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Mathematics History

· History in its bearing with the idea history

Mathematics early from assumption basic or tread (on the foundation), if following to mean as follower foundation. Found of mathematic deflect to mean remain to and walk. Meaning remain to for example sturdy building which is early from geometry. Ahead early from gathering, but no have change. While found of mathematic, meaning to walk or do not see the missal etymology. Definition of Etymology it self is science that learning sources of how mathematic obtains: get its object. Mathematic develop; boiled by on the basic of critical way of thinking (so called mathematic critics).

Synthetic a priory as basic for the mathematics, it self mathematic have to have the character of critical. Synthetic a priory represents the contradiction which must be proved (example: Marsigit is a lecturer). While a priory its meaning not yet seen the object but have analyzed. Opponent from synthetic that is analytic which it’s meaning as according to hokum identity (follow the example of the: Marsigit is Marsigit).

Science obtained from contradiction rule. Science is built the above growth, and science of pursuant to common institution (considering being feeling). Such but here is a place of is nesting of mathematic fact. Intuition expands from time to time. Famous figure in this case is Drower. He does not take the definition, but meaning a place or framework of space and time. Its meaning is mind trussed with the space and time.. “if I am my institution, so I present in the space and time”.

Mathematics has some version such as system, structure, language, and body of roulade. According to Plato, mathematic is mind. But his opinion was opposed by Aristoteles, according to him mathematic above experience. And mathematic have the characteristic, that is absolute (its figure: idealist Plato, rationalist Rene Descartes and others), and also mathematic have the character of always correctness (its figure: Aristoteles, David and others).

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Papyrus

1. Papyrus Moscow

Mathematics of Papyrus Moscow have been noted since year 1850 BC, time of Abraham V.S Golenishchev obtain ; got it at 1893 and brought it to Moscow. This Papyrus is high fairish 8cm and wide 540cm and contained 25 problems and its solution. Most interesting problems in Mathematics of Moscow Papyrus was problem of concerning volume calculation from a limas. If the limas was limas with the pallet of square and its pallet side is connective a and a line of pallet with the pallet top is side b and if height is h, hence volume limas is h (a²+ab+b²)

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If b=0, we will express the formula of volume limas with the pallet of square that is a²xh

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2.Papyrus Rhind

A sheet papyrus highly 33cm and wide 565cm have been found in Egypt. This Sheet Papyrus have been bought by a market in Luxor at 1858 by Scotlandian 25 years old, Alexander of Henry Rhind. After its death at 30 years old, this found sheets was placed in Museum English in London at 1864. This Sheet Papyrus is often referred as Papyrus of Mathematics Rhind.

Mathematics of Papyrus Rhind copied from a so called writer of Ahmes Year 1650 BC. Mathematics of Rhind Papyrus exposed to promise the reader about this following sentence " By learning those good everything, all knowledge will be exist and knowledge from hidden secret will be expressed. Mostly the problem of Papyrus of Mathematics Rhind took form of the arithmetical puzzle. One of them is : Seven house contained seven cat, each ; each of cat killed seven mouse, each of mouse ate seven items of rice field, each ; each item of rice field produced seven bunch of grist. How many totalizing from all that?

Mathematic of Papyrus Rhind contained the problems connected with trigonometry. Besides, it showed knowledge of linier similarity solving one ordo, the arithmetical addition, and the perfect number. The other problem in the Papyrus Rihnd was about algebra and geometry.

Mathematics of Papyrus Rhind showed us about how the Egyptian divided, done the square root and solved the linear similarity using formula π x r² to calculate the area of circle. For example, it have been claimed by that half from circling pyramid pallet by dividing based the height or as proportion with 3,14. So, we assume that the Egyptian had known the value π until 2 numbers of behind the comma.

3. Papyrus Rollin

Nowadays Papyrus Rollin is looked after in Louvre, contained some detailed calculation about the prices bread and showed the using of big numbers during that period.

4. Papyrus Harris

A document arranged by Rameses IV, when he abdicated. This document elaborated the works from his father, Rameses III. Registration of the temple properties during that period exemplified the best something about practical bookkeeping had come until to us and the ancient Egypt.

