Electronic Proceedings of the 13^th Asian Technology Conference in Mathematics

 ISSN 1940-2279 (CD) and ISSN 1940-4204 (Online)

 

Abstract for 14754
Conics and Parametric Curves with Geometry Expressions
Authors: Philip Todd
Affiliations: Saltire Software
Keywords:

In this workshop, we will explore the use of the Geometry Expressions software in the study of curves. First, we’ll look at two ways of drawing an ellipse: Archimedes Trammel (which gives principal axes directly), and the string and pin method, (which gives foci and major axes directly). We will use Geometry Expressions to work out what length string to use, and where to put the pins to replicate the curve drawn by a specific trammel. Bothe geometric and algebraic representations will be used, and insight will be gained from each.
Secondly, we’ll look at involutes, caustics and other derived curves both in the context of specific and general given curves. We’ll learn how to examine implicit and explicit curve equations, how to specify the parametric location and observe the Cartesian location of a point on a curve, and how to work with generic curves. We may even prove a differential geometry theorem.
No experience with Geometry Expressions is necessary.