Knowing Pythagoras' Theorem and Its Historical Importance One of the most well-known mathematical theorems, the Pythagoras Theorem is frequently taught in schools across the globe. But it's possible that a lot of people are unaware of the intriguing historical setting and importance of this theorem. In this article, we will examine the Pythagorean Theorem, its relation to Babylonian mathematics, how it is used to interpret the square root of two geometrically, and how it is demonstrated to be an irrational number. Square of a Unit and its Diagonal The idea of a unit square, or a square with side lengths equal to one unit, is at the foundation of Pythagoras' Theorem. A straight line, commonly referred to as the square's diagonal, is the quickest way to get from one corner of the square to the other. This diagonal's length, x, has the special characteristic that its square is equal to two. Or to put it another way, x is the square root of 2. Consider two unit squares stacked on top of one another to create a two by two square with side lengths of two units to illustrate this concept. We can locate an inner square with side length x in the center if we concentrate on the midpoints of the sides of this square and connect them with diagonals. The area of this inner square is equal to two units when the areas of a few triangles are added together. As a result, the square of the integer x is equal to two. 2 2 2 𝑐 =𝑎 +𝑏 The Pythagorean Proof and the Yale Tablet The Yale Tablet, a prehistoric clay tablet, is where the Pythagoras Theorem and Babylonian mathematics first intersected. The earliest known demonstration of Pythagoras' theorem may be found on this tablet, which was created roughly a thousand years before Pythagoras. The demonstration on the tablet shows that the square root of two is in fact x, the size of a unit square's diagonal, by applying a strategy similar to the one described above. The Theorem of Pythagoras and Isosceles Triangles The connection between the sides of a right-angled triangle serves as the foundation for Pythagoras' Theorem. The Pythagorean Theorem asserts that the square of the length of the hypotenuse (the longest side), which is a triangle with two equal side lengths, is equal to the sum of the squares of the other two sides. An isosceles triangle with side lengths of one unit can be scaled up to illustrate this theorem. The square root of two a, all squared, which is equal to two a squared, or a squared plus a squared, is equal to the length of the hypotenuse, denoted by the letter c. The Importance of Pythagoras' Theorem The Pythagorean theorem has broad applications and is often utilized in many branches of science, mathematics, and engineering. It may be used to figure out the separation between two points, the size of a right-angled triangle's sides, and the angle between two lines. In addition to serving as a cornerstone of trigonometry, the Pythagorean theorem is also essential to the study of geometry, number theory, and calculus.