THE HISTORY OF PYTHAGORAS

·Brief Profile of Pythagoras

Pythagoras born in island of Samos, Greek South, around 580 BC, borned as child of Mnesarchus, a merchant from Tyre. Well-Traveled Pythagoras to Babylon, Egypt and estimated by have reached India. In Babylon, Pythagoras braid relation with mathematicians. At 18 year old he meet with Thales. Thales, an oldman, defining mathematics to Pythagoras by way of Anaximander (Thales pupil). But confessed by Pythagoras as teacher is Pherekydes. Pythagoras leave Samos in 518 BC. After a few times he open school in Croton which accepting pupil without differentiating gender. That school become very famous and finally Pythagoras married with one of his pupil. Illustration detailed about Pythagoras not too clear. Told afterwards, he go to Delos in 513 BC to take care of benefactor at the same time its teacher, Pherekydes. Pythagoras remain to over there until he die 475 BC. After Pythagoras death, Croton school drag one's feet and many internal conflict, but can continue to walk until 500 BC before becoming political appliance.

· Pythagoras Theorem

In mathematics, Pythagoras theorem is a relation of Euclides geometry between three side a right triangle. This theorem is named according to name of philosopher and Greek mathematician in sixth century BC, Pythagoras. Pythagoras often considered to be inventor of this theorem though in fact this theorem facts have been known by India mathematician (in Sulbasutra Baudhayana and of Katyayana), Greek, Tionghoa and Babylonia far before Pythagoras born. Pythagoras get credit because his first prove universal truth of this theorem by mathematical verification.

There is two contemporary evidence which can be considered to be eldest note regarding Pythagoras theorem: one can be found in Chou Pei Suan Ching (about 500-200 BC), the other one again in Element book of Euclides.

From perception of Pythagoras see Egypt people use comparator string and ruler to measure height of building - hence he inspired to make mathematics law to measure height and right triangle hypotenusa. Of visit to Egypt that's Pythagoras introduce principle which we recognize with law of Pythagoras, what of course useful for not only to measure height of piramid or obelisk, but also to measure height and distance almost everything in the earth, including when modification of this Pythagoras law is used by Eratosthenes to measure earth circumference. Result of his calculation only clinged 40 km, from result of modern calculation.

Theorem of Pythagoras express that :

Amount of square wide at a right triangle feet is equal to wide of square in hypotenuse.

A right triangle is triangle which have a right angle; this feet is two sides which form this right angle, and hypotenuse is third side which in the face of the right angle. At the picture under here, a and b are right triangle feet and c is hypotenuse

Pythagoras express this theorem in goemetrical style, as statement about wide of square:

Amount of wide blue square and red is equal to wide of purple square.

As respects to him, Sulbasutra India also express that:

String that stretch as long as diagonal length of square will produce wide which produced vertical side and horizontal.

Using algebra, we can repeat formulating this theorem into modern statement by taking note that wide of a square is quadrate from side length:

If a right triangle have feet with length of a and b and hypotenuse with length of c, hence a² + b² = c²

· The Weakness of Pythagorean Doctrine

Number zero do not get space in the framework of Pythagorean. Number zero is unknown in Greek dictionary. Using number zero in a ratio seems break the natural law. A ratio becoming not meaningful because " interference" of number zero. Number zero divided by a number can break logic. Zero making " hole" at universe in the Pythagorean version, for this reason the attendance of number zero cannot be tolerated. Pythagorean can't solve " problem" of mathematics concept - irrasional number, what in fact also represent peripheral product (by product) formula: a² + b² = c². This concept also attack their viewpoint, but hotly brotherhood remain to be taken care as a secret. This secret have to remain to be taken care of don't leak or their cult fall to pieces. They don't know that irrasional number is " time bomb" to framework think Greek mathematics.

Ratio between two number at the most compare two line with different length. Elementary opinion of Pythagorean is sensible everything in universe relate to neatness, proportion without handicap or rational. Ratio written in form of intact number a/b, like: 1, 2 or 17, where b may not equal to zero because with that will generate disaster. Needn't be explained again, universe disagree with this method. Many number cannot be expressed easy into ratio of a/b. Attendance of irrasional number cannot avoid again and Greek mathematics consequence.

Rectangle is simplest form in geometry, but it consist of irrasional number. If you make diagonal line at rectangle - emerge irrasional, and later the level of determined by number root. Irrasional number happened and will always happened at all of geometry form. Other exampl, right triangle with both sides length is one, can be calculated the length of other side - with Pythagoras formula, that is: . Very difficult to hide this matter to someone who understand ratio and geometry.

· Discovery of root 2 ()

Early from weakness of Pythagorean doctrine, Hippasus from Metapontum ( ca. 500 BC) is a Ancient Greek mathematics and philosopher, pupil of Pythagoras. He is considered to be inventor of irrasional number, specially prove that square root from 2 , , is irrational number. Ironically, his invention exactly cause he death.

Till invention of Hippasus, Pythagoras and his follower assume that all number have the character of rationally, or can be expressed in comparison of integer. But, by using reductio ad absurdum (verification through contradiction) proven that it is irrational number. Pythagoras cannot argue verification of Hipassus, but irrational number oppose against embraced by philosophy is Pythagoras. Phytagoras do not want to confess mistake of his philosophy, and allege Hippasus as follower of errant teaching. Hipassus is finally sentenced to death by engulfed.

Without effort clarifying which is real correct, but expression by Hippasus convulse foundation of Pythagoras doctrine. In this case Pythagorean consider that irrasional number only as an exception. They cannot prove that irrasional number contaminate their view about universe

· Pythagoras Contribution

West philosophy influenced by Pythagoras idea - as does Aristoteles doctrine, in the reality can stay almost 2 milenium. Number zero and irrasional number oppose against the doctrine, but giving the foundation for next mathematician so that paying attention number zero and irrasional number

Pythagoras assume that numbers as forms, as exist in game card or dice. We even also still inheriting it until now by using term like square number or quadratic number and cube number for number in a good position three, which none other than terms coming from Pythagoras. He even also use parallelogram number term, triangle number, pyramid number, etc. That numbers frankly deputize the amount of cobblestone used to compile pertinent forms.

Mathematics combination and theology, begining from Pythagoras, have inculcated characteristic philosophy which is have religion pattern in Greek, in Middle Ages and modern-day till Immanuel Kant. But strarting Plato era and Descartes era happened by circumstantial solidarity between religion and logic, between moral aspiration and logic attitude glorifying all which eternal. This matter do not get out from influence predominate pure mathematics of that time

Pythagoras invention in music and mathematics be alive till now. Pythagoras theorem remain to be taught in schools and used to measure the distance of a triangle side. Before Pythagoras there is no verification of assumptions. Pythagoras is the first person triggering that axioms, postulates require to be formulated beforehand in developing geometry

This benefit, later, making mathematics remain to earn to be used as appliance assist in doing calculation for natural phenomenons perception, after passing completion and development by mathematician after Pythagoras. Pythagoras theorem constitute the existence of Fermat theorem (year 1620): xn + yn = zn that can be proved by Sir Andrew Wiles in 1994

Reference :

Eves, Howard.1963.An Introduction To The History of Mathematic: University of Maine

http://www.mate-mati-kaku.com/matematikawan/phytagoras.html

http://www.wikipedia.com

Alfian Tyas Kurniawan

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