## Selasa, 13 Januari 2009

### SERVICE PYTHAGORAS OF MATHEMATICS AND SERVICE OF MATHEMATICS FIGURE WHICH SEJAMAN BY PYTHAGORAS

A. Antecedent

Pythagoras born in island Samos, South Greek about 580 SM ( Pre-Christian). He are well-traveled to Babylon, Egypt and estimated have reached India. In Babylon, above all, Pythagoras braid the [relation/link] with the mathematician. After llama explore the isle, Pythagoras leave the its birth land;ground and move to Crotona, Italian. Estimated by Pythagoras have seen 7 world miracle ( ancient), where one of them temple Hera which is located in its birth town. Pythagoras leave the Samos in the year 518 SM. After a few times he/she open school in Croton accepting pupil without differentiating gender. Go to school that become very famous even Pythagoras finally menikah wrongly its one pupil. Picture detailed about Pythagoras do not too clear. Told afterwards, he go to Delos in the year 513 SM to take care of the benefactor at the same time its teacher, Pherekydes. Pythagoras remain to over there until he/she die in the year 475 SM. Sepeninggalnya, go to school the Croton walk the terseok-seok and many internal conflict, but can be continued to walk until 500 SM of before becoming political appliance.

B. Service Pythagoras

Pythagoras even also do not miss from " trap" myth of about number. He teach that: number one to the reason of, number two for the opinion of, number three for the potency of, number four for the justice of, number five for the marriage of, number seven for the secret of healthy always, figure of eight [is] marriage secret. Even number is anomalous number and woman / odd is man. " Bless the us, deity number," is citation from all follower Pythagoras giving special treatment to number empat,"yang create the deity and human being, pregnant holy O Tetraktys grow on and source of creation coming from outside human being.

Number worship of like within reason sorcerer with its crystal ball perhaps - later on day, constitutoing all mathematics after Pythagoras. Utterance Plato " God comprehend the geometry" or citation Galileo " Biggest Book about nature written with the mathematics symbol." [Whether/ what] that the including sorcery or mathematics. clear of mathematics more difficult to be comprehended the.

Mathematics with the near by music once. It is not a wonder if Pythagoras also can become a musicians. myth of Number Pythagoras consisted in to pass the " keajaiban" pentagram. Form the segi-lima which small more and more until takterhingga..

Theorem of following made algebraically, first time we obtain;get the algebra form from trilateral, bujursangkar and clear number segitiga.Secara that trilateral n number , Tn given from quantifying of deret aritmatika.Tn=1+2+3+….+n=n(n+1) / 2 n represent the number bujursangkar.Sn [is] n^2.Teorema is first time formed algebraically that is Sn=N^2=N(N+1)/2+(N-1)N/2=Tn+T_(N-1 , n of pentagon number, Pn also give from amount of deret aritmatika Pn=1+4+7+…..+(3N-2)

= n(3n-1) / 2 = n+ 3n(n-1) / 2

= n+3T_(n-1) this theorem represent the verification theorem.

Closely related with the theorem Pythagoras is determination of integer a,b,c deputizing foot/feet and hypotenuse at trilateral of siku-siku.Suatu tripel from this similar number recognized by tripel is Pythagoras from Plimpton 322 giving evidence assuring that ancient people babilonia know its way the similar tripel.Pengikut-pengikut Pythagoras viewed as inventor of formula M^2+?((M^2-1)/2)?^2=?*((M^2+1)/2)?^2 , by m anomalous number.similar formula to yield tripel Pythagoras( 2m)?^2+?(m^2-1)?^2 by m as even number / have been made for the purpose of same and looked into to come from plato

SERVICE of MATHEMATICS FIGURE WHICH SEJAMAN BY PYTHAGORAS

Thales

Pioneer of Mathematics and Greek philosophy is Thales. Born and die in small town of Miletus which is located in Small Asia west coast, a town becoming commerce center. Merchant ship easily sail to Nil in Egypt, while karavan the journey pass the land into the city Babylon. Pendudulk Militus like to [do/conduct] the contact trade with town in Greek and citizen Phoenisia. In this town also represent the meeting place world East And West, and its birth place is Thales. Initially, Thales is a merchant, profession making well-traveled it. In opportunity trade to Egypt and Babilonia at hence governance Nebukadnesar), during spare time, Thales study the astronomy and geometry. This matter [is] triggered [by] a interest [it] that by using ' appliance' the, they earn the memprediksi of sun eclipse every year nya

