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 Subject: RE: Pythagorean Tree Sketchpad help Author: David Chandler Date: Nov 23 2005
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