One of the Geometry app I am currently enjoying playing is the PolygonFlux iPad app. This app shows the path of a point reflected inside a regular polygon creating beautiful patterns. The location and direction of the emitter can be changed, so you can create as many patterns as possible.
This application costs $0.99.
You can choose different polygons: triangle, square, pentagon, or polygons up to 14 sides. You can also choose from different themes and send your patterns to friends through email.