# Pythagorean Theorem

## Who Is The Inventor of Phythagorean Theorem?

This famous theorem is named for the Greek philosopher, Pythagoras. Pythagoras intended to use this theorem more frequently in advanced math/algebra. The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. Pythagorean Theorem about triangles containing a right angle. The theorem stated algebraically is a (squared) + b (squared) = c (squared).

## Where do I find this? (Right Triangle)

You can find the right triangle in Pythagorean Theorem when a triangle has a right angle (90 degrees), and squares are made on each of three sides. c is the longest side of the triangle, and a and b are the other two sides. The longest side of the triangle (c) is called the "hypotenuse". If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. This formula only works on right angled triangles!

## Where Do I Find This? (Pythagorean Theorem)

Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle's legs is the same as the square of the length of the triangle's hypotenuse. This property has many applications in science, art, engineering, and architecture, and is now called Pythagorean Theorem. Before Pythagoras derived his theory, he studied right triangles, and the relationships between the legs and the hypotenuse of a right triangle.

## Process

In math class, we learned a few mini lessons on how to use Pythagorean Theorem, and once we showed that we knew how to use this theorem, we started to work on our wheels. On the first day of designing my wheel, I started to measure out the lengths for the different triangles, that only took me one class period, and then I began to think about what I was going to do as a design with each triangle. Thinking about what to do for each triangle was really hard because I am not artistic whatsoever. I then decided that I was going to do the top 17 ranked college volleyball teams, and I had begun to trace my drawings on tracing paper, until I realized that when I would go to put the drawing onto my wheel, it would turn out backwards. I did not realize this would happen until I got to the point where I was all finished tracing. I thought there was no way to fix the problem, but I found a way. After I was done with tracing all of the logos, I had begun to do the math for the project. This project was really fun, and I learned some new and interesting things that I thought were very cool.

## What Is A Right Triangle?

A right triangle is a triangle having a right angle. Right triangles are shown and used in various branches of mathematics. A right triangle can also be isosceles if the two sides that include the right angle are equal in length. A right triangle can never be equilateral, since the hypotenuse is always longer than either of the other two sides. You can construct right triangles with a compass and straightedge given various combinations of sides and angles.

## What Do The Squares Mean/Do?

Since the longest side of a triangle is called the "hypotenuse", in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The squares are made on each of the three sides of the triangles so that the biggest square has the exact same area as the other two squares put together. In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

## What Is A Square Root?

A square root is a number that produces a specified quantity when multiplied by itself. Finding the square root of a number is the inverse operation of squaring that number. The square of a number is that number times itself. The perfect squares are the squares of whole numbers. You can also square negative numbers because a negative times a negative gives a positive. A square root goes the other way: 3 squared is 9, so a square root of 9 is 3. A square root of a number is a value that can be multiplied by itself to give the original number.

## What Did The Final Project Look Like?

The final project looked very similar to the theorem photos, it was just designed to look semi-similar to a wheel. The wheel that I created had a total of 17 right triangles, and i had to find the hypotenuse's of 5 triangles. I just used the formula (a² + b² = c²) to find each hypotenuse. I also had to make sure that all of the hypotenuse's on my project lined up with the others. In the beginning, it was somewhat tough to measure out the lengths for each triangle, so I had to redraw some of the triangles on my wheel. While I was finding each hypotenuse I had to think about the next triangle, and how I was going to use the formula for that one as well. Not all lengths on each of the triangles were the same so I had to think about how to measure, and successfully use the formula too.