Theorema Thales

Thales tell the proposisi recognized by theorema is Thales, yaitu:Lingkaran divided by two by line passing its center is so-called by diameter.Besarnya is same trilateral base angle multiply is same of vertical besar.Sudut-sudut is which is formed of two crosscut parallel line by a straight line traverse, is same of besarnya. a couple of its side, a couple of angle;corner which lay by that side and a couple of located angle;corner before that side is of equal size nya, hence that trilateral told is same of sebangun.Segitiga with the pallet known and certain angle;corner applicable to measure the ship distance.

In geometry, he get the appreciation from its invention result as follows 1. A[N circle divided is same by each;every diameter 2. Angle;Corner - base angle from isosceles trilateral same 3. Angle;Corner leave for the back forming by two proportioned line is same 4. Two trilateral is congruent if they have two angle;corner and a same side 5. A angle;corner painted in semicircle a right angle

Euclid

Euclid can be conceived by a especial mathematics. He is recognized by because its ommission in the form of mathematics masterpiece decanted in book of The Elements very monumental. Fruit think infused a the book make the Euclid considered to be a mathematics teacher during the time and biggest matematikawaan of Greek.

Personal of Euclid described by one who kindhearted, downright, patient and always ready to assist and work along with the others. Many theorema-theorema formulated represent result of previous thinker masterpiece is including Thales, Hippokrates And Pythagoras

Many wrong information about Euclid. There is mentioning that he is child Naucrates which born. Tyre. Other Information tell that in delivering birth Megara.is true there is same name, Euclid and born in Megara, but that thing [is] happened by 100 year of before birth of Euclid and profession Euclid from Megara is philosopher. Euclid by xself born in Alexandria. Mistake of[is name of this plural happened by because during the period so called many people of Euclid

Masterwork Euclid

The Element can be told by masterpiece fenomenal in those days. Consist of by 13 structured book pursuant to theme and this topic of. Each;Every book of early by difinisi, postulate ( just for book I), preposisi, theorema of before covered with verification by using is mentioned difinisi postulate and. This book out year Greek 1482, translated to Latin and Arab, and also become the textbook of geometry and logic in the early year 1700-an. Outline fill the each book.

Book I : Elementary of geometry: trilateral theory, parallel and wide of

Book II : Geometry Algebra

Book III : Theory of about circle

Book IV : Way of making tortous picture and line

Book V : Theory of about abstraction proportion

Book VI : is same Form and proportion in geometry

Book VII : Elementary of number theory

Book VIII : Continuation Proportion in number theory

Book IX : Number Theory

Book X : Classification

Book XI : Geometry three dimension

Book XII : Measuring forms

Book XIII : Forms Tri-Matra ( three dimension)

Euclid trigger 5 postulate which later;then become the discussion fundamental. In order not to be happened wrong of interpretation, hence fifth postulate is also presented in English. This matter is intended, because appearance of geometry non-Euclidian, blazed the way by Gauss, early by assuming total wrong fifth postulate 1. Straight line can be drawn from ( sembarang) dot until ( other sembarang) dot 2. Tip of straight line can be continued to be continued by as straight line 3. Radian can be drawn from any dot center and with the radius differ 4. All right angle;corner beside the level is equal to other side 5. If straight line cuted in two by a straight line, angle;corner beside in [both/ second] line is same side than two parallel angle;corner, if continued to ( infinite titik), will be proportioned side where its angle;corner is compared to by smaller of angle;corner which is formed of by two line

Source Of :

WWW.MATE-MATI-KAKU.COM

Howard Eves, 1964.An Introduction to the history of mathematic

### MATHEMATICS HISTORY GEOGRAPHICALLY

1. Algebra

Babilonia

Algebra Retoris, have been solved [by] a square equation, rank equation three and bikuadrat

