The mathematics concepts, mathematics problems, and mathematics solutions

1. I found the mathematics concepts, mathematics problems or mathematics solutions in old period that nowadays still used, that are

a) Mathematics concepts
--zero number concept, which zero number concept found in old period. It was found for the first time in India, applied by Aryabhata. He was entered zero number in amount system, not only empty space. Then we still use zero number nowadays.
--negative number concept, the first introduced by Bragmaghypta, mathematician from India.
--irrational numbers. Pythagoreans found it. Although the root of two couldn’t realized even with fraction, but it’s used to found the side long of triangle.
--Pythagoras theorem. We still use it nowadays to find usually the aslant side of triangle, or the one side of triangle.
--calculus. It was developed almost together by Newton and Leibniz.

b) Mathematics solution
mathematics solution with descendent used rule to solve the limit functions that is L’hospital.

2. I found the mathematics concepts, mathematics problems or mathematics solution in old period which not used nowadays, that are

a) Mathematics concept
--Galileo show that each integer have only one perfect quadrate, and each perfect quadrate is quadrate of only one positive integer.

b) Mathematics solution
--in old period of Egypt, they were solve the broad or circumference of circle with π = 3,16. But nowadays we use π = 3,14.

3. I found the mathematics concepts, mathematics problems or mathematics solutions, which is no relation with mathematics in old period.

We find many mathematics problems nowadays, that is about solving mathematics problems used open-ended problems and open problems. We don’t know certainly the procedure to solve this problem. We may find many solutions for this problem.

Reference:
http://mathematicse.wordpress.com/2007/12/25/open-ended-problems-dalam-matematika/
http://www.marxist.com/reason-in-revollt-bab-16-matematika.htm

The results of study history of mathematics

Every people doing activities always have the purposes and results that they want to reached. It is like we read a book, our purpose is to expand our knowledge.
I’m study the history of mathematics, I search and collect information from some sources. The one is I got from the internet. Study result which I got are
CALCULUS
Do you feel that calculus is difficult? Yes, I do.
We look the development of calculus. The calculus development can mentioned by 3 periods, that are ancient period, middle period, and modern period.
1. Ancient period
Some ideas about calculus integral was appear, but didn’t developed well and systematic. Archimedes develop idea about account volume (prominent function of calculus integral) farther and create ‘heuristic’ closed to calculus integral.
2. Middle period

The mathematician of India, Aryabhata, used unlimited small concept in 499 and expressioned astronomy problem in basic diferensial similarity. In this period, calculus develop more progressive than the ancient period.
3. Modern period
Independent discovery happened in beginning 17th century in Japan by mathematician like Seki Kowa. In Europe, mathematicians like John Wallis and Isaac Barrow give new innovation in calculus. In 1668 also James Gregory proved a specific problem from basic theorem of calculus. Leibniz and Newton are the contributor of calculus.
Since that time, many mathematicians that gave contributions to development of calculus. Calculus became the general topic in Senior High School and University nowadays. And mathematicians in the world give contribution to development of calculus continually.

The foundation of mathematics

The foundation of mathematics have two characteristics, that are constant and temporary.
1.The constant foundation, example: Geometry.
2.The temporary foundation, example: Epistimology foundation. Science that study the sources of knowledge.
Mathematics developed with contradiction and intuition.
It is about critical thinking. Synthetic a priory : we can think it although we never see it.
Mathematics is intuition. The figure is Brower. He is not taking any reason. Intuition is a place or framework: space and time. It means that our mind about mathematics stay in space and time.

The versions of mathematics are
1)Mathematics as system
2)Mathematics as structure
3)Mathematics as language
4)Mathematics as body of knowledge

Mathematics figure:
1.Plato, an idealist one. He said that mathematics is on our brain. Mathematics is given by God. Plato and Aristoteles were in contrary.
2.Aristoteles. He said that mathematics is in our experiences.
3.Descartes
-Universal method. Elementary problem of knowledge philosophy is why we earn to make by mistakes.
-Inductive method. This method come from result of perception and research until universal method.
-Deductive method.This method is compare between theory and purpose.

Reference:
Mr. Marsigit’s speech
www.wikipedia.com

JOHN WALLIS

John Brehaut Wallis was born in Ashford, Kent, November 22nd 1616, the third children or Reverend John Wallis and Joanna Chapman.
He began like mathematics when he 15 years old.
In 1655 Wallis published one of his book. In this book he wrote the curve and drawn as curve from the second degree.

The most important of his work is his Arithmetica Infinitorum, which was published in 1656. In there have any analysis methods from Descartes and Cavalieri that is systematic and very extensive, the reasonable instructions. This case that made this book as standard material and use continued by the next writers.
From this innovation he leave many applications algebra similarity, next continued to find the others method that didn’t separated.

