By: Shaina Grover
The Pythagorean Theorem: a^2 + b^2 = c^2. It’s likely that, at one point or another, you’ve heard this equation mentioned in your math class. Typically, this equation is used to determine the length of a right angle triangle’s longest side. In order to understand it, you must have some knowledge of a right triangle’s vocabulary. The height and base are known as legs, and the longest side is known as the hypotenuse. In the equation, “a” and “b” are variables for the legs and “c” is a variable for the hypotenuse.
The Pythagorean theorem was proven by Pythagoras, a Greek philosopher. However, contrary to popular belief, Pythagoras’s main focus was not just math. He had a large interest in the soul and death, particularly reincarnation, and he was an expert on religious rituals.
Unfortunately, there is not a lot of substantial evidence regarding Pythagoras and his achievements. However, we do know that he led the Pythagoreans, a group of mathematicians who made significant advances in the mathematical field. We also know that Pythagoras was born on the island of Samos, which is off Asia Minor, and that he received a proper education because his father was a wealthy merchant. Additionally, some sources suggest that Pythagoras spent time studying in Babylon and Egypt. Interestingly, many believe that the Babylonians were actually the first to discover the Pythagorean Theorem, and that Pythagoras was just the first to prove it.
Due to the high level of secrecy Pythagoras wanted from his students, none of his writings are available to study today. What we have been able to find, however, suggests that Pythagoras should be credited with bringing the idea that the soul was immortal as it migrates into other animals after death to Greece.
As a Greek Philosopher who taught others about reincarnation, Pythagoras was a vegetarian who refrained from engaging in any “worldly pleasures” in order to be free of distractions and improve his soul. He believed that this would help purify his soul, which was necessary due to the fact that it would continue to live on even after his death.
In addition to math and the study of the soul, Pythagoras also made many discoveries in music. Although it is unknown as to how Pythagoras made this discovery, Pythagoras determined that the ratio of the interval between two notes can determine if the sounds are dissonant or consonant. If there is a whole number ratio between the notes, then there is consonance and the notes are harmonious. A whole number ratio also means that the gap between the notes is a full octave and the notes are essentially the same. Interestingly, the myth behind this discovery—it’s been proven false—is that Pythagoras hit four hammers in various pairs on a table and heard the differences in their ringing. When he checked the pitches, he supposedly found that the ones that were harmonious were an octave apart.
Pythagoras lived from c. 570 BCE to 490 BCE. However, he would continue to have an impact on the philosophical world after his death, with his work influencing countless other philosophers, such as Plato and Aristotle. Additionally, his extraordinary work in math, astronomy, music, and philosophy still influence our lives today! So next time you need to find the hypotenuse of a triangle, just remember, a2 + b2 = c2!
Question 1: What is an example of another math discovery that Pythagoras made?
Another one of Pythagoras’ discoveries was the sum of interior angles theorem for polygons. Specifically, the discovery was actually made by the group called the Pythagoreans. They found that the angles of a triangle add up to 2 right angles (to make a total of 180 degrees). This lead to the sum of ‘n’ sides of a polygon has a sum of 2n-4 right angles
Question 2: Aside from finding the hypotenuse, what else is the Pythagorean Theorem used for?
The Pythagorean theorem can also be used to find the shortest distance between two points or the distance between two points on a graph. In football, the Pythagorean Theorem can be used to find what distance a player needs to run and at what angle. In conics (a more advanced math topic) you use variations of the Pythagorean theorem to find the value of certain variables (usually referred to as ‘c’).
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