Ryzhik (geometry)

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Rose (3d) SineCosine (simple)

Ryzhik (geometry)

Example:    Ryzhik.eli
Modified:   June 2, 2000
Version:    2.0
Author:     Peter Moxhay
E-mail:     moxhay@bestpraceduc.org

Copyright © 2000 Elica Group

Choose an arbitrary point t on some side of a triangle. Draw a perpendicular to the "next" side (accordingly to some order). Iterate.

For what triangles does this process converge?

What is the resulting locus?

Suggested by Dr.Valerii Ryzhik, ryzhik@school.ioffe.rssi.ru

run "geomland
run "geomex

make "a point -50 - (random 150) -50 - (random -50)  [labeled]
make "b point random 150 -50 - (random 50) [labeled]
make "c point 150 - (random 300) 50 + (random 50) [labeled]
make "ab dotted line :a :b
make "bc dotted line :b :c
make "ca dotted line :c :a

make "abd fat segment :a :b
make "bcd fat segment :b :c
make "cad fat segment :c :a

make "t pointon :bc random 2 * (length :bc)

make "s [ca ab bc]
make "st (set :t)
make "ss (set)

to aStep
	make "st lput isec : (first :s) line last :st 90 + (heading : (first :s)) :st
	make "ss lput segment last :st last bl :st :ss
	make "s se bf :s first :s
end

repeat 4 [aStep]

eps 2

while not pointon? last :st last bl bl bl :st [aStep]

make "a11 fat red last :ss
make "b11 fat red last bl :ss
make "c11 fat red last bl bl :ss

make "c1 last bl bl :st [labeled]
make "a1 last bl :st [labeled]
make "b1 last :st [labeled]

Rose (3d) SineCosine (simple)