Turtle Geometry

The Computer as a Medium for Exploring Mathematics

A lovely book on how to think geometrically and algorithmically, using a simple programming language to produce pictures and prove theorems, starting from Eucliedean Geometry and ending with the curving space-time of Einstein’s theory of General Relativity.

Sounds like a tall order! But the reader is led to develop the mathematics herself, by working through examples, learning to develop and prove theorems and write programs to explore examples. The language is LOGO, which was designed for teaching elementary school children to program. The semantics of LOGO are quite advanced: but the syntax is straightforward and, as with the mathematics, the reader is led more-or-less gently along the path of acquiring the sophisticated ideas.

A wonderful book.

(See also The Shape of Space, Visual Modeling with Logo and Exploring Language with Logo)