Pythagoras And His Great Mathematical Achievements

Pythagoras was considered to be an influencer of many people and things around him. He was said to be interested philosophy, astronomy, and music. He was greatly motivated by Pherekydes, Thales, and Anaximander. But one of his main achievements that people know him for is being the first real famous mathematician. 

Pythagoras was born approximately 569 BC at the island of Samos Greece. Historians are not really sure when he died but it is said that he died around 500 BC to 475 BC in Metapontum, Lucania, Italy. He was around 75 years old when he died. Pythagoras’s mother’s name was Parthenis, she was a native of Samos. She was from one of the islands most aristocratic families. His father’s name was Mnesarchus, he was a wealthy merchant of Phoenician heritage who had settled on Samos. Pythagoras father’s business was trade and mostly traveled a lot. It was even said that he had two or three brothers. There also was a theory that he was married to a woman named Theano but others believed that it was one of his students that he was the teacher for. Some sources said he was treated like a God. He was also the first to believe that the earth was round. 

Pythagoras was most famous for a theory that he did the first proof on called the Pythagorean Theorem. This theory evolved in the world very quickly. This means that a right triangle the square of the hypotenuse is equal to sum of two squares of other two sides. The equation was and still is a^2+b^2=c^2 Once this was put out to the world most people started to experiment with it. This is even still being used to this day in most math school settings like in geometry and algebra classes. 

My own Pythagorean Theorem examples 

a^2+b^2=c^2

10 + 24 = x 15 100 + 576 10 576 = x 24 = x x 

a^2+b^2=c^2

35 35 + 15 = x 

1225 + 225 15 1450 = x 38 = x x 

He was also famous for some other theories too. He figured out that musical notes could be changed into mathematical equations. During his lifetime Pythagoras was also famous for some of his quotes that he wrote. One of the quotes was “There is geometry in the humming of the strings, there is music in the spacing of the spheres.” Another one was “Geometry is knowledge of the eternally existent.” “All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understand through mathematics.” 

He also had many other quotes that did not pertain to math but he was famous for them too.” One was “Above the cloud with its shadow is the star with its light.” He and his followers (which were called Pythagoreans) believed that everything can be a made into a number. They were also known for representing numbers by a series of equally spaced numbers by lines, triangles, and so on. This was a way that Pythagoras was able to see and change the shape with every number given. He and the Pythagoreans put the most important numbers into four basic groups. They are: triangles, squares, and gnomons. Triangular numbers include any numbers that can form/be shaped into a triangle by a series of dots. An example would be the numbers 3 and 10. There are also square numbers that are spaced into squares. An example would be the numbers 4 and 9. He was also known for something called Pythagorean triples. It is described as a group of positive numbers that follow the Pythagorean theorem formula a^2+b^2=c^2. One of them is (3,4,5). 

Pythagoras also discovered that math can be used in music. He used to play the instrument called the lyre. When he played it, he realized that when he was playing a tune there are proportional numbers being involved. Some were 2:1 3:2 and 4:3. The ratio 2:1 represents a musical octave, 3:2 represents something called a musical fifth and 4:3 represents something called musical fourth. He even found out that his knowledge can be used in other instruments too.

 With this Pythagoras and the Pythagoreans believed that music was the expression of harmony around the world. This was one of the many things that Pythagoras and the Pythagoreans were able to figure out the official connection with music and numbers.