HISTORY MATHEMATICS ABOUT CONCEPT, PROBLEM,AND SOLUTION MATHEMATICS IN THE PAST WHICH STILL USING/NOT

By: Winda Oktavia PMNR’08

Last week ago, my lecture, Mr. Marsigit give task to search about concept, problematic or mathematics solutions in old period which still use or not in this period. In there I will explain what I get when I doing the task.

As we know, concept and problematic in mathematics was happen very long time. Many concepts were found in old period, even though before century. History of mathematics was start when people must note number of count which bigger than one. From this problem and many others problem born mathematicians who try to solve this problem with their concept. And before century mathematics was develop very good and many concept mathematics was born. Many concept still using now, but together with the time walking, many other concept and problematic in old period not using again, and there is many other concept or problematic and mathematics solutions which founding modern period and never found in old period.

1. Concept and mathematics solutions from the past and still us now, are :

a. Thales Theorem
Thales bring proposition which known with Thales Theorem, there are:
• Circle divide by two lines which pass to the centre of the circle call diameter.
• The measure of angle in equilateral triangle’s base is congruent.
No note again about Thales credit in memorizing, but concept of diameter in Thales Theorem Still use now.

b. Pythagoras Formula
Pythagoras theorem only used in right angled triangle. Pythagoras explains that: c2 = a2 + b2. If there is three numbers a, b, and c which complete with c2 = a2 + b2 concept, so those three numbers called Triple Pythagoras.
And this formula still use now, we usually use it when we solving problem in right angled triangle.

c. Zero Number Concept
The first time zero numbers concept found are in the old period, exactly in India. People who found zero number is Aryabhata. He was entered zero in calculation system and just not the empty place. Then zero number still using in this period, we still use this concept in integers.

d. Irrational Numbers
In the Pythagoras period appear a problem which can’t finished by rational number. If a flat line with point 0 and 1, point 0 lie in the left 1 and the negative lie in the right 1. Then q fraction can show with point which divided each unity in the same part of q. The problem is there are points at the line which can’t represent by rational number. So, they must create a new number to show this number, from this problem the irrational number was born. For a several time square root of 2 is the only one of irrational number. Now in every matter in mathematics we still found irrational numbers.
e. L’Hospital Rule
This is a mathematics solution that is the rule of descent to solve limit function which usually we know as “L’hospital Rule” finding and prove by De L’Hospital. That concept still using now.

2. Concept and problematic in mathematics in the past and not use again now, are :

a. Phi (π) in Old Egypt Period
By what I was learning, there is solving problem in Old Egypt Period that didn’t use now. This is about solving to find circle area. Papyrus Rind said that π = 3, 16. But now we use π = 3, 14 to find the circle area.

b. Zeno Paradox
Zeno is the mathematician who said about unlimited number. In fact, Zeno was claim one contradiction in mathematics minded which must waiting for two thousand years to finish. Zeno said six paradoxes. This is problematic that Greek filose can’t solve with their logic, but no one can find the wrong in Zeno Paradoxes. From his six paradoxes, the most popular is run competition between Achilles and turtle.

3. Whom I found in mathematic concept mathematic problem or finished mathematic in this can with mathematic in old period.

That in these kinds about task mathematic no talks with mathematic with used closed problems, open - ended problem, and open problems. So in this period, modern period, many problematic in mathematics which didn’t found in old period. For example, in the start or twenty century, in 1930, when Kurt Godel published his popular theorem, which provocation of crisis, even though asking the background method of mathematics and classic mathematics. And there is many other problematic in mathematics which turn up in this modern period.

