Essay on Pythagoras and His Contributions to Modern Mathematics

Being one of the greatest philosophers of his time, Pythagoras created a society of skilled mathematicians who worked together to facilitate mathematics, showed how numbers can be independent, and proved the Pythagorean theorem, making him iconic in mathematics today. His discoveries of simple yet essential methods are prevalent today throughout many mathematical fields in which they are treasured.

Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were

The Pythagorean School, for example, contributed many ideas to the mathematic community, among them, studies of geometry and the theory of proof.5 Euclid also lived in the time of ancient Greece and became a prominent mathematician, as well as author of a book about geometry called, The Elements, considered the second best-selling book of all time.6 The works of Pythagoras and Euclid have become fundamental building blocks for any person with an eighth-grade understanding mathematics. With these advancements, as well as innovations from Archimedes and Apollonius of Perga, Islamic scholars translated their works and contributed even more, growing the worldwide understanding of mathematics.7 Greek progressions in geometry as well as the theory of proof contributed greatly to our ultimate understanding of contemporary mathematics, without which, our modern society would be

Pythagoras also contributed to the music world. He expressed the musical harmony in formulas. He created a scale layout with gongs in different sizes and he proved that in the resonance of the gongs he hit, 1 octave interval is equal to 2:1 proportion, the perfect fifth is equal to 3:2 proportion, perfect four is equal to 4:3 proportion and whole notes are equal to 9:8. This, later started to be known as “Pythagorean Tuning.”

Hipparchus was a greek astronomer, geographer, and mathematician born 190 B.C. in Nicaea and died in 120 B.C. Rhodes, Rhodes, Greece. Hipparchus is accredited as the inventor of trigonometry because of his discovery of the first table of chords and also because he's the only person with valid data of the discovery and usage of trigonometry. In order to calculate the rising and setting of zodiacal signs, Hipparchus brought to light the division of circles into 360 degrees and the calculation of chords by looking at the triangles (spherical triangles or triangles that made up a circle) differently. Hipparchus experimented putting all triangles to be within a circle and with the three points each touching the

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

Did you know that Pythagorean Theorem was actually created well before our generation’s time period? Yes, it seems that is pretty basic knowledge, but did you know it was actually created in B.C. and instead of A.D.? The brilliant mind to thank for such an achievement is the man who goes by the name Pythagoras. However the Pythagorean Theorem isn’t his only accomplishment, he was so advanced for his time, that he had many achievements. But to the best way to examine these accomplishments is to start at the beginning.

The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.

A few things I found interesting when I watched “Donald In Mathmagic Land”, was an ancient Greek man named Pythagoras also known as the father of mathematics. He discovered many fundamental things such as fractions that helped him create a formula that soon became the basis to music with the help of his fraternity as well. A secret pentagram was used as a password entry to for their meetings in order for them to speak about their mathematical discoveries. I did not know that mathematics was essential in order to create music. Pythagoras also discovered the pentagram had many mathematical functions such as the golden section and many shapes. One of the shapes found within the pentagram was the golden rectangle which helped create famous sculptures,

Geometry first originated as a way to solve problems in architecture and navigation. A famous figure in geometry is Euclid. Around 300 BC, he published a book, The Elements, which contained definitions, axioms, and postulates that would be regarded as a standard of mathematical reasoning for the next two thousand years (Mueller, 1969). Euclid basically gave the foundation of what is now called Euclidean geometry. However,

Pythagoras the master of the sum of the angles of a triangle which is equal to two right angles, also the theorem of Pythagoras, which is for a right-angle triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides, an actual fact is that the Babylonians understood this thousand years earlier, but Pythagoras was the one to prove it. Yet its is known that Babylonians he or his students handled Pythagorean the numbers differently and he did found some kind of proof but hasn't been found in the cuneiform

Greeks such as Aristotle, Pythagoras, and Hippocrates have left concepts still used in modern science and mathematics. Their ideas laid a basis for future European thoughts and studies in the fields. Their contributions such as the creating the Pythagorean theory, the writing a comprehensive classification of species and the systematizing of medical knowledge would influence the way Europeans thought and studied the world. Hippocrates’ Oath is still sworn by all medical practitioners. The contributions of the Ancient Greeks in science and math built a foundation upon which future Europeans would build and lead to the development of modern

There are many great philosophers in this world. Some of which are extremely well known and almost everyone knows their names like Socrates, Plato Aristotle Locke and so very many more. Pythagoras is a less known philosopher who had a lot of discoveries while leading a life in a secretive manner. He was an enigma and the leader of a religious sect cult who believed the universe to consist solely of whole numbers and their ratios. Pythagoras said "Do not talk a little on many subjects, but much on a few." Has one ever wondered where did he learn his vast knowledge of mathematics and religious aspects leading to the Pythagorean cult, or what was all of his discoveries besides

Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall, 150. ISBN 0-02-318285-7. “Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287–212 B.C.), the most original and profound mathematician of antiquity.”

Euclid’s assumptions about his postulates have set the groundwork for geometry today. He provided society with definitions of a circle, a point, and line, etc and for 2000 was considered “the father of geometry.” His postulates proved to be a framework from which mathematics was able to grow and evolve, from two thousand years ago, till Newton and even to all our classrooms today.