Ancient Egypt

HavePattern to of Additive of multiplication and division conducted with the multiplication operations two, avoiding calculation use the fraction

Ancient Greek

Not many expanding

India

Making abbreviation in the form of algebra, confessing number negative and irrational " Chinese " Writing all number - number with word

2. Number system

Babilonia

Number System with the bases 60

Ancient Egypt

System of Number hirogliph

Ancient Greek

Number Symbol come from letter from name acrophonic system learel of gift assess at alfabeth

Chinese

Number System local numeral and system of number have sign

3. Number of zero

Ancient Egypt

There no number of zero because all fold number of zero

Greek Kono

As empty penanda place

India

As empty penanda place

4. Geometry

Babilonia

Relate to the practical development and have pattern to algebra

Ancient Egypt

Relate to the measurement formula to count wide of land;ground

Ancient Greek

Exeed in geometry so that expand better

India

Inexpert in geometry, most pursuant to experience with the measurement

Chinese

Not many invention of only classic translation of yunani

### MATHEMATICS HISTORY of PURSUANT TO FIGURE

1. Euclid

¢ Straight line can be depicted from other titik(sembarang)titik sampai(sembarang)titik

¢ Tip of straight line can be continued to be continued by as straight line

¢ Radian can be depicted from any dot center with with the different radius

¢ All right angle;corner beside the level of equal to the other side

¢ If proportioned straight line become two straight line , angle;corner beside in line at is same side than two parallel angle;corner, if continued until ketitik do not till will be proportioned at side of where its angle;corner is compared by smaller angle;corner which is formed of two line

2. Thales

¢ divided by Radian two by two line passing its center is so-called with the diameter

¢ Level of isosceles trilateral base angle is the level of same

¢ Sudut-sudur Vertical which formed of two proportioned parallel line by a straight line traverse of equal size

¢ If its side couple, a couple of angle;corner which lay by that side of equal size nya hence that trilateral told is same wake up

3. Pythagoras

¢ Each;Every number is symbol / symbolising something that of related to metaphysics

¢ long Square is simplest form in geometry, but returning of consisted in by a irrational number

4. Archimedes

¢ Radian Form, elliptical, and hyperbola can be formed by only bagimana of[is way of we mark with lines the area

¢ Parabola is special form from taking sunshine from direction manapun and focussed at one particular dot and concentration of all energy light at narrow;tight area to be re-transmitted in binding very hot

¢ Counting wide of parabola, hyperbola, and determine the dot center the grafitasi at semicircle and one circle

5. Fibonacci

¢ Year 1202 publishing book of Liber Abaci by using what referred as with the algebra , by using numeral hindu Arabic

¢ Finding deret number called by like its own name that is deret Fibonacci that is 1, 1, 2, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987

¢ In book of Liber Abaci did explain the process aritmatik, including the way of searching number root

¢ Defining number of zero and count the atypical nature pattern and at the same time elementary member at recognition of algebra of kedunia west

### ACTIVITY REPORT AND RESULT OF ME [of] IN SEARCHING, COLLECTING, STUDYING, ANALYZING, DISCUSE IN MATHEMATICS HISTORY DURING THE TIME

A. Activity

Searching source or book of related to mathematics history entitling, mathematics Yunani after Euclid , Comprehending content of the book the, Result from that report is study about Mathematics yunani after Euclid.

B. Result of

Mathematics Yunani after Euclid

1. History Background

Town Iskandaria have many many especial, and which do not generate the coveting is the existence of very peace of lama.Selama of governance of dynasty ptolomeus, that goes on during hamper 300 year, the town free from in and also from outside.

glorious Konstantian is first emperor romawi embrace the Christian religion and he express that immeasurable of Christian is religion which resmi.Pada year 330, onstantin remove capital of from Roma to Byzantium, what is called by konstantinopel.Pada year 395, empire romawi divided to become two that is empire of east and west and yunani enter part of east.

