# Pythagorean triple

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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° measured: 38.66°-51.34°-90° 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.