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Activities/Turtle Art/Tutorials/Euclid
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Revision as of 01:54, 12 August 2011

338 bytes removed
, 01:54, 12 August 2011

→Euclid for Turtles: Link to new page

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~~[[File:TAEuclideanConstructionsProgram.png]]~~+
−~~"~~The advantages of the method of postulation are great. They are the same as the advantages of theft over honest toil.~~"~~
−~~* 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.~~

Then we have to think about what a Turtle knows about any point. The Turtle knows nothing about any point other than the point where it is currently located, unless we give it a memory for points. How we can tell it to move to other points, and draw lines between them?

Then we have to think about what a Turtle knows about any point. The Turtle knows nothing about any point other than the point where it is currently located, unless we give it a memory for points. How we can tell it to move to other points, and draw lines between them?

−With all of these objections that I have been raising, you might wonder how I got the Turtle to carry out the three Euclidean constructions in the first illustration above. That's easy. I cheated.

+With all of these objections that I have been raising, you might wonder how I got the Turtle to carry out the three Euclidean constructions in the first illustration above. That's easy. I cheated. Take a look at the [[Activities/TurtleArt/Tutorials/Euclid/Cheating|program]] for these postulated constructions to see how.

−''The advantages of the method of postulation are great. They are the same as the advantages of theft over honest toil.''

−Bertrand Russell

Bertrand Russell

−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]].

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]].

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