foundation's of mathematic

mathematic of foundation's


learn history of matemaika can start with we study definition of mathematics science, and continued to mathematics of foundation, and if us study [him/it] by like this, hence way of us learn to have the character of pragmaticly.
learn pramagtis [is] learning by crosscut us a[n science link as base early to study a[n science as a whole.
and when us have the character of pragmaticly, that is taking one of [the] link of science as base think, hence us also have the character of as clan of foundations.
and let us analyze one by one about mathematic of foundations, and under colour of us of berfikirt [is] opinion [all] philosophy [in] mathematics area.
and following [is] opinion [all] mathematics philosophy about definition of mathematics ;
According to method of aksiomatik, where the nature of is certain ( unidentified on the contrary) structure taken and later;then logically effect [of] that acre of then logically degraded, Bertrand Russell say:
Mathematics can be defined as subyek of[is which we have never tau whereof which we [is] discuss, and also what we [do] not tell correctness.
Possible this explain why John Neumann von say a[n times;rill:
In Your mathematics [of] takkan comprehend matter. You really taking [him/ it] first.
About respecting of mathematics, Bertrand Russell say in Study Mathematics of:
Mathematics, have as proper as looked into, do not only owning truth, but the beauty [of] is highest - chilled and good careful, like that basrelief, without drawing each;every part of nature of weakening us, without beautiful decoration [of] music or painting, still purification [is] at all, and ability of hard perfection like only biggest art can demonstrate. Easiness [soul/ head] truthfully, supremacy, body meaning more than human being, representing highest excellence testcase, to be found in mathematics like of course poem.
Elaborating symmetry [among/between] creation aspect and mathematics logic, W.S. Anglin perceive, in Mathematics History and:
Mathematics is not movement go down to beware of free roadway, but journey in foreign wilderness, cruiser where often loss. Hardness will become sign for historian of[is which map have been made, and real explorer have gone to other place

Hilbert, D 1972, concerned that in fact, mathematics is replete with examples that refute Brouwer's assertions existence statement; the examples cited are , however, only arbitrarily selected special cases, as the significance of the consistency proof as a general method of obtaining finitary proofs from proofs of general theorems that is say of the character of Fermat's theorem that are carried out by means of the e function.

hlbert toke a proof for fermat's great theorem, a proof in which the logical function e was used and make a finitary proof out of it as first to let assume that numerals p,a,b,c (P>2) satisfying Fermat's equation a+b = c are given; then indicated this equation as a provable formula by giving the form of a proof to the procedure that the numeral a+b and c coincide; on the other hand, according to his asssumption he has a proof of the formula
from which


hilbert, d.1972 claimed that the value of pure existence proofs consist precisely in that the individual construction is eliminated by them and that many different constructions are subsumed under one fundamental idea, so that only what is essential to the proof stands out clearly; brevity and economy of thought are the raison d'etre of existence proofs; he then notified that pure existence theorems have been the most important landmarks in the historical development of our science. But such considerations do not trouble the devout intuitionist. According to Hilbert, the formula game that Brouwer so deprecates has, beside its mathematical value, an important general philosophical significance; for this formula game is carried out according to certain definite rules, in which the technique of our thinking is expressed and these rules form a closed system that can be discovered and definitively stated. Hilbert insisted that the fundamental idea of his proof theory is none other than to describe the activity of our understanding, to make a protocol of the rules according to which our thinking
and from some definition example [of] , menunjukan that science of matemaetika have wide [of] congeniality, and also aspect which there are in mathematics science even also very immeasurable. Like logic, calculus, geometri,aljabar and others. With keberagaman of aspect exist in in the mathematics many from [all] philosophy taking one of [the] aspect of mathematics as basis for develop mathematics science. And usually base which [in] taking to develop its enthusiasm [is] pursuant to their enthusiasm to mathematics aspect. And their enthusiasm to mathematics aspect can be seen from way of mathematics mendefiisikan meeka.
Like phytagoras defining mathematics science based on number science hence its base him [him/ it] surely [pass/through] number science and system which there are in mathematics also number science. Medium kant imanuel as modern mathematics, and he always have the character of skeptik and he study mathematics of its own criticisms so that he/she express mathematics base of dalah itself mathematics epistemologis
And to [all] man of science / its philosophy [of] him even also surely take base of berfikir their [is] aspect in mathematics which they enthuse.