Invention of Number Irrational

The integer numbers was the abstraction of arising out in calculating limited objects. To answer the demand of this measurement, not only required by the integer, but also the fraction. The rational number can be interpreted with the simple geometry that was marked by a contour line with the point 0 and 1 ( point 0 located on the left of point 1 ). Here the negative numbers shown at the point on the left of point 0, the integer number (for example: p) located on the right of point 1, while fraction ( for example : q ) can be expressed with the points dividing every set of difference from same shares of q. By this way, it arise the difference that there are the point at that line that did not deputize whatever the rational number. This invention was one of result from brotherhood Pythagoras. All follower Pythagoras indicated that there was no rational number expressing of point p in that line a parting from 0 or 0p equal to diagonal or square with the side of equal to 1 set of.

So, it necessary to create a new number to express that number. Here was the source of the irrational number. To prove that that diagonal length is not deputized by the irrational number, it is same to prove? 2 it is irrational number. Something we required in this case take an example √2 rational number, its meaning √ 2=a? b, where a and b as prima integer, so :

√ 2=a √b

a=b?2 or a²=2b²

Because a= multiple 2 of an integer number, so a² even so that even a also. Taking example a=2c so the similarity become: 4c²=2b²

2c²=b²

So that b² even and also b. But this not possible because a and b not possible are even because representing relative primus number.

So, the assumption that ? 2 having the character of that rational was wrong. We open the other; dissimilar verification having the character of geometric by indicating that side and diagonal square don't have set of same size. Now we take example on the contrary. According to this example, there will be similar segment AP in such a way so, that diagonal of AC and side AB from square ABCD represent the circular multiplication from AP, its meaning that AC and B have set of same size AP. At AC, measure the CB1=AB and draw the B1C1 vertical with CA. It’s easy to proved that C1B=C1B1=AB1, so AC1=AB – AB1 and AB1 will have less equal set with AP. But AC1 and AB1 are diagonal and the sizes of square that smaller than the original square side. Being repeating this way, finally we will find a square with the diagonal of ACN and side ABN which can be measured by AP, while ACN.

Euclid

A few information a Mathematics professor at University Iskandaria and become the founder from School of Mathematics Iskandaria.It possible that he got material of mathematic at Platonic school in Athena. Long years later, that time he compared Euclid with Appolonius, Pappus praised Euclid because he was kind gentle. He put a story in Eudemian Summari-Nya, story about Euclid answer to Ptolomeus question can be given by a practical solution ; ‘’there is no roadway in geometry". The same story narrated about Manaechmus when he worked as a teacher to Iskandaria. Other story narrated by Stobaeus, a student which learn the geometry below Euclid, asking what will get by learning the science. Euclid commanded a slave to give a currency to the student “because he had to get the advantage from what learned".

1. Euclid equipments

It’s important to comprehend the subject of any kind of we which can do with the ruler and expect. With our ruler, we can paint a straight line which unlimited length passing 2 different points, while with our meter we can paint a circle with a certain point as center and passing each every the certain second point.

Because postulate - postulate from masterpiece Euclid limited the using of ruler and expect pursuant to above order, so the used equipment become famous as a means of Euclid equipment.

2. Euclid element book

Euclid became famous because of his The Element book. In the reality marvelous masterpiece immediately and perfection can overcome all previous Element : in fact there was no secondhand which left behind from antecedent efforts.

Actually it was not found by copy Element from that real Euclid correctness have date from life spans its author. Modern printing; mould from Element relied on a renewal compiled by Theon from Iskandaria almost 700 years after original masterpiece write. Recently, start of century 19th found by an older copy was library Vatikan.

Complete first Latin Translation from Element was not made of a Greek but Arab Language. And in year 1120 a so called English master of Adolard Of Both, making Latin translation from Element among other things that the old man Arab translation. Other Latin translation made in Arab Language by Gherard from Cremona ( 1140-1187). Complete first English translation from Element translation Billingsley published in year 1570.

3. Fill of the Euclid element book

Book of Element Euclid besides studying Geometry explanation of theory of elementary algebra and number.

Book I

Learning postulates and axiom, there are 48 theorems. 26 first theorem study the nature of trilateral and theorem congruency. Theorem 27-32 placing theory base mark with lines similar and prove that trilateral sum from the aspect of its equal to right angle; right corner. While at theorem 47 studying theorem Pythagoras.

Book II

Studying elementary change algebra and Madzab Pythagoras. In this book is we meet the geometric equivalent from a number of algebra identity. Last two Theorem place the generalizing base from theorem Pythagoras, what now we know as the “law cosines".

Book III

Studying about circle, bow string, pertinent tangent measurement and from that connected corner.

Book IV

There are solution about Pythagoras, with the ruler and expect about triangle.

