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matqkks
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Where they aware of 3,4 and 5; 5, 12 and 13?
Thanks. Much appreciated.jedishrfu said:I would say yes based on the clay table of pythag triplets shown in this presentation:
http://www.f.waseda.jp/sidoli/MI314_02_Egypt_Babylon.pdf
Check at slides 33-35 or thereabouts. It's a pretty cool presentation.
Thanks for this information. Very relevant to my question.fresh_42 said:From Wikipedia:
The cuneiform Plimpton 322 contains 15 different Pythagorean triples, e. g. ##(56,90,106)\, , \, (119,120,169)\, , \, (12709, 13500, 18541)##, which suggests that more than ##3,500## years ago a method of calculating such triples was already known.
Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the Pythagorean theorem, a^2 + b^2 = c^2. This means that when the three numbers are the lengths of the sides of a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The Sumerians were a civilization that flourished in ancient Mesopotamia (present-day Iraq) from around 4000 to 2000 BCE. They were known for their advanced knowledge in areas such as mathematics, astronomy, and agriculture.
The Sumerians used a numerical system based on the sexagesimal (base 60) system, which allowed them to easily calculate and work with Pythagorean triples. They also had a deep understanding of geometry and were able to apply the Pythagorean theorem to solve practical problems.
The Sumerians were known to have knowledge of several Pythagorean triples, including (3, 4, 5), (5, 12, 13), and (8, 15, 17). However, there is evidence to suggest that they may have known about even larger Pythagorean triples.
The Sumerians used Pythagorean triples in a variety of ways, including in construction and surveying. They also used them to solve practical problems related to land area, such as determining the area of a field or the length of a diagonal fence. Pythagorean triples were also used in religious rituals and believed to have mystical properties.