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Pythagoras and his contribution to mathematics
Pythagoras and his contribution to mathematics
Pythagoras and his contribution to mathematics
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Pythagoras was a mathematician who has influenced the math culture until this day. His studies in math are more noted than his contributions to philosophy as well as religion. Due to the fact Pythagoras lived between roughly 520-495 bc there is very little information about him. In fact his exact birthday and death date are mainly estimations based on other historical events. Whatever we know about him is information learned after his death. Most of his writings were not published so we do not have many of his personal notes. Pythagoras is popularly known for his ligating the Pythagorean theorem used in geometry.
It is reported that Pythagoras was born anywhere between 520 to 570 on the Samos island, which was part of Greece . His father's name was Mnesarchus, and he was a merchant while his mother's name was Pythias(School of Mathematics and Statistics University of St Andrews, Scotland, 1999) . Being that his father was a merchant he travelled often to bring back items to sell in Samos so Pythagoras gained the opportunity to travel often with his father(School of Mathematics and Statistics University of St Andrews, Scotland, 1999). When Pythagoras was young it is said that he was very intelligent and worked with Pherekydes, Thales, and Anaximander who helped in shaping his future ideas (School of Mathematics and Statistics University of St Andrews, Scotland, 1999). Thales influenced him in math and astronomy, Anaximander in philosophy and geometry while Pherekydes influenced him in philosophy (Math Open Reference, 2009). He was able to recite Homer as well as being able to play the lyre and learn poetry(School of Mathematics and Statistics University of St Andrews, Scotland, 1999). In around 535 B...
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...Morris & University of Georgia). That is the fundamental thought of the the theorem and can be expanded to solve more complex problems. Another contribution he made are the Pythagorean triples which are three positive integers that follow the a2 + b2 = c2 pattern (Wikipedia , 2013). When a triangle fits into this mold, they are referred to as Pythagorean Triangle (Wikipedia , 2013). Examples would be, 3,4,5 and 5,12,13. When those sets of numbers are seen it can be assumed that the triangle is a right triangle so you can go forth and using the Pythagorean Theorem to solve it. To get a triple set, you need to use Euclid’s formula (Wikipedia , 2013) .
Pythagoras made multiple contributions to math. He also contributed to science and philosophy. His contributions are seen as important today because they act as stepping stones in solving different problems.
Through history, as said before, many philosophers have supported and developed what Pythagoras first exposed to the world. One of the most important philosophers to support Pythagoras’s ideas was Plato. In some of his writings he discusses the creation of the universe based on the musical proportions discovered by Pythagoras (Timaeus), and the explanation of the sound emitted by the planets, which is exposed in the “Myth of Er” in The Republic. It talks about a man who died and came back to life who narrates how he saw the space and how, in every “sphere,” there was a being singing constantly, each one in a different tone, so a perfect harmony was built. Nevertheless, not everyone agreed with this theory, being one of its most important critics Aristotle, who claimed that Plato’s arguments where false in his text On the Heavens. He acknowledges that it is a creative and innovative theory, but it is absurd to think that such music, which is imperceptible to us, exists in a harmonic way up in the heavens. I am not going to go deeper into that for it is not relevant for the text. As the years went on, many people continued developing this theory. Nevertheless, this philosophical theory, not truly explained until later on, was an inspiration for many artists and that is why not only philosophers but many other artists mention and base their works upon this theory.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Pythagoras was one of the first true mathematicians who was not only known for the famous Pythagorean theorem. His father was from Tyre while his mother was from Samos but when Pythagoras was born and growing up he spent most of his time in Samos but as he grew he began to spend a lot of time with his father. His father was a merchant and so Pythagoras travelled extensively with him to many places. He learned things as he went along with his father but the primary teacher known to be in his life was Pherekydes. Thales was also a teacher for himself and he learned some from him but he mainly inspired him. Thales was old when Pythagoras was 20 and so Thales told him to go to Egypt and learn more about the subjects he enjoyed which were cosmology and geometry. In Egypt most of the temples where the learning took place refused him entry and the only one that would was called Diospolis. He was then accepted into the priesthood and because of the discussions between the priests he learned more and more about geome...