Book V

Explanation from Eudexus of about proportion. Theories which can be recognized at this size measure have solved the “logic scandal" created by invention Pythagoras of concerning number of irrational and definition two ratios. Size measure told to have the first same ratio to third and second to fourth if ever from the first and the third taken by random, the second and the fourth taken same also. So it will have the excess, same insuffiency or equality. Equally if A, B, C, D, representing sign element do not A and B of its inclusive of same type ( the two shares mark with lines the, angle ; corner, wide / volume) thereby ratio A:B = C:D.

Book VI

Settling proportion theory of area geometry expressing that trilateral to bisector from the aspect of cut the side which looks out on in proportionate shares two other sides. To show of verification difference of according to Pythagoras and Eudexus about a theorem which is concerning proportion explained by that triangle wide highly is same proportional with its pallet Book VII, VIII, IX

Loading entirely 102 theorem and study the elementary number theory. Book VII, starting by to divide the biggest federation from 2 integer or more which nowadays known as Algorithm Euclid and use it as tester two number primus relative.

Book VIII

Studying comparison partake and pertinent row of measure.

While at book IX explain about all integer of larger ones from n, can be expressed by as result multiply from primus ( number do not be divisible ) with and only one way of Book X.

Studying problems irrational, cutting - incommensurable line cutting with the certain other line cutting.

Book XI, XII, XIII

Studying about solid geometry. Start theorem ( XI ) representing base from way of later Exhaustion used in book XII , if a size measure lessened with the shares which is not less than as half as in the end will be left behind by a size measure which is smaller than all size measure of a kind determined. Definitions of theorem about line and area in space and theorems about all of Lelelipod there are in book XIII.

history mat

Solution

At the first knew that there was a subject of mathematic history in the schedule, in our mind actually that mathematic also has the history. Then the writer tried to look for about the historic mathematic, by browsing internet, borrowed the book from the senior students or discussed with the them selves.

1. Result of internet browsing

It was started from origin of word of itself mathematics. The word of mathematics come from word mayhems in Language of Greece interpreted as” science, science or learn" also mathematic interpreted as” love to learn ".

Especial discipline in mathematic based on this requirement of calculation. This requirement generally connected with the 3 division of mathematic area: study about structure, space, change.

Lesson about structure started with the number. Science about space started from geometry, that was geometry of Euclid and trigonometry, and then it also generalized to geometry was not Euclid. Understood and described the changing at amount that can be calculated is an ordinary in the sciences and calculus built as a mean for that purpose. The first draft is used to explain the changing of variable and function.

2. Discussed

Activity which the writer done in searching various reference sources which related to mathematic history that discussed with the others. In this case, the writer discussed with the senior students. There were many things which writer found after discussed about mathematic history.

In mathematic history, many figures of the world participated in mathematics science. Besides the mathematic figures, we also had to know anything in it. For example: in geometry Euclid, a circle was gathering of all the points at the area in certain distance called fingers, from a certain point called center.

The other mathematics also gave the great idea that was Pythagoras. The theorem of right angle that square of trilateral in right angle was the square amount of two other sides, or called triple Pythagoras.

3. Result of class activities

From various way or activities which writer done to get the material about mathematic history, one of them was by following lecturing of mathematic history class taught by Mr. Marsigit.

During thrice meeting, he has given some materials. At the first meeting, he explained about the kinds of history, there was history of opinion and history of artifact. At second meeting, writer got the task to make the short paper about mathematic history, by the chosening topics which have been determined. Its aimed all the participants (included of writer) becoming more recognized of mathematic history deeply and also knew about the masterpieces work which have been found by all mathematics. And at third meeting, the material was explained using Britannica Encyclopedia containing a lot of material about science world especially itself mathematic. He also showed the example of profiles from famous mathematics such as Leibniz and Pythagoras.

geographically

Geographically

1. Mesopotamia

Ø Invented numerical system, heavy system and measuring system

Ø Recognized about mathematical such as zero draft and the division of circle into 360⁰

Ø Firstly, the numerical system symbolized by the palm leaf rib carving at the clay. The number of 1 – 10 symbolized by horizontal palm leaf rib and tens and the multiplication symbolized by vertical palm leaf rib

Ø At 2500BC decimal system wasn’t used anymore and palm leaf rib was substituted by the notation formed wedge

