Turtle Geometry: The Computer as a Medium for Exploring MathematicsTurtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates. |
Contents
Introduction to Turtle Geometry | 3 |
Exercises for Section 1 2 | 30 |
Exercises for Section 1 4 | 50 |
Exercises for Section 2 3 | 85 |
Exercises for Section 2 4 | 99 |
Vector Methods in Turtle Geometry | 105 |
Exercises for Section 3 2 | 135 |
Topology of Turtle Paths | 161 |
A Second Look at the Sphere | 288 |
Exercises for Chapter 7 | 301 |
Exercises for Section 8 2 | 330 |
Exercises for Section 8 3 | 338 |
Exercises for Section 9 2 | 370 |
Exercises for Section 9 4 | 387 |
Writing Turtle Programs in Conventional Computer | 405 |
Hints for Selected Exercises | 423 |
Other editions - View all
Turtle Geometry: The Computer as a Medium for Exploring Mathematics Harold Abelson,Andrea Disessa No preview available - 1986 |
Turtle Geometry: The Computer as a Medium for Exploring Mathematics Harold Abelson,Andrea Disessa No preview available - 1986 |
Common terms and phrases
algorithm angle excess ANGLE1 atlas axis basic loop chapter circle commands coordinates corresponding crosscap crossing point cube curvature density deflection deformation demon turning display screen distance dot product draw DUOPOLY edge equation Euler characteristic example excess face formula GAPRATIO glued GOSUB heading implement inputs integer interior angles intersection Klein bottle LEFT length LEVEL look Lorentz rotations Möbius strip monogon moving multiple of 360 operation perpendicular pieces piecewise flat surface planar plane Platonic solids POLY polygon position problem projection proof radial radius recursive region REPEAT FOREVER RETURN segments sequence shown in figure shows simulation slot spacetime spacetime diagrams spatial specified speed sphere spirograph square straight subroutine subsection symmetry theorem three-dimensional space topological disks torus total curvature total turning triangle turtle geometry turtle line turtle path Turtle Procedure Notation turtle program turtle walking turtle's vector velocity vertex vertices wedge map world line zero