# 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.

-55-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

#### Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited page

Mindstorms: Children, Computers, and Powerful Ideas

Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
• Bookmarks
• Highlights & Notes
• Citations
/ 230

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.