File:Quadrature of rectangle.svg
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Summary[edit]
| 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[edit]
#!/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[edit]
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- 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.
|
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/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:16, 1 March 2024 | | 512 × 768 (3 KB) | Cmglee (talk | contribs) | {{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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