Kenneth Appel and of Wolfgang Haken

Kenneth Appel and of Wolfgang Haken- Four Problem of Colour [is] famous and unsolved during through years.

Kenneth Appel
Appel, borne [by] Brooklyn, Metropolis of New York, he [is] educated [by] [in] University of Michigan, he finish title of Phd its [in] university of Michigan in the year 1959. After working for two year [in] Institute Analyse Defence of Princeton, he joint forces with faculty of pancaindera [in] University of Illinois, Urbana, where he act as mathematics professor from 1991 until 1993. He later;then take hold of as departmental chief [of] mathematics [in] University of Hampshire new.
In the year 1976,ia working along with Wolfgang Haken ( 1928--Sp;-Sp;), Appel announce one of [the] solution of mathematics which [is] its long standing problems and not yet four-color theorema terbongkar,yaitu. In the year 1852 Francis Guthrie have also noted that map of manapun, [so that/ to be] anampak [is] by colouring map, assuming nations with frontier of public have been coloured differently, without there [is] more than four colour. Guthrie enough intrigue to developing [him/ it] craftily matematik and ask a[n the anticipation evidence by finding the problem of which do not difficult diduga-duga in the reality, as does succeed to replace generation [all] expert of matematik.
Appel And of Hagen use a[n variation [of] a[n first method [of] times;rill tried by Arthur Kempe in the year 1879. and That depend on the fact that map have to contain certain unavoidable configuration- Appel And of Hagen recognize 1482 colour . and Them later;then use a[n computer to indicate that all this can reduce to configuration 4 colour . They start work [in] year 1972 until 1976, and that them enough with its analysis and also program of mereka.dan that take more than 1200 computer time [hour/clock] to prove the theorem.
Kenneth Appel borne in the year 1932. he [is] expert of matematik which is, [in] soybean cake 1976 with friend work Wolfgang Haken [in] University of Illinois [at] Urbana-Champaign, solving one of the most famous problems [in] theorem four-color dalam)matematika,yaitu. They prove that any two-dimensional map, with certain demarcation, can plow under with four colour without is adjacent " nations" sharing [is] same colour . Children of Appel'S, including Laurel of Appel, Petrus Appel, and Andrew Appel, now a[n professor [at] Princeton, assisted [by] [is] inspection to the 1000 case topological constitutoing this evidence.
Voucher have come to one of the most fond of to debate for modern mathematics because of depended heavy [at] computer " number-crunching" to sort;jenis [pass/through] possibilities. Even Appel have agreed, in many interview, that it lacking of accuration and [do] not present any [of] new insight which have guided mathematical research into future.

