiful designs based on practical principles using Geometry Expressions.

### Stained Glass Designs

Students apply graphic methods to design various shapes on the plane to create patterns similar to what stained glass artists create.

### Translation Along Coordinate Axes

Students investigate the effects of a generic function f(x) when translating it around the axes.

### From Inductive Reasoning to Proof by Induction

We use Geometry Expressions to calculate the radii of circles in a particular Pappus Chain. We will use inductive reasoning to conjecture a general form for this sequence of radii. We will then use mathematical induction to prove the formula for a general member of the Pappus Chain.

### Light Caustics

If you look at light reflected within a cylinder, you see a bright curve caused by the light being concentrated into a specific region. This curve is called a caustic.

### Sketching an Ellipse at the Beach

If you were on a Pacific beach and found a piece of old fishing net, and you unraveled some string from it, you'd find a couple of pieces of driftwood, tie the string to it and trace out an ellipse in the sand. Wouldn't you?

### Trammels

Archimedes Trammel is a device consisting of a handle attached at two pivot points to sliders which can slide to and fro in perpendicular slots. In this activity, we will investigate the curve formed by the trammel.

### Rugby Kick Problem

Where should you take a conversion kick in Rugby in order to get the best angle on the goal?

### Triangle Areas

Investigate areas of some triangles.