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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())
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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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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:16, 1 March 2024 | | 512 × 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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