Wolfgang Haken
Other Orang)Yang, have showed [him/it] to work as start a[n sea-change in expert attitude of matematik base on computer, they have underestimated as a means of for engineer rather than for teoritius leading to creation from what [is] sometime conceived of " experimental mathematics."
In the year 1976 together with friend of k Kenneth Appel erja [in] University of Illinois [at] Urbana-Champaign, Haken solve one of the most famous problems in mathematics, theorem four-color. They prove that any two-dimensional map, with certain demarcation, can plow under with four colour without is adjacent " nations" sharing [is] same colour.
Haken have introduced some important idea, including manifold Haken, Limited Kneser-Haken, and a[n extension of work of Kneser into a[n theory about normal surface. Many its work have a[n aspect / director of algorithmic, and he [is] one of [the] figure having an effect on in topology of algorithmic. One of the contribution the key [at] this area [is] a[n algorithm to detect if a[n gin / node [is] [do] not be bound.
Which Four Problem of Colour [is] famous and unsolved during through years. [Is] there any which [is] solved?
Story of[is problem of
Since its time mapmakers start to make a map of showing different area ( like state or nations), that have been recognized [by] among them trading, that if you plan well enoughly, you will never need more than four colour to colour map which you make.
Rule basis for colour a[n map [is] that [there] no two area sharing a[n boundary earn [is] same colour ( Map will see rancu from a distance.) acceding to two area which only meeting [at] single dot to be coloured [by] [is] same colour, however. If you pay attention a[n map some or a[n atlas, you earn verification that . this [is] how all coloured familiar map.
Mapmakers is not [all] expert of matematik, so that statement which only four colour will which necessary for all map obtain;get acceptance in society map-making from year to year because not a single person have stumbled above map needing usage five colour. When [all] expert of matematik take the problem of conversation , they start with question like: Is sure you that four colour [is] enough? How do you know that not a single person can draw a[n map needing five colour? Whereof that the way of which [is] area arranged and touched one another in a map to make matter like that correctness?
When question come to Society Mathematics [in] Europe by the end of century which is 19th, matter of I tu have been felt [by] when drawing but earning dipecahkan.,terkemuka And experience of the who is [all] expert of matematik doing that problem, have been surprised by ketidak-mampuan of them to solve that. Take example [of], account / this tg-jawab from Four Colouring Problem: Assault And of Conquesst [ by / with] Saaty And of Kainen:
expert of Matematik big, Herman Minkowski, once when telling [all] its student 4-Color not yet been setled because only [all] expert of matematik lowgrade have related/relevantly [of] their x'self with that " I trust I earn to prove that," he announce. After a[n period of lame, he [ confessing / permit " Heaven made angry by my arrogancy; my evidence [is] also handicap ( Saaty& Kainen, 1986,p.8):
[At] 1976, anticipation [is] seen to be proved by Wolfgang Haken And of Kenneth Appel [in] Which [is] Univeristiy for Illinois constructively a[n computer. Program which they write [is] thousands of form and take over 1200 [hour/clock] to run Since then, a[n collective effort by [all] expert of matematik which interest to have come to on the way to check that program] So far the single mistake which have been found [by] [is] complement and [is] easy to specified. Many [all] expert of matematik accept theorem as something right.
Voucher 4-Color-Theorem [is] a[n door enter / exit to some drawing question about role of human being manage and [count/calculate] machine [in] ( mathematics dalam). Is ( itu) `` fair'' to accept when what correctness a[n computer can verification, even though single nobody? Do experiencing of or jacquards from what human being can find [about/around] their world change with usage of computer when thinking tool sebaai? Computer [is] strength and very sophisticated , but limited will its use idea iperkakas sebaga finally limit? This issue [is] lifted and considered [by] Advertisement of Infinitum: Spectre in Machine of Turing'S by Rotman Brian, and Pi ( 22:7) blue in the sky by Yohanes Barrow.

CARL FRIEDICH GAUSS - 1796

Kenneth Appel and of Wolfgang Haken- Four Problem of Colour [is] famous and unsolved during through years.

Kenneth Appel
Appel, borne [by] Brooklyn, Metropolis of New York, he [is] educated [by] [in] University of Michigan, he finish title of Phd its [in] university of Michigan in the year 1959. After working for two year [in] Institute Analyse Defence of Princeton, he joint forces with faculty of pancaindera [in] University of Illinois, Urbana, where he act as mathematics professor from 1991 until 1993. He later;then take hold of as departmental chief [of] mathematics [in] University of Hampshire new.
In the year 1976,ia working along with Wolfgang Haken ( 1928--Sp;-Sp;), Appel announce one of [the] solution of mathematics which [is] its long standing problems and not yet four-color theorema terbongkar,yaitu. In the year 1852 Francis Guthrie have also noted that map of manapun, [so that/ to be] anampak [is] by colouring map, assuming nations with frontier of public have been coloured differently, without there [is] more than four colour. Guthrie enough intrigue to developing [him/ it] craftily matematik and ask a[n the anticipation evidence by finding the problem of which do not difficult diduga-duga in the reality, as does succeed to replace generation [all] expert of matematik.
Appel And of Hagen use a[n variation [of] a[n first method [of] times;rill tried by Arthur Kempe in the year 1879. and That depend on the fact that map have to contain certain unavoidable configuration- Appel And of Hagen recognize 1482 colour . and Them later;then use a[n computer to indicate that all this can reduce to configuration 4 colour . They start work [in] year 1972 until 1976, and that them enough with its analysis and also program of mereka.dan that take more than 1200 computer time [hour/clock] to prove the theorem.
Kenneth Appel borne in the year 1932. he [is] expert of matematik which is, [in] soybean cake 1976 with friend work Wolfgang Haken [in] University of Illinois [at] Urbana-Champaign, solving one of the most famous problems [in] theorem four-color dalam)matematika,yaitu. They prove that any two-dimensional map, with certain demarcation, can plow under with four colour without is adjacent " nations" sharing [is] same colour . Children of Appel'S, including Laurel of Appel, Petrus Appel, and Andrew Appel, now a[n professor [at] Princeton, assisted [by] [is] inspection to the 1000 case topological constitutoing this evidence.
Voucher have come to one of the most fond of to debate for modern mathematics because of depended heavy [at] computer " number-crunching" to sort;jenis [pass/through] possibilities. Even Appel have agreed, in many interview, that it lacking of accuration and [do] not present any [of] new insight which have guided mathematical research into future.

