Pythagorean Theorem

Pythagorean Theorem

1. The Pythagorean Theorem was established by Pythagoras, who was a Greek mathematician and philosopher. He lived from 569 BC - 490 BC.

   • The Egyptians knew that a triangle with sides 3, 4, and 5 make a 90o angle. They used this to build perfect corners in their buildings and pyramids.
     • Even though the theorem was known long before his time, Pythagoras generalized it and made it popular. It was Pythagoras who is attributed with its first geometrical demonstration.

2. Pythagorean Theorem is a theorem used to this day in order to determine whether a triangle is a right triangle or not.

   • Sometimes using a protractor is not available to people so they may not know whether a triangle contains a right angle or not. Even by looking it can be difficult to determine if a traingle is a right triangle. So, the pythagorean theorem allows for people to easily determine if a triangle is a right triangle.

3. When determining whether or not a triangle is a right triangle different equations can be used for different scenarios. The most common equation used is a² + b² = c².

   • Other equations that can be used to determine if a triangle is a right triangle include:
     • √a² + b² = c
     • c² - b² = c²
     • c² - a² = b²
     • b² + a² = c²

4. The Pythagorean theorem is highly connected with squares and squareroots. Because of this, it is important to understand and be able to solve scenarios which include finding the square and the square root of a number.

   • When finding whether a triangle is a right triangle, we have to know the areas of the "squares" connected to all of its sides. We do this by getting the square of one of the sidelengths.
   • Learning how to square and square root numbers is quite easy. As long as you understand the concept that it is simply a number that is multiplied by itself twice you can start learning the Pythagorean theorum.

5. Applications of the Pythagorean Theorem in Real life

   • Square Angles In Buildings To make sure that the buildings are in square shape, Pythagorean Theorem is used.
   • Architecture and Construction If you are given a set of straight lines then Pythagoras Theorem can be used to calculate the diagonal connecting them.
   • Painting on a Wall The painter needs to determine how tall a ladder should be, as it will help to safely determine the distance at which the base needs to be placed away from the wall so that it won’t tip over.