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History and contribution of Pythagoras in mathematics
History and contribution of Pythagoras in mathematics
History and contribution of Pythagoras in mathematics
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Rationale:
The pythagorean theorem is a simple equation that has been taught to pupils from the beginning of middle school. a2+b2=c2 is the basic formula to calculate any one of the sides on a right angle triangle. Although starting with basic reinforcement for use of this theorem, usages of this theorem escalate alongside the years achieved in school. It is established into trigonometry, aiding students to solve non-right angle problems combining several mathematical methods. The pythagorean theorem assists many architects, engineers, and chemists in their respective careers. Through this exploration, I wanted to delve further into the mathematical world and see to what extremes math can be interpreted by those who have the affluence to do so. Fermat’s last theorem is a very complex and winding theorem that took many centuries to solve, with just the single inquiring thought to start it all off.
One of the many proofs for the Pythagorean Theorem.
Pythagoras Theorem:
Pythagoras was a mathematician in Ancient Greece who came up with the equation a2+b2=c2for proving that the hypotenuse of a right angle triangle can be found by adding the squared values of the two adjacent sides. Although there are many proofs to affirm this theorem being true, I have shown above one that is well-known, and used in basic school lessons for a clearer understanding of the equation. If one were to take the lengths of sides a and b, then square both values, they would arrive to squares that, when rearranged, would fit the bigger square of the hypotenuse. The Pythagorean Theorem is what had brought Fermat to think of his own theorem, as he had wondered if there could be more possibilities originating from this equation.
Introduction:
Pierre de Fe...
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...roj/pf2html/proofs/pythagoras/pythagoras/ (accessed November 22, 2013).
Works Cited
Frizzell, Roberto. Interview by author. Personal interview. Edmonton, AB, Canada, November 19, 2013.
Fermat's last theorem. Film. Directed by Simon Singh. London: BBC, 1996.
Lipovski, Aleksandar . "Visualization of some simple algebro-geometric ideas." Visualization of some simple algebro-geometric ideas. http://vismath2.tripod.com/lip/ (accessed November 22, 2013).
Savant, Marilyn. "Pierre de Fermat and the Last Theorem." In The world's most famous math problem: the proof of Fermat's last theorem and other mathematical mysteries. New York: St. Martin's Press, 1993. 20-31.
Slany, Wolfgang. "A visual proof of the Pythagorean theorem." A visual proof of the Pythagorean theorem. http://www.dbai.tuwien.ac.at/proj/pf2html/proofs/pythagoras/pythagoras/ (accessed November 22, 2013).
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.
Here Pythagoras, better known as a mathematician for the famous theorem named for him, applied theoretical mathematics and the theory of numbers to the natural sciences (Nordqvist, 1). Pythagoras equated the duration of the lunar cycle to the female menstrual cycle and related the biblical equation of infinity as the product of the number seventy and forty to the normal length of pregnancy at 280 days (Nordqvist, 1). More practical, Pythagoras also contributed the idea of medical quarantine to the practice of medicine setting a forty-day period standard quarantine to avoid the spread of disease. While Pythagoras chose the number forty for its perceived divine nature his practical application of a quarantine must have been based on the observation that in some instances disease spreads through contact. The concept of Quarantine is still in use to this day and is an example of how Pythagoras contributed to modern medicine even while his methods were based on “mystical aspects of the number system” Pythagoras and his followers did “attempt to use mathematics to quantify nature” and as a result, medical practice (Ede, Cormack,
The contemporary world is full of marvels. Technological advances have enabled mankind to fly in the heavens, instantaneously communicate with distant relatives thousands of miles away, construct buildings that are able to withstand many natural disasters, cure deadly diseases, and even travel to and study areas beyond the confines of planet Earth. While there are many factors that contributed to man’s ability to overcome what many once thought were impossible feats, it is the study of engineering that has enabled one to study the elements and leverage all that they have to offer. Mathematics lies at the heart of all science, including engineering. Without progressions in mathematical concepts, engineering principles and applications would not have advanced as quickly as they have throughout history.
Although we have some idea of what Pythagoras studied (properties of numbers that are similar to modern mathematics, such as even and odd numbers, triangular numbers, perfect numbers) his teachings within the schools and the society were very secretive and mysterious. There is little information pertaining to his process of creating famous mathematical formulas such as the Pythagorean Theorem (a2 + b2 = c2).
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
10 J.V. Field, Galileo Galilei. School of Mathmatics and St. Andrews, Scotland, August 1995; available from http://www.history.mcs.standrews.ac.uk/history/mathmatics/galileo.html;Internet.
Over the course of these past few weeks, we have learned all sorts of math that we will utilize in our everyday lives. They have all been very interesting; my favorite subjects were learning about how voting works and how to calculate owning a home. For our final math project in our math modeling class, we had to choose a topic that interested us, yet had something to do with mathematics. For this presentation, I decided to research the history of math and art and how the two have been used together to create amazing artwork. This project most definitely gave me the opportunity to extend some research into the history behind all of mathematics and art.
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.
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...
No other scholar has affected more fields of learning than Blaise Pascal. Born in 1623 in Clermont, France, he was born into a family of respected mathematicians. Being the childhood prodigy that he was, he came up with a theory at the age of three that was Euclid’s book on the sum of the interior of triangles. At the age of sixteen, he was brought by his father Etienne to discuss about math with the greatest minds at the time. He spent his life working with math but also came up with a plethora of new discoveries in the physical sciences, religion, computers, and in math. He died at the ripe age of thirty nine in 1662(). Blaise Pascal has contributed to the fields of mathematics, physical science and computers in countless ways.
» Part 1 Logarithms initially originated in an early form along with logarithm tables published by the Augustinian Monk Michael Stifel when he published ’Arithmetica integra’ in 1544. In the same publication, Stifel also became the first person to use the word ‘exponent’ and the first to indicate multiplication without the use of a symbol. In addition to mathematical findings, he also later anonymously published his prediction that at 8:00am on the 19th of October 1533, the world would end and it would be judgement day. However the Scottish astronomer, physicist, mathematician and astrologer John Napier is more famously known as the person who discovered them due to his work in 1614 called ‘Mirifici Logarithmorum Canonis Descriptio’.
It is well known that in the past, Renaissance artists received their training in an atmosphere of artists and mathematicians studying and learning together (Emmer 2). People also suggest that the art of the future will depend on new technologies, computer graphics in particular (Emmer 1). There are many mathematical advantages to using computer graphics. They can help to visualize phenomena and to understand how to solve new problems (Emmer 2). “The use of ‘visual computers’ gives rise to new challenges for mathematicians. At the same time, computer graphics might in the future be the unifying language between art and science” (Emmer 3).
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
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).
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.