# Mindstorms: Children, Computers, and Powerful Ideas

By Seymour Papert | Go to book overview

Chapter 3
Turtle Geometry. A Mathematics Made for Learning

TURTLE GEOMETRY is a different style of doing geometry, just as Euclid's axiomatic style and Descartes's analytic style are different from one another. Euclid's is a logical style. Descartes's is an algebraic style. Turtle geometry is a computational style of geometry.

Euclid built his geometry from a set of fundamental concepts, one of which is the point. A point can be defined as an entity that has a position but no other properties -- it has no color, no size, no shape. People who have not yet been initiated into formal mathematics, who have not yet been "mathematized," often find this notion difficult to grasp, and even bizarre. It is hard for them to relate it to anything else they know. Turtle geometry, too, has a fundamental entity similar to Euclid's point. But this entity, which I call a "Turtle," can be related to things people know because unlike Euclid's point, it is not stripped so totally of all properties, and instead of being static it is dynamic. Besides position the Turtle has one other important property: It has "heading." A Euclidean point is at some place -- it has a position, and that is all you can say about it. A Turtle is at some place -- it, too, has a position -- but it also faces some direction -- its heading. In this, the Turtle is like a person -- I am here and I am facing north -- or an animal or a boat.

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