Turtle Geometry

Imagine that you have control of a little creature called a turtle that exists in a mathematical plane or, better yet, on a computer display screen. The turtle can respond to a few simple commands: FORWARD moves the turtle, in the direction it is facing, some number of units. RIGHT rotates it in place, clockwise, some number of degrees. BACK and LEFT cause the opposite movement.

Turtle Geometry: The Computer as a Medium for Exploring Mathematics by Harold Abelson and Andrea diSessa¹ calls itself “a computer-based introduction to geometry and advanced mathematics at the high school or undergraduate level” — a book of figures to draw and exercises to work, all steered through that turtle. I’m working through it, generating the figures and doing the exercises. The series began in Racket, and the posts so far show that code; the work is moving to x/Logo — x-logo, Logo hosted on x-lang, a language of my own — in turtle-geometry-x-logo. The title link above is an open-access edition of the book, if you’d like to follow along.

Posts

• Jun 28, 2024 Turtle Geometry: 0.1. An Introduction
• Jun 30, 2024 Turtle Geometry: 0.2. Turtle Procedure Notation
• Jul 12, 2024 Turtle Geometry: 1. Introduction to Turtle Geometry
• Jul 30, 2024 Turtle Geometry: 1.1.1 Procedures