and 'c' (a being the shortest side, c the hypotenuse): a2 + b2 = c2
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
Parmenides was a Pre-Socratic philosopher who lived from 515-445 B.C. He was born in Elea (now Velia), a Greek city in southern Italy. His city was at the far end of the known world on the other side of Greece where Heraclitus and the Ionians lived. He escaped his town to study in Athens, the center of the known world. Most likely he was a student of Anaximander and was also influenced greatly by the teachings of Pythagoras. Parmenides joined the religious and philosophical following of Pythagoras in Crotona.
For the Greeks philosophy wasn’t restricted to the abstract it was also their natural science. In this way their philosophers were also their scientist. Questions such as what is the nature of reality and how do we know what is real are two of the fundamental questions they sought to answer. Pythagoras and Plato were two of the natural philosophers who sought to explain these universal principles. Pythagoras felt that all things could be explained and represented by mathematical formulae. Plato, Socrate’s most important disciple, believed that the world was divided into two realms, the visible and the intelligible. Part of the world, the visible, we could grasp with the five senses, but the intelligible we could only grasp with our minds. In their own way they both sought to explain the nature of reality and how we could know what is real.
Even though Aristotle’s contributions to mathematics are significantly important and lay a strong foundation in the study and view of the science, it is imperative to mention that Aristotle, in actuality, “never devoted a treatise to philosophy of mathematics” [5]. As aforementioned, even his books never truly leaned toward a specific philosophy on mathematics, but rather a form or manner in which to attempt to understand mathematics through certain truths.
...gs. The voice of Pythagorus rings out when we measure a right triangle, as well as when Socrates is credited by modern day thinkers.
Pythagoras led an interesting life to say the least, but one of the most influential and important aspect of his life was the discovery and study of Pythagorean Theorem. If you’ve gone through almost any level of math you’ve most likely had to use this formula;〖 a〗^2+b^2=c^2. The equation is defined as the “area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides.” Although the theorem is believed to be created by Pythagoras had been used by before his time by Native Americans and the Babylonians, but it is believed that he and his students did create the first proof. Pythagoras is also known for creating many theorems and mathematical discoveries such as;
Since the beginning of human history, math has been essential to our species. One needs it daily - even if one is not a math teacher, or a rocket scientist! From paying for gas at Goco’s to making an A on the next math test, everyone needs math. How a man or woman can manipulate numbers the way a certain man, Pythagoras, did in the past is beyond my level of comprehension. But who exactly is Pythagoras?
He made several contributions to science and religion. Pythagoras’ teachings were centered on the doctrine of metempsychosis. He believed that a person’s soul does not die and is destined to a cycle of rebirths. The soul is freed from the cycle of births only through the purity of its life. His doctrine later came to be known as “Pythagoreanism,” which emphasized on esoteric and metaphysical ideologies. Proverbs 4:7 says, “Wisdom is the principal thing, therefore get wisdom: and with all thy getting get understanding.” Wisdom is the greatest possession anyone can have; Pythagoras obtained it. One of Pythagoras’ quotations which I found interesting is “There is geometry in the humming of the strings, there is music in the spacing of the spheres.”
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know whether they are true or not. The first one is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. This is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The next type of information is that Euclid was born at Megara. But this is not the same Euclid that authors thought. In fact, there was a Euclid of Megara, who was a philosopher who lived approximately 100 years before Euclid of Alexandria.
Aristotle made contributions to logic, physics, biology, medicine, and agriculture. He redesigned most, if not all, areas of knowledge he studied. Later in life he became the “Father of logic” and was the first to develop a formalized way of reasoning. Aristotle was a greek philosopher who founded formal logic, pioneered zoology, founded his own school, and classified the various branches of philosophy.
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).