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Topic: Pythagorean Tree Sketchpad help


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Subject:   RE: Pythagorean Tree Sketchpad help
Author: aterner
Date: Nov 23 2005
David,
Thanks. I tried your directions, but then changed them a little. I wanted the
triangle to move in a semi-circular arc, so that it would be a right
triangle.
Then I hid the arc.
I need to work on color to use parametric color, but that is for another day.


On Nov 23 2005, David Chandler wrote:
> I tried another Pythagorean tree, this time not requiring the
> triangle to be isosceles.  The problem is the iteration algorithm
> needs to know how to construct the apex point of the triangle for
> the iterated figures.  If it is an independent point it can't do
> this.  So rather than placing it as an independent point, construct
> triangle similar to the one you want elsewhere on the screen,
> then...

--Measure the two base angles of the triangle
--Use the
> Calculate feature under the Measurement menu to create the negative
> of the right base angle measurement
--Double click the top left
> corner of the square to make it a center of rotation
--Right click
> the left base angle measurement and Mark the angle
--Select the top
> right corner of the square
--Rotate by the marked angle
--Use a
> line (not a segment) to connect the rotated point to the top left
> corner of the square
--Similarly, double click the top right corner
> of the square, mark the negative angle measurement, rotate the top
> left corner of the square, and use a line to connect it with the top
> right corner of the square.
--Create the intersection point
--Hide
> the construction lines and connect the newly constructed
> intersection point to the top corners of the square with line
> segments.
--Now select only the bottom two corners of the square
> and iterate as before.  Since the apex of the triangle has been
> constructed from parameters, the iteration algorithm will be able to
> duplicate the construction in each of its iterations.

By the way,
> don't forget to increase the number of iterations with the + key
> before pushing the final iterate button and closing the iteration
> dialogue.  The asymetric tree has some interesting properties.
> Check it out.

David Chandler

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