Reference :
http://www.marxist.com/reason-in-revollt-bab-16-matematika.htm
 http://id.wikipedia.org
Para mahasiswa. 2008. Sejaran Matematika Berdasarkan Tokoh dan Karyanya. Yogyakarta: UNY
http://mathematicse.wordpress.com/2007/12/25/open-ended-problems-dalam-matematika/

SPEECH BY MR MARSIGIT

Mathematic Based On Idea
Mathematic as an exact science has a foundation, this is called Foundation of Mathematic. There are two types, the first is permanent foundation and the other is moved or walks foundation.
1. Permanent Foundation
For example, in English the foundation of mathematic is geometry.
2. Moved Foundation
It’s not visible, but it is a foundation of mathematic. In this part, the foundation called epistemology. Epistemology is theory about knowledge which includes reality and veil of knowledge, imagination, foundations and responsibility above the knowledge we have. Are we having knowledge about our destiny in a real mean? This question becomes a beginning of the declaration which comes from Aristotle and Francis Bacon. Immanuel Kant is the mathematician who claims that foundation of mathematic is epistemology. Its build based on the deeply think, in here mathematic called as “synthetic apriority”. In fact this declaration takes from Law of Contrariety. In here the meaning of contrariety is in idea not in our heart so this can produce science.
They are many versions about mathematic:
1. System
2. Structure
3. Language
4. Body of knowledge
The are the other sciences which have connection with mathematic:
• Philosophy of mathematic
• Sociology and anthropological
• Universal history
They are 2 method of history, based on:
1. Idea, how far we can explain that idea.
2. Artifact

The raises of idea in history of mathematics Pythagoras Theorem. The important think of Pythagoras Theorem beside triple Pythagoras is the idea about irrational numbers.
Immanuel Kant is mathematician who has an idea that the foundation of mathematics is dynamic. But, there are we have Brower, he said that mathematics didn’t have foundation, this is intuition mathematics. Brower said and develops anti-foundation mathematics. But some other mathematicians try to develop mathematics with strong foundation or formal foundation. The example is Hilbert, he said that foundation of mathematic is logic. Gödel, Hilbert pupil’s, prove that what his teacher say, is wrong and fail.
Now, mathematics in modern life is multi faset, its mean mathematics not only have one foundation.
The truth of science from its history, divide become two parts :
1. Inside of our mind
Mathematician who claim that mathematics inside of our mind his mind. But there is different with mathematics which inside of mind but still moving. The way to get mathematics according Plato is out from Plato Cave.
2. Outside of our mind
Mathematician who claim that mathematics out side of our said that mathematics outside of our head or in the up of experience. And he also said that mathematics is human produce. Aristotle has pupil, his name David Hume. David Hume is mathematician who doubt about Cause and Consequent law. Contradiction between Plato and Aristotle still continue during 2 century. Finally, this problem finished by Immanuel Kant. His opinion, both of them is true and both of them are also wrong. He said mathematics have a “Synthetics Apiary” characteristic.
Mathematics develop with critical mathematics, there is:
1. Synthetics Apiary
2. Analytics Mathematics
3. Contradictions
4. Intuition
Science building by development that is Mathematics.

DHIOPHANTUS, THE FATHER OF ALGEBRA

Diophantus of Alexandria, who lived in the fourth century A.D., is generally credited with being the originator of algebra. He was the first to use letters to represent numbers and symbols to represent operations. Although some of his writings have survived, the lay unheeded for twelve hundred years and were not fully appreciated until Fermat worked on some of his problems in the seventeenth century.

Since good notation in a mathematical problem is a valuable tool, the improvements in notation which Diophantus made were of great significance. He not only introduced letters as generalized symbols for numbers, but he also made beginning in expressing powers of a number with exponents.

When you come to work with quadratic equations you will discover the phrase “square half the coefficient of x”. This phrase comes from Diophantus, who made a thorough study af such equations. He also worked with some third ad fourth degree equations. Since negative numbers were unknown at that time, he was limited to solutions involving positive integers and fractions. He spoke of the impossibility of solving 4=4x+20; he even called it an absurd equation.

Diophantus was so thorough in his treatment of indeterminate equations that even today they are known as Diophantus equations. An indeterminate equation involves the solution in integers of common fractions of a single equation in two or more variables.

Diophantus also posed the problem of breaking up a square into the sum or two others squares, again limiting the solutions to whole numbers or common fractions. A simple illustration of a problem involving Diophantine equations is the following puzzle: Admission prices for an entertainment were men, $1.00; women, $.50; children, $.25. 100 persons attend and the receipts were $50.00. how many men, women, and children were in the audience? A complete theory for the solution of Diophantive equations was completed about 100 years ago by H. J. S. Smith.