# Which Pythagorean triples did the Sumerians know?

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• matqkks
The Sumerians were the first people to develop a written language, and they used cuneiform script on clay tablets to record their laws, business transactions, and literature. They were also skilled mathematicians and used a sexagesimal number system, which is based on the number 60. This system was used to calculate areas of land, volumes of grains, and other practical applications. However, it is not clear if they were aware of the Pythagorean theorem or used it to calculate Pythagorean triples. The Babylonians, who followed the reign of the Sumerians, are credited with developing a method for generating Pythagorean triples, as evidenced by the cuneiform tablet Plimpton 322, which dates to around
matqkks
Where they aware of 3,4 and 5; 5, 12 and 13?

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.

pinball1970, matqkks and jedishrfu
Btw., Wikipedia mentions Babylonians, not Sumerians. Those are not identical. The Sumerer developed the cuneiform, the Babylonians adapted it and followed the reign of the Sumerians.

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.
Thanks for this information. Very relevant to my question.

Plimpton 322 dates around 1800 B.C. long after the Sumerians.

## 1. What are Pythagorean triples?

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.

## 2. Who were the Sumerians?

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.

## 3. How did the Sumerians know about Pythagorean triples?

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.

## 4. What Pythagorean triples did the Sumerians know?

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.

## 5. How did the Sumerians use 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.

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