Pythagoras Theorem is an important topic in Mathematics, which explains the relation between the sides of a right triangle. It is called Pythagoras Theorem Because of The Greek Mathematician who discovered it Namely-“Pythagoras”.

## Introduction :

Pythagoras theorem affirms that “**In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides**“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the **hypotenuse** is the longest side, as it is opposite to the angle of 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

According to the Syrian historian **Iamblichus** (250–330 CE), Pythagoras was introduced to mathematics by **Thales of Miletus** and his pupil **Anaximander**. In any case, it is known that Pythagoras travelled to Egypt about 535 BCE to further his study, was captured during an invasion in 525 BCE by **Cambyses II of Persia **and taken to **Babylon** and may have visited India before returning to the Mediterranean. Pythagoras soon settled in **Croton** (now Crotone, Italy) and set up a school, or in modern terms, a monastery, where all members took strict pledges of secrecy, and all new mathematical results for several centuries were attributed to his name. Thus, not only is the first proof of the theorem not known, but there is also some doubt that Pythagoras himself proved the theorem that bears his name.

## Practical Applications :

But why did they create the theorem?, Lets Find Out:

Given two straight lines, the Pythagorean Theorem allows you to calculate the length of the diagonal connecting them. This application is frequently used in architecture, woodworking, or other physical construction projects. For instance, say you are building a sloped roof. If you know the height of the roof and the length for it to cover, you can use the Pythagorean Theorem to find the diagonal length of the roof’s slope. You can use this information to cut properly sized beams to support the roof, or calculate the area of the roof that you would need to shingle.

The Pythagorean Theorem is also helpful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. For example, if you are at sea and navigating to a point that is 100 miles north and 200 miles west, you can use the theorem to find the distance from your ship to that point and calculate how many degrees to the west of north you would need to follow to reach that point. The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be diagonal. The same laws can be used for air navigation. For instance, a plane can use its height above the ground and its distance from the destination airport to find the correct place to begin a descent to that airport.

This Theorem is also used in Surveying which is the process by which cartographers calculate the numerical distances and heights between different points before creating a map. Because the terrain is often uneven, surveyors must find ways to take measurements of distance systematically. The Pythagorean Theorem is used to calculate the steepness of inclines of hills or mountains. A surveyor looks through a telescope toward a measuring stick a fixed distance away, so that the telescope’s line of sight and the measuring stick form a right angle. Since the surveyor knows both the height of the measuring stick and the parallel distance of the stick from the telescope, he can then use the theorem to determine the length of the slope that covers that distance, and from that length, conclude how steep it is.

In Short, Pythagoras Theorem Is Very Important for our World due to several needs increasing in our day-to-day life.

**References:**

https://www.mathsisfun.com/pythagoras.html

https://en.wikipedia.org/wiki/Pythagorean_theorem

https://www.cut-the-knot.org/pythagoras/index.shtml

https://www.britannica.com/science/Pythagorean-theorem

http://www.geom.uiuc.edu/~demo5337/Group3/hist.html

https://betterexplained.com/articles/measure-any-distance-with-the-pythagorean-theorem/

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