Economic structure from that two empire in the first place didasrkan at agriculture by using similar slave belian.Keadaan energy generate the illiquidity of original erudite job/activity and idea which downhill productive gradually stand-out especially in west shares, because there slavery done by besar-besaran.Pasaran is slave start downhill, causing the destruction of downhill economics Romawi.Maka science until storey;level which evanescent biasa.Madzab iskandaria with destruction of ancient society 2.

2. Archimedes

One of the biggest mathematician as long as epoch and definitive in former epoch is Archimedes, aborigin Syracusa, Greek in island Sicilia.Ia borne at 287SM danmeninggal on the happening of robbery in town Syracusa by people yunani at 212 SM. He Astronomical putra expert and he represent the people looked into by eye of king Heron from Syracusa.Ada history saying that he stop by some times [in] mesir, likely enough [in] university Iskandaria, because among its friends is referred by Conon, Dositeus, and eratostenes.Dua of first person is substitution Euclides and which terkhir is a University Iibrarian .historian of Nation Romawi continue the story withdrawing from very famous Archimedes of adalh of[is description of sophisticated appliance [is] which is planned to do maintain the Syracusa to siege conducted by General of Romawi marcelus

Archimedes of many doing geometry by hence painting - painting which is making at ash or oil- oil [used up/finished] bath which is [in] usapkannya of its badannya.Menurut story is he die at the time of happened by the robbery of its Syracusa attention time [is] poured at one particular diagram drawn above basin of pasir.Ada story expressing that Archimedes mamarintahkan [of] [at] a soldier Romawi which rob [so that/ to be] backing from the diagram and that robber become to fulminate then jab the that old fellow body by using lance.

Masterpiece - masterpiece Arkhimedes represent the excellent masterpiece in mathematics growth and many menyerupi article in magazine modern.Karya - that masterpiece [is] done careful considerably and solid presentation and show the authenticity, cleverness menghitung.Kira-kira [of] there [is] sepuloh brochure which come up with the us and many bundles which hilang.Mungkin once smallest contribution in this masterpiece to mathematics [is] growth [of] early from some ways from integral calculation.

Three from Archimedes masterpiece study the that area datar.Karya-karya geometry [is] radian measurement, kuadratur [of] [at] parabola and first spiral.Pada masterpiece [of] Archimedes introduce the way of classical in second perhitungan.Dalam masterpiece indicating that wide [of] parabola segment [is] 4 / 3 from wide [of] trilateral in which [is] same memilika pallet and top dot which lay in [by] dot with the parallel tangent by alas.Karya [is] third load 28 theorem [regarding/ hit] the nature of bent line which [is] nowadays recognized by spiral [is] Archimedes and having polar equation [of] r = wide [of] k?.khususnya limited with that bent line and two radius have been found by which is on in essence look like what will be [done/conducted] these days with calculus.

A writer arab express that Archimedes [is] inventor from very famous formula that is Two among Archimedes masterpiece [of] about gometri three dimension [is] about ball and cylinder and also about concoid and spheroid.Pada bodywork written down [by] dalan du book loading 60 theorem [of] there are theorem giving wide [of] ball with one pallet and fill the ball with one alas.Dalam book two there are problem [of] about ball bisection become two shares with the content [of] according to the content tertentu.Soal bear a[n cubic equation [is] which its resolving [is] not given in brochure which have come up with the us, but met by euterus from a fragment of Archimedes.Terdapat solution [of] about conditions which diperukan [of] a[n cube [of] [so that/ to be] having real root and the positif.Tinjauan [do] not there are in Europe mathematics [of] during more than a thousand this tahun.Risalah [is] terminated with two theorem draw that is:

1. If and representing content and wide [of] from a ball which dibelah by a area non-diametral, v and s of is including the lion's share, hence

From all unsure-unsur of ball have pallet one having wide is same area, having biggest content ball cleft.

Archimedes write two short brochure [is] which interact to [regarding/ hit] the mathematics, but one among others have existing hilang.Karangan entitle the Sand Reckener shown [at] Eelon, prince heron and use the system mathematics to express the big number to find the highest boundary to amount of sand item to fill a ball with its center under the sun with the tired radius [of] sun.