Some years later, in 1659, Wallis published one level filled by the solution of problem that was suggestioned by Pascal. He said how the principals placed in his Arithmetica Infinitorum can used to correction of algebra curve; and give one problem solution to correction the parabol, that was founded by his student William Neil.

In 1685 Wallis published Algebra, previoused by subscribe histories from development the main material, filled by many value informations.
The second edition, published in 1693 and shape the second volume from his opera, with larger. This algebra is important like the systematic use of formulas.
A mulberry that given here representatived by kwantitative comparison which bring to unit about the same kind of mulberry.

Wallis’s life was to create many works, and up to he was died in October 28th 1703.

Reference:
http://en.wikipedia.org/wiki/John_Wallis
http://www.maths.tcd.ie/pub/HistMath/People/Wallis/RouseBall/RB_Wallis.html

According to geographic

1. Mesopotamia
-found the first number for the first time
-found the heavy system and measure system
-they had knew aspect of mathematic like zero concept and division the circle into 360 degrees

2. Babilonia
-use the system of decimal and phi=3,125
-founder the calculate for the first time
-knew geometry as the basic of astronomy calculation
-use approximation for quadrate root
-their geometry have an algebra character
-their arithmetica develop well became rhetorical algebra, can solve quadratic similarity

3. Egypt
-had knew formulas to calculate the wide and volume
-knew the system of number and symbol
-knew triple Pythagoras (right angle)
-knew the theorem of Pythagoras

4. Greek
-Pythagoras proved the theorem of Pythagoras through mathematical (the best)
-Diophantus founded arithmetica
-Diophantus just knew rational and positive answers; he has estimation for zero and escape from negative coefficient
-was born the sphere trigonometry

5. India
-Aryabhata founded the relation of circle circumference
-strike theory "stanam stanam gunam" : the basic of modern decimal theory
-Bramaghypta found the negative number
-zero number used as marker of the empty space

6. China
-knew the character of triangle
-the power of old mathematic located in algebra
-used the negative number long time before other culture

Pythagoras

I want to tell about Pythagoras and his contributions.

Pythagoras is a mathematician and philosopher of Yunani who the most famous with his theorem.

Known as “Father of Number”, he gave the important contribution into mathematic and philosophy in the last 6^th century BC.

His life and his teaching were not clearly because many false stories about himself.

Pythagoras was born about 572 BC in Samos Island, but then leave his hometown and go to Crotona in South Italia. In there, he established a school or Pythagoras teaching, which is an academy to study the philosophy of mathematic and science. According to a note, Pythagoras might died because had been killed in old age between 75 up to 80.

Pythagoras group considered that every mathematic finding as together fortune, although must to keep it secretly from foreign person.

The teaching of Pythagoras have an oral character, and because this group usually for return all finding to the establisher (Pythagoras), so it is difficult to know which is mathemathic finding by Pythagoras own or others in this group.

-Pythagoras arithmetica

Once upon a time, Iamblicus, the Neoplatonis philosopher that influence about 320 BC, appointed Pythagoras as founder of friendly numbers or amicable numbers.

-Theorem of Pythagoras

One of Pythagoras contribution that well-known is Pythagoras theorem, said that hipotenusa quadratic from right triangle is same with the sum quadrate of foots.

Although the fact in this theorem was knew before Pythagoras born, like people of Babilonia at Hamurabi period was knew 1000 years ago, but this theorem given to Pythagoras. This case because he is the best and the first that could prove this theorem mathematically.

The figures of mathematics

• Thales. He is the first figure that found the theorem. He was also found applied knowledge.
  
• Pythagoras. He is the first figure who said that axiom of postulates need to analysed before, if we want to expand the geometry. He was successfull prove the theorem Pythagoras the first and the best.
  
• Eodoxus. He had made the definition about approximate length of irrational number with cross multiplying method.
  
• Archimedes. He could applicate the mathematics. He is interest in pure mathematics : number, geometry, count the wide of geometry shapes.
  
• Diophantus. He had wrote "Arithmetica", it contains of expanding the algebra that he did with make some similarity.
  
• Al Khawarizmi. The great work are at algebra and astronomy. The algebra had been started from definition the principle of number and gave the solutions. Six chapters which he was wrote consist of six kinds similarity included three kinds operation : root, quadrate, and number.
  
• Fibonacci. Expanded the zero number and count the patterns of nature which was unusual, even gave the basic of introducing algebra to Western Countries. He found the row of number that called like his own name : Fibonacci row = 1,1,2,3,5,8,13,21,34,55,89,144,233,377, ...
  
• John Napier. He found the basic concept of logarithm.
  
• Rene Descartes. He was connected algebra ang geometry.
  
• Isaac Newton. The idea of calculus is from him.
  
• Jean Baptiste Joseph Fourier. He studied about trigonometry and theory function of real variable.