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

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

 

Abstract for 14753
Discovering and Proving Theorems with Geometry Expressions
Authors: Philip Todd
Affiliations: Saltire Software
Keywords:

In this workshop we will use Geometry Expressions to discover and prove a number of theorems in elementary geometry, both familiar and less familiar. We will learn how to define basic geometric figures involving points, lines and circles using a constraint based geometry system. We will observe how sophisticated conjectures are facilitated by the symbolic nature of the program. We will use Geometry Expressions both on its own and in conjunction with a CAS to make conjectures, to prove theorems automatically and to suggest traditional pencil and paper proofs.
We will start by proving simple circle angle identities. We will continue by proving identities involving incircles and excircles, and finally look at mixtilinear incircles and excircles.
Together, we will explore the role of this new technology in the mathematics classroom of the future.
No experience with Geometry Expressions is necessary.