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Summary

Description Straightedge and compass construction of a square with the same area as a given oblong by CMG Lee.
Source Own work
Author Cmglee

Python script to find examples with integer coordinates

#!/usr/bin/env python
import re, math
def print_keyval(dic, re_key=r'^[^_]'):
 print('\t'.join(['%s=%s' % (key, dic[key]) for key in dic
                  if not isinstance(dic[key], __builtins__.__class__) and
                     not callable(dic[key]) and re.search(re_key, key)]))
for  m in range(1, 60 + 1): ## 60 avoids 5-digit x or y
 for n in range(1, m):
  if m & 1 == 1 and n & 1 == 1: continue ## at least one even
  if math.gcd(m, n) > 1       : continue ## coprime
  a = 2 * m * n
  b = m * m - n * n
  c = m * m + n * n
  for (x, y) in [(c + a, b), (c + b, a)]:
   rxy = (x * y) ** 0.5
   if abs(rxy - int(rxy)) < 1e-5: print_keyval(locals())

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
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  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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Date/TimeThumbnailDimensionsUserComment
current13:16, 1 March 2024Thumbnail for version as of 13:16, 1 March 2024512 × 768 (3 KB)Cmglee{{Information |Description=Steps to construct a square with the same area as a given oblong by CMG Lee. |Source={{own}} |Date= |Author= Cmglee |Permission= |other_versions= }} Category:Ruler-and-compass construction Category:Rectangles and squares Category:Geometric mean theorem Category:Area

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