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File:Trisected perimeter point 3-4-5.svg

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Original file (SVG file, nominally 540 × 421 pixels, file size: 2 KB)

Description The trisected perimeter point of a 3-4-5 right triangle.
Date
Source Own work
Author David Eppstein
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code

This diagram was created as a pdf file by the following Python code, then recolored and labeled in Adobe Illustrator and converted to SVG.

from pyx import canvas,path,color

def meet(p,q):
    return [p[i-1]*q[i]-q[i-1]*p[i] for i in [2,0,1]]

def sign(p,r,q):
    L = meet(p,q)
    return sum(L[i]*r[i] for i in [0,1,2])

A = [0,3,1]
B = [0,0,1]
C = [4,0,1]

lo = 0
hi = 3
for i in range(40):
    x = (lo + hi) / 2.0
    AP = [4-x,0,1]
    BP = [4-0.8*(4-x),0.6*(4-x),1]
    CP = [0,x,1]
    if sign(meet(A,AP),meet(B,BP),meet(C,CP)) < 0:
        hi = x
    else:
        lo = x

c = canvas.canvas()

def line(p,q):
    c.stroke(path.line(p[0],p[1],q[0],q[1]),[color.rgb.black])

for p,q in [(A,B),(A,C),(B,C),(A,AP),(B,BP),(C,CP)]:
    line(p,q)

c.writePDFfile("Trisected perimeter point 3-4-5")

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depicts

21 April 2008

File history

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Date/TimeThumbnailDimensionsUserComment
current00:37, 22 April 2008Thumbnail for version as of 00:37, 22 April 2008540 × 421 (2 KB)David Eppstein{{Information |Description=The trisected perimeter point of a 3-4-5 right triangle. |Source=self-made |Date=April 21, 2008 |Author= David Eppstein |Permission={{PD-self}} |other_versions= }} ==Sou

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