There [is] two Archimedes composition which nowadays there [is] still that is hitting mathematics terapan, [is] about mathematics of area balance and about object float the 3. Eratostenes

Eratostenes come from Cyrena, coastal [of] middle sea south and only some years more young from its[his] young Archimedes.Masa [is] he live in the Athena and [at] age [of] about 40 year asked by Ptolomeus III from Egypt [of] [so that/ to be] coming to iskandaria to educate the putranya and to work as library head [in] university.

Eratostenes have a gift for in all science branch from zamannya.Menurut anticipation [of] some people, this is cause he [is] nicknamed the " beta".Ia [is] notable atlet, enchanter, astronomer, geodesy, most erudite and matematika.Hasilnya history [is] about earth measurement.

In mathematics of[is name of eratostenes referred [as] [by] referring to way of to find all prime number which besarya less than a[n composite number tertentu.Bilangan-bilangan in that sequence [is] filtered by scoring out, every third number after 3, all fifth number after 5, then all seventh number after 7, hereinafter eleventh number after 11 and so on 4. Prime number

Prime number represent the building base used to make all reached especial integer lainnya.Hasil [of] ancient time [is] verification Euclid, that prima amount [is] takterhingga and filter Eratostenes to find all prime number [of] below/under certain integer n.

Way of practical to test the primalitas [is] from big number not yet been known, and effort needed in testing certain special number [is] very besar.Selama 75 biggest number year [is] which have been proved [by] as prime number [is] number by 39 [is] number given by mathematician of prancis Antolo Lucas in the year 1876.Pada year 1952, machine EDSAC [in] Cambridge, inggris prove the primalitas from very big number ( 79 angka).180?(2^127-1)?^2+1 and since then other digital computer have proved the primalitas from number 2^n-1 remarkable [is] level of for the n of= 521,607,1279,2203,2281,3217,4253, and 4423.

A desire from number theorist is to find the function f(n) for the integer of positive [of] n will only yield the number - prime number and concevutive prime number that got by contain the different prime number in number which takberhingga.Dengan that way f(n)=n^2-n+41 yield the prime number to each;every n<41 [of] except f(41)=?(41)?^2 representing composite number.

Prime number have been specified by Lejeune Dirichlet ( 1805-1059) able to indicate that each;every deret aritmatika a, a+ad, a+3d …. By a and d [is] prime number [of] relative contain the prime number in number tek till.

According to perception Golbach, each;every even integer except 2 can be expressed [by] as amount from two number prima.Dengan that way 4=2+2, 6=3+3, 8=5+3,….,16=13+3,…. And so on

Conclusion

From result which have been elaborated [by] hence inferential that :

Mathematics have been studied [by] since llama even pre-christian in the year,

Pre-Christian in the year have borne the very bright mathematics,

Mathematics finding by pre-christian mathematics in the year in the reality [do] not fail with the mathematics finding [of] [at] to the present day study the science and technological rapidly grow,

Archimedes have found the formula to [count/calculate] wide [of] trilateral measured third [is] its side,

Arkhimedes succeed to write the book entitling Sand Reckener,

Archimedes write down about mathematics terapan [of] about area balance and about object float the

marked Matematikawan Yangbernam eratostenes in all kinds of ilnu knowledge

In the field of aritmatika , Aristoteles have found the sumua prime number

Source Of:

WWW.MATE-MATI-KAKU.COM

Howard Eves, 1964.An Introduction to the history of mathematic

## Sabtu, 13 Desember 2008

### sejarah matematika

Nama : Dwi Asri Lestari

Nim : 05301244059

Prodi : P.matematika NR‘05C

Ruang : 108 pindah ke ruang sidang lantai 2

Jam : 13.00-14.40

HISTORY OF MATHEMATIC

Especial discipline in mathematics relied by a calculation requirement in commerce, measurement of land;ground and memprediksi event in astronomy. Third this requirement in general relate to third the division of public of mathematics area of study about structure, room and change.Study about structure started with the number, very [common/ public] and first is number of natural and integer and operate for the arimetic, all that formulated in elementary algebra. Nature of more circumstantial integer studied in number theory Science about room of early from geometry, that is geometry of Euclid and trig from room three dimension ( what is applicable also to other dimension), latter later;then also generalizing to geometry Non-Euclid playing central role in [common/ public] theory of relativity

Important in area terapan mathematics is statistic, using probability theory as a means of and give that deskripsi, analyse and phenomenon estimate and used in entire/all science. Analyse the number

investigating theory which precisely utilize to solve kinds of problem of mathematics in at number of compute and take the by mistake totally into my report of 1 added by 1 is equal to 10.

