kirby urner schrieb:
I'm glad turtle graphics intersected my thinking re extended precision
decimals (Decimal type) on edu-sig just now.
I've updated my tmods.py to contain a turtle rendering the plane-net of a T-mod:
http://www.4dsolutions.net/ocn/python/tmod.py (runnable source)
http://www.flickr.com/photos/17157...@n00/4147429781/ (GUI view)
Nice tiny app! Albeit not an example for using the if statement ;-)
Just to show you how turtle.py enables you to implement this
using quite different approaches to doing geometry, I'd like to add
two more implementations.
Besides you may notice that these do not rely on rather complicated
calculations of distances and angles, using the Pythagorean theorem
and trigonometrics but only on a few more fundamental properties of
the figure.
##### Version 2 - using coordinate geometry without coordinates ;-)
# a different implementation for Kirby's "Plane Net for T-module"
from turtle import *
from math import sqrt
PHI = (sqrt(5)-1)/2
def planeNet(h=500):
setup(560,560)
title("Plane Net for T-module")
penup()
back(h/2); left(90); back(h/2); right(90)
pendown()
forward(h); left(90)
forward(h*PHI); A = pos(); forward(h-h*PHI); left(90)
forward(h*PHI); B = pos(); forward(h-h*PHI); left(90)
forward(h); C = pos()
for P in A, B, C:
goto(P)
##### Version 3 - stamping simple transforms of the shape of
##### an isosceles rectangular triangle:
from turtle import Screen, Turtle
from math import sqrt
GOLDEN_RATIO = (sqrt(5)-1)/2
def planeNet(h=500.0, phi=GOLDEN_RATIO):
s = Screen(); s.setup(560,560); s.title("Plane Net for T-module")
s.register_shape("recttriangle", ((0, 0), (h, 0), (0, h)))
designer = Turtle(shape="recttriangle")
designer.color("black","")
designer.penup()
designer.goto(-h/2, h/2)
for width, height in ((1, 1-phi), (phi, 1-phi), (phi, 1)):
designer.shapesize(width, height)
designer.stamp()
designer.forward(h)
designer.right(90)
designer.hideturtle()
Hoping, you will find this a bit interesting,
best regards
Gregor
Here's the graphical output:
http://www.flickr.com/photos/17157...@n00/4148139184/in/photostream/
(Python 3.1)
If you actually wanna fold the T, you need to snip off the cap and
reverse it, per this diagram:
http://www.rwgrayprojects.com/synergetics/s09/figs/f86515.html
120 of them, 60 folded left, 60 folded right, all of volume 1/24, make
the volume 5 rhombic triacontahedron.
http://www.rwgrayprojects.com/synergetics/s09/figs/f86419.html
If you blow up the volume by 3/2, to 7.5, the radius becomes phi /
sqrt(2) -- what we're showing with Decimals.
The reason this seems unfamiliar is the unit of volume is the
tetrahedron formed by any four equi-radiused balls in inter-tangency.
I'm spinning this as Martian Math these days, yakking on
math-thinking-l about it, learned it from Bucky Fuller, Dave Koski et
al.
Kirby
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