Pythagoras theorem also known as Pythagorean theorem is a quite interesting concept, every Maths student would be familiar with the word, even non-maths students also would have gone through it in their school time. This theorem gives the fundamental aspect in Euclidean Geometry connecting the three sides of a triangle provided the triangle must be right-angled. Geometrically it would be amenable to allude the properties and its various dimensions, the pictorial representation of the theorem, its application to real-life is an accolade. Its geometrical and metric representations are vast and enormous to deal with, it is not possible to derive it in a single post as it requires elaborate information to deal with angles and its functions. Let us see the important facts which allure us to read the post and feel us interesting.

## Introduction

Pythagoras theorem was introduced by the Greek Mathematician Pythagoras of Samos. He was an ancient Ionian Greek philosopher. He started a group of mathematicians who works religiously on numbers and lived like monks. Finally, the Greek Mathematician stated the theorem hence it is called by his name as ‘Pythagoras theorem.’ Though it was introduced many centuries ago its application in the current era is obligatory to deal with pragmatic situations.

## Right-angled triangle

A right-angled triangle is a triangle in which one angle is the right angle that is the value of theta which is very common in trigonometry, which is the measurement value of ϴ = 90ᶿ. The side opposite to the right angle is called the hypotenuse side or simply hypot, the other two sides near the right angle are called the opposite side and adjacent side.

## Pythagorean triangle and triples

Let us take a right-angled triangle which trifurcates into 3 portions its sides are namely a,b,c. The hypotenuse side is called a, adjacent and opposite sides are called b and c respectively. The hypotenuse side is always the longest side of a triangle which is always consistent in measurement and it occupies a big portion in the triangle.

If the length of all the three sides taken into account of a right-angled triangle are integers then it is called the Pythagorean triangle and the length of the sides a,b,c are collectively known as Pythagorean triples.

## Statement of Pythagoras theorem

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the square of the other two sides. (that is adjacent and opposite side)

Let us take three people father, mother, and daughter who are celebrating their only daughter’s birthday with cake cutting event. The square bought by her mother is square. Now the kid cut the cake slantingly. That is four sides are A, B, C, D. She makes cuts on the diagonals that is endpoint A and C. Now the square cake has become two triangles her mother advised her daughter to take the first half(first triangle) and it was shared as follows

The three portions similar to a right-angled triangle a is the hypotenuse side the larger one which the parents gave it to the birthday girl and the remaining portion that is opposite and adjacent are shared between the parents. The same trifurcation can be made for the second half triangle cake portion also.

According to the Pythagoras theorem, the main idea is, if we take measure the sum and squares of b and c side it should be equal to the sum and square of the child’s share that is a.

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Mathematically it is stated as follows.

= +

- a – the largest portion, child’s share, hypotenuse side
- b – Father’s share, Opposite side
- c – Mother’s share, Adjacent side

Applications of Pythagoras theorem

Though it is necessary to learn the basic concepts such as theorem statement and its mathematical representation, we would be more curious in understanding the applications of Pythagoras theorem which we decapitate in day to day life situations.

### Engineering and Construction fields

Most architects use the technique of Pythagoras theorem to find the value as well as when length or breadth are known it is very easy to calculate the diameter of a particular sector. It is mainly used in two dimensions in engineering fields.

### Face recognition in security cameras

We are more familiar with face recognition nowadays it reduces the turmoil in investigating the crimes in the security areas. It undergoes the concept of the Pythagorean theorem that is, the distance between the security camera and the place where the person is noted is well projected through the lens using the concept.

### Woodworking and interior designing

As the main concept indicates if the cardboards being square can be made into a triangle easily by cutting diagonally then very easily the Pythagoras concept can be applied. Mostly woodworks are made on the strategy which makes the designers easier to proceed.

### Navigation

It’s a very amazing fact but people traveling in the sea use this technique to find the shortest distance and route to proceed to their concerned places.

### Surveying

Usually, surveyors use this technique to find the steep mountainous region, knowing the horizontal region it would be easier for them to calculate the rest using the Pythagoras concept. The fixed distance and the varying one can be looked through a telescope by the surveyor which makes the path easier.

## Summary

Though the Pythagoras theorem has vast applications very few are mentioned in this blog. Many theorems are stated only with the fundamental concept of the theorem. I think readers after reading this blog would get a clear picture of what Pythagoras theorem is about.