Mathematics come from clan foundation consisted of remain to with the meaning sturdy building and walk with the meaning do not visible of the example that is estimologi and source of knowledge.

Mathematics woke up by on the basis of critical idea, mathematics is also looked into by sintetic is apriory with the meaning us not yet seen the the object but have thought.For example, is planet.It is a contradiction with the analytic mathematics opponent with its law is identity

There are expressing that mathematics as language.Many of expert mathematics, for example, expert of theory model in also deepen the philosophy at the opposite of mathematics concepts compromise that any mathematics concepts universally there are in mind of each;every human being.

Become studied in mathematics is various symbol and expression to communicate. For example Javanese verbally give the number symbol 3 by telling " Telu", while in Indonesian, the number is symbol [pass/through] the utterance " Three". This is cause, many expert group the mathematics in Ianguage group, or more generally in group ( alat) communications, non science.

In the eyes of formalis, mathematics is observation of abstraction structure defined axiomatically by using symbolic logic and mathematics notation; there are also other view, for example which discussed by a mathematics philosophy.

Specific structure investigated by mathematics frequently come from natural sciences, and very common in physics, but mathematics also define and investigate the internal structure in itself mathematics, for example, for the generalizing of theory to some sub-field, or appliance assist for the calculation of ordinary. Finally, many mathematics learn the area conducted by them for the cause of just just aesthetic, see hematics as artistic form than as practical science or terapan.

Used by Advanced mathematics of appliance to study various complex physical phenomenon, specially various nature phenomenon perceived, so that structure pattern, change, room and nature of phenomenon can be come near or expressed in a systematic formulation is form and full of various convention, symbol and notation. Result of formulation depicting prilaku or process the the physical phenomenon ordinary referred by a mathematics model from phenomenon

## Minggu, 30 November 2008

### sejarah matematika

Tugas Sejarah Matematika

Nama : Dwi Asri Lestari

NIM : 05301244059

P. Mat NR'05 C

Di ruang 108 pindah ke Ruang Sidang Lantai 2

Jam 13.00-14.40

For some students, sometimes, math is seen as a scary thing. If the students are asked about their favorite lesson, there will be only a few of them choose math as their favorite lesson. Besides, some will deliberately say that math is absolutely bored lesson. Contrast with the fact that only a few student like math and some also say math as a bored lesson, still only a few also can deny that math is not hard to be solved.

If math is seen as a lesson which is so scary, so it can be said also that all the components included in math such as arithmetic, algebra, geometry, trigonometry, calculus, and other application theory; are scary also. In fact, all of those components in math are having their own characteristics which different from each other. For example, arithmetic and algebra as a supporting subjects in math. The very simple way to learn arithmetic is counting. And so to Geometry with its interesting ideal things inside .On the other hand, trigonometry is used as the language for its count. While calculus and its application matter such as statistic, chance, a computer language program that it crosses to other part of field of studies that are not as horrified as math.

The way to increase the student’s attention to study math seriously can be done by asking about the student’s good and happy experiences. However, the creativity to learn math is needed and need to be developed even math itself is an exact study. The teacher can give a very attractive way of learning with new sty and performance that interest the students. Later, the students will find the main function of learning math through the lesson that they have learnt.

Knowing the math history is one of the ways to introduce math to the students. The math scientist can give indirect motivation fro the students to learn and to try on learning math. The very best of learning math history is the students will know descriptively about the biography of the math scientist. The understanding of math then shows to the students that math is not so far away from their ordinary world.

Learning the history of math can increase the student’s spirit to solve the problem of socializing in society. Of course, the students will be motivated to learn math. So, the students will not think that math is a hard lesson.