# Which Pythagorean triples were known by the Sumerians?

• MHB
• matqkks
In summary, Pythagorean triples are sets of three positive integers that follow the equation a² + b² = c², and were used by the ancient Sumerians for practical and mystical purposes. The Sumerians were an ancient civilization in Mesopotamia from approximately 4000 BCE to 2000 BCE, and they discovered Pythagorean triples while working with right triangles in their architectural and surveying practices. The most well-known triple among the Sumerians was (3, 4, 5), but they also knew others such as (5, 12, 13) and (8, 15, 17).
matqkks
Where they aware of 3,4 and 5; 5, 12 and 13?

## 1. What is a Pythagorean triple?

A Pythagorean triple is a set of three positive integers that satisfy the Pythagorean theorem, a^2 + b^2 = c^2, where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.

## 2. How did the Sumerians use Pythagorean triples?

The Sumerians used Pythagorean triples to create right angles and build structures such as temples and palaces. They also used them in astronomy and land surveying.

## 3. How were Pythagorean triples discovered by the Sumerians?

The Sumerians did not discover Pythagorean triples in the same way that Pythagoras did. Instead, they used a list of pre-calculated triples that were likely derived from practical applications and observations.

## 4. How many Pythagorean triples were known by the Sumerians?

It is estimated that the Sumerians knew at least 15 Pythagorean triples, including the well-known 3-4-5 and 5-12-13 triples. However, there may have been more that have not been discovered or recorded.

## 5. How did Pythagorean triples contribute to the development of mathematics?

Pythagorean triples were one of the earliest mathematical concepts and played a significant role in the development of geometry and algebra. They also helped to lay the foundation for the Pythagorean theorem, which is still used in mathematics and other fields today.

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