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A Pythagorean triple is a set of three positive whole numbers a, b, and c that are the side lengths of a right triangle.
Remark: there is no Pythagorean triple that approximates the angle of 51.84° of the Khufu (Cheops) Pyramid (see value for angle β). Taking the lenghts of 440 cubits and the height of 280 cubits we get proportions of a=22 to b=28 to c= 35.6 (or 11-14-17.8). This corresponds to a seked of 5 1/2 palms.
| Pythagorean triple | numbers added |
A multiple of 12? |
c² = b²
+ a² |
α-β-γ |
|
| 12knot-rope | part of 60 |
||||
| 5 4 3 | 12 | x |
x |
5² = 4² + 3²
Angle of Khafre's pyramid |
36.8°-53.1°-90° |
| 10 8 6 | 24 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 13 12 5 | 30 | x |
13² = 12² + 5² | 22.6°-67.4°-90° | |
| 15 12 9 | 36 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 17 15 8 | 30 | x |
17² = 15² + 8² | 28°-62°-90° | |
| 20 12 16 | 48 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 25 24 7 | 56 | 25² = 24² + 7² | 16.2°-73.4°-90° | ||
| 25 20 15 | 60 | x |
x |
deduced from 5 4 3 | 36.8°-53.1°-90° |
| 26 24 10 | 60 | x |
deduced from 13 12 5 | 22.6°-67.4°-90° | |
| 29 21 20 | 60 | x |
x |
29² = 21² + 20²
Angle of Red pyramid |
43.6°'-46.4°-90° |
| 30 12 18 | 60 | x |
x |
deduced from 5 4 3 | 36.8°-53.1°-90° |
| 34 30 16 | 80 | deduced from 17 15 8 | 28°-62°-90° | ||
| 35 28 21 | 84 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 35.6 28 22 | |
Angle of Khufu's pyramid |
35.6°-51.8°-90° | ||
36 28 23 45 35 28* |
87 |
Angle of Menkaure's pyramid |
39.70°-51.05°-89.24° |
||
| 37 35 12 | 84 | x |
37² = 35² + 12² | 18.9°-71.1°-90° | |
| 39 36 15 | 90 | deduced from 13 12 5 | 22.6°-67.4°-90° | ||
| 40 32 24 | 96 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 41 40 9 | 90 | 41² = 40² + 9² | 12.7°-77.3°-90° | ||
| 45 36 27 | 108 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 50 40 30 | 120 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 51 45 24 | 120 | x |
deduced from 17 15 8 | 28°-62°-90° | |
| 52 48 20 | 120 | x |
deduced from 13 12 5 | 22.6°-67.4°-90° | |
| 53 45 28 | 126 | 53² = 45² + 28² | 31.8°-58.1°-90° | ||
| 55 44 33 | 132 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
| 60 48 36 | 144 | x |
deduced from 5 4 3 | 36.8°-53.1°-90° | |
* This seked is closer to the angle of 51.34° which was measured (28.1² + 35.1² = 45²) and also gives a right angle. Either this or the pyramid builders made some mistakes.
Links 
Wikipedia English:
Pythagorean triple (also called triplets)
The
Pythagorean theorem on www.mathepower.com
|
Credits: |
Copyright 2006: |
Franz Löhner www.cheops-pyramide.ch |
| Concept and Design, Text: |
Teresa (Zubi) Zuberbühler www.starfish.ch |