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Minggu, 30 November 2008

ACTIVITY REPORT AND MY RESULT IN SEARCHING, COLLECTING, STUDYING, ANALYZING, DISCUSING MATHEMATICS HISTORY DURING THE TIME

1. Activity
At first time I'm join university lecture I'm interest with mathematics history subject. In my opinion history interesting to be studied, moreover relate to mathematics. When finding of theorems, how to find it, who is the inventor figure. It's my reason want to know more and understand what mathematics history is.

In Junior High School, first mathematician that I know is Pythagoras. It’s because of in Junior High School teach how to find hypotenuse of right triangle if the other side are known. And his theorem was used in here. It’s the begin I know mathematic history.

In Senior High School, my knowledge about history mathematic be promoted. I know more the mathematicians, like Pascal, Aristoteles, Algebra, etc. Although I know them in other subject not in mathematics. In that time, I’m very amazed with them because in all limitation they can discover new things that amazing at this time. I can’t imaging how to expand their thinking and realize it with their experiment.

In both time, I’m only limited to know the formula and the mathematician who discover it. I’m only know how to use formula, I don’t know how to prove it.

In college, I meet with mathematic history subject. I feel it’s very interesting, in there I can know the prove of the mathematics theorems. At this time, my lecturer use group presentation in the class. So that the class let to make the group and discuss the problem sets. One group give one discussion material and must present it in the front of class.

From the presentations, I know more about mathematics history. And my admiration with the mathematicians more over. I know how they can discover the theorems and the prove of it. And I know the growth of mathematic history from the past to this time. They do wonderful things that very rare people do at this time, it’s very amazing!

2. Result
The profit that I get from studying mathematic history is when I must make the paper. In here, I must have concept, look for reference, and arrange the paper. At first, I feel it’s very difficult and tiring. But at least I know the benefit from it and enjoyed it. My lecturer always teach me how to make good paper, so, there no reason for me can’t make the paper.

With Mr.Marsigit, my mathematic history lecturer, mathematic history class always interesting. There are new things that I know every meeting. Not always the reference from the book, but it can be from encyclopaedia software from computer. It’s really outside idea of me, what possible only have directive to books and articles. In this software, not only past history but also the history until 2007. How to discover it, what is the discovery, who is the discoverer, all of it avalaible in this software. It’s very amazing and facilitating for me.

Now, I can answer question one who enquire about mathematics history, although only limited to ability of me. A lot of things which I can study from mathematic history, like philosophy, spirit, intuition of mathematics figure, giving my spirit to study mathematics.

3. CONCLUSION
Mathematic history is the interesting lesson for me. A lot of things that can be studied in mathematic history. How to we can recalling and say thanks if we don’t know who mathematician is. We not only use the formula and theorems, but also we can prove it and know the forming of it. So, we can recalling mathematics and mathematicians which have meritorious.

My ability increasing with studying mathematic history. I learn how to make paper from mathematic history. Mathematic history have open my mind, that source of science not only from books but also can be from the other media. I’m really grateful that my chance to studying mathematic history. More over ridde that I don’t know. More question which not answered yet. And I can know all of it with continue to learn and curious.

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

07301244016

Pend.Mat NR C