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→Euclid for Turtles: How to cheat at geometry

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Bertrand Russell

Bertrand Russell

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+* To join two points with a line, I actually set the Turtle on a point, set its heading (the direction it was pointing) and sent it off in that direction both to draw the second point and to draw the line joining the points.

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+* To extend a line, I drew it, and then told the Turtle to go forward in the same direction.

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+* To draw a circle, I put the Turtle at the outer end of the line, and told it the radius length.

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+In order to do these three postulated constructions without this level of cheating, we have to tell the Turtle explicitly where points are in a coordinate system that it understands, and do some high-school level algebra and trigonometry in order to find out the direction to point the Turtle in and the distance it should move, or the radius of the circle. We have two relatively simple ways to tell the Turtle where a point is. Assign its x and y coordinates to [[Activities/TurtleArt/Tutorials/Variables|variables]], or put the values on the [[Activities/TurtleArt/Tutorials/Stack|stack]].

==Euclidean Algebra==

==Euclidean Algebra==

It turns out that the three Euclidean constructions can give us new points from older ones by combinations of addition, subtraction, multiplication, division, and taking square roots, but cannot do anything else.

It turns out that the three Euclidean constructions can give us new points from older ones by combinations of addition, subtraction, multiplication, division, and taking square roots, but cannot do anything else.

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