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File:Non-Desargues configuration.svg

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Original file (SVG file, nominally 540 × 531 pixels, file size: 6 KB)

Summary

Description A 103 configuration that is not incidence-isomorphic to a Desargues configuration. Redrawn more accurately from a bitmap image by Michael Hardy, en:Image:Pentagrams.png.
Date
Source Own work
Author David Eppstein

Source code

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

from pyx import canvas,path,color
from math import *

rot = [e**(pi*0.4j*i) for i in range(5)]

def orient(p,q):
    return p.real * q.imag - p.imag * q.real

def testx(x):
    p = rot[1].real + 1j * x
    return orient(p - 1, p * rot[3] - 1)

lo,hi = 3,4
while hi - lo > 1e-8:
    mid = (lo+hi)/2.0
    if testx(mid) < 0: hi = mid
    else: lo = mid

c = canvas.canvas()

scale=2.0
def edge(p,q):
    c.stroke(path.line(p.real*scale,p.imag*scale,q.real*scale,q.imag*scale),
             [color.rgb.black])

def point(p):
    c.fill(path.circle(p.real*scale,p.imag*scale,0.08*scale),[color.rgb.red])

for i in range(5):
    p2 = 1 * rot[i-4]
    p3 = (rot[1].real + 1j * mid) * rot[i]
    p4 = p3 * rot[2]
    edge(p3,p4)
    edge(p4,p2)

for i in range(5):
    point(1*rot[i])
    point((rot[1].real + 1j * mid) * rot[i])

c.writePDFfile("Non-Desargues configuration")

Licensing

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.

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depicts

8 April 2008

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current05:33, 9 April 2008Thumbnail for version as of 05:33, 9 April 2008540 × 531 (6 KB)David EppsteinRecolor more boldly
01:15, 9 April 2008Thumbnail for version as of 01:15, 9 April 2008348 × 342 (5 KB)David EppsteinDraw it as an actual configuration without splitting some of the lines into two segments. Should be no visible change from this version to the previous.
01:08, 9 April 2008Thumbnail for version as of 01:08, 9 April 2008348 × 342 (6 KB)David Eppstein{{Information |Description=A 10<sub>3</sub> configuration that is not incidence-isomorphic to a Desargues configuration. Redrawn more accurately from a bitmap image by Michael Hardy, [[:en:I

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