The Pythagorean theorem is one of the most common and well-known theorems among the educated classes, which is the area of the square created on the hypotenuse of a right-angled triangle equal to the sum of the areas of the two squares on the other two sides.
A2 + B2 = C2
where A and B are the lengths of the sides of a right triangle and c is the length of the hypotenuse.
The Pythagorean theorem was used to create the right angle, and this idea was used for many things, including construction.
It was common in the past that geometry and arithmetic were two separate topics, and each of them discussed a different topic until the Pythagorean theorem came and it was the beginning for a strong relationship between geometry and arithmetic, and after the Pythagorean theorem, it was discovered that the square root of two is not rational.
Pythagoras lived around 500 BC, but thinking about this theory was from the days of the Babylonians, and the common issue was to find three numbers A, B, and C so that
A2 + B2 = C2
Now it is called the Pythagorean triples such as: (3, 4, 5) / (8, 15, 17) / (6, 8, 10) / (9, 12, 15).
The issue of finding Pythagorean triples was considered an important issue among the ancient Chinese (200 BC to 220 AD) and in India (500-200 BC).
The best results obtained in this regard were obtained by the ancient Greeks (300 BC to 250 AD).
As I said, it was believed that arithmetic and geometry have no relationship between them and the Pythagorean theorem showed this relationship and the reason is that the Pythagorean theorem was proven in 1925 using geometry.
For the Greeks it was not possible to link between geometry and numbers. This is due to the linking error that was prevalent.
The Babylonians were afraid of the geometric interpretation of the Pythagorean theorem, so they focused their thinking on the Pythagorean triples and discovered lengths that could not be considered in the form of an integer multiplied by the same unit, so they called the ratio between these two lengths irrational
And it was the Pythagoreans who discovered that the root of the number two, which is the length of the diameter of the unit square.
The first person who disclosed this secret was sentenced to death by throwing him into the sea.
At that time, the square root of the two was not accepted as a number, but was considered only the length of the unit square's diameter .
Likewise for the rest of the lengths, they were considered separate from the numbers, with the exception of the relative numbers, which the Greeks established the relationship between them and the lengths.
Not enough information was available about Pythagoras, because there are no documents from that era in which he lived, and all the stories that were passed down from generations until finally were recorded.