2. Babylonia

v Used the decimal system and π = 3,16

v The Babylonian people was the inventor of calculator

v Recognized Geometry as the basic of astronomic calculation

v The Babylonian people used approach for root of quadrate and number of zero and number of zero quadrate such as 17⁄12 for √2

v The geometry is algebraic

v The Babylonian arithmetic had grown well became the theorist algebraic, it had been solved the similarity of quadrate by the equivalence and the substitution

v The Babylonian known the geometrical that the triangle drawed an a half of circle has right angle

3. India

o Brahmagypta introduced the negative number, zero, and the similarity of quadrate solving

o Brahmagypta discovered the relation around circle

o Aryabrata discovered “stanam – stanam gunard”, means that the basic of modern decimal rotation

o Brahmagypta discovered the negative number

o Subasutra was the inventor of the first formula a²+b²=c²

o The geometry is almost based on the experience and generally deal with the measurement

4. Ancient Greece

Pythagoras proved the Pythagoras formula

The next person continued the first draft 0 was Al – Khwarizmi

Archimedes discovered the name of parabola means that cone right angle part

Apollonius was the initiator{used that} of the fast calculation

Diophantus was the inventor of arithmetic ( analysis discussion about theories and number contained the developing of algebra by making a similarity)

Archimedes discussed geometry of flat field

Archimedes the inventor of formula L=√S(S-a)(S-b)(S-c)

The beginning of ball trigonometry

Recognized the first rate number

Hipassus was the inventor of the irrational number

5. Ancient Egypt

· Recognized the numerical system and symbol at 2100BC

· The carefulness researching at 2700BC

· Recognized the triple of Pythagoras ( right angle )

· The Egypt numerical system was addictive design from arithmetic

· Used several symbol in the Egypt algebraic

· Recognized the theorem of Pythagoras

· Used the number in the Papyrus Moscow

· Recognized 2 of the numerical system, hieroglyph and digital

· It had reached the carefulness researching at 2700BC

6. China

ü Recognized the characteristic of the right triangle

ü The beginning of 11BC century, develop the negative number, the decimal number, the decimal system, the binger system, algebra, trigonometry and calculus

ü It had discovered the method to solved several kinds of similarity, those were the similarity of quadrate, cubic, and quatic

ü The algebra used the horner system to solved the degree of similarity

Figure

1. Thales (624 – 550 BC)

v The inventor of the standard comparison of the triangle characteristic 3 : 4 : 5

v The applied scientism had been discovered by Thales

v The inventor of the theorem or proportion

2. Pythagoras (582 - 496 BC)

· The first initiator that axiom postulates have to be explained firstly in the developing of geometry

· He was successful prove the theorem of Pythagoras for the first time and being the best

3. Eodoxus (408 – 355 BC)

Ø Developed the theory of proportion

Ø He had made the definition about view forecast an irrational number by crossed multiplication

4. Euclid’s (330 – 275 BC)

§ Added the new theorems : curves, circles, and another form were learned likes the straight line and flat field

§ Learned the first rate number and the other was not

§ Never successful determining the first rate number, but he was successful gave the answer about it. It was unbounded

5. Archimedes (287 – 212 BC)

His interest on original mathematic : numeric, geometry, calculated the wide of geometrical forms

Was successful applied the mathematic

He had tried to calculated the wide of parabola, ellipse, hyperbola, and determined the gravity centre on a half circle or circle

6. Diophantus (200 – 250)

o Wrote the arithmetic contained the developing of algebra by making several similarity

7. Al Khwarizmi (780 – 850)

ü The great successful in algebra and astronomy

ü The algebra started by the definition of numeric principles and gave the solution

ü Six chapters he wrote divided in to six types of similarity include 3

8. Fibonacci (1170 – 1250)

§ Recognized the number of zero and calculated the unusual nature patterns, and gave the basic of introducing algebra to the western

§ Discovered the numerical row name Fibonacci : 1, 1, 2, 3, 5, 8, 13, 34, 55, 89, 144, 233, 377, 610, 987

9. John Napier (1550 – 1617)

v Discovered the logical basic draft

10.Rene Descartes (1596 – 1650)

o Connected Algebra and Geometry. The similarity of Algebra can be expressed into geometry formed, the form : ellipse, hyperbola, parabola

11.Isaac Newton (1642 – 1727)

Ø Idea of calculus started from Newton, because he saved most of his idea, so Leibniz came with the more brilliant idea and the familiar notation

12.Jean Baptize Joseph Fourier (1768 – 1830)

Learned about trigonometry and theory of function variable real