Wolfgang Haken
Other Orang)Yang, have showed [him/it] to work as start a[n sea-change in expert attitude of matematik base on computer, they have underestimated as a means of for engineer rather than for teoritius leading to creation from what [is] sometime conceived of " experimental mathematics."
In the year 1976 together with friend of k Kenneth Appel erja [in] University of Illinois [at] Urbana-Champaign, Haken solve one of the most famous problems in mathematics, theorem four-color. They prove that any two-dimensional map, with certain demarcation, can plow under with four colour without is adjacent " nations" sharing [is] same colour.
Haken have introduced some important idea, including manifold Haken, Limited Kneser-Haken, and a[n extension of work of Kneser into a[n theory about normal surface. Many its work have a[n aspect / director of algorithmic, and he [is] one of [the] figure having an effect on in topology of algorithmic. One of the contribution the key [at] this area [is] a[n algorithm to detect if a[n gin / node [is] [do] not be bound.
Which Four Problem of Colour [is] famous and unsolved during through years. [Is] there any which [is] solved?
Story of[is problem of
Since its time mapmakers start to make a map of showing different area ( like state or nations), that have been recognized [by] among them trading, that if you plan well enoughly, you will never need more than four colour to colour map which you make.
Rule basis for colour a[n map [is] that [there] no two area sharing a[n boundary earn [is] same colour ( Map will see rancu from a distance.) acceding to two area which only meeting [at] single dot to be coloured [by] [is] same colour, however. If you pay attention a[n map some or a[n atlas, you earn verification that . this [is] how all coloured familiar map.
Mapmakers is not [all] expert of matematik, so that statement which only four colour will which necessary for all map obtain;get acceptance in society map-making from year to year because not a single person have stumbled above map needing usage five colour. When [all] expert of matematik take the problem of conversation , they start with question like: Is sure you that four colour [is] enough? How do you know that not a single person can draw a[n map needing five colour? Whereof that the way of which [is] area arranged and touched one another in a map to make matter like that correctness?
When question come to Society Mathematics [in] Europe by the end of century which is 19th, matter of I tu have been felt [by] when drawing but earning dipecahkan.,terkemuka And experience of the who is [all] expert of matematik doing that problem, have been surprised by ketidak-mampuan of them to solve that. Take example [of], account / this tg-jawab from Four Colouring Problem: Assault And of Conquesst [ by / with] Saaty And of Kainen:
expert of Matematik big, Herman Minkowski, once when telling [all] its student 4-Color not yet been setled because only [all] expert of matematik lowgrade have related/relevantly [of] their x'self with that " I trust I earn to prove that," he announce. After a[n period of lame, he [ confessing / permit " Heaven made angry by my arrogancy; my evidence [is] also handicap ( Saaty& Kainen, 1986,p.8):
[At] 1976, anticipation [is] seen to be proved by Wolfgang Haken And of Kenneth Appel [in] Which [is] Univeristiy for Illinois constructively a[n computer. Program which they write [is] thousands of form and take over 1200 [hour/clock] to run Since then, a[n collective effort by [all] expert of matematik which interest to have come to on the way to check that program] So far the single mistake which have been found [by] [is] complement and [is] easy to specified. Many [all] expert of matematik accept theorem as something right.
Voucher 4-Color-Theorem [is] a[n door enter / exit to some drawing question about role of human being manage and [count/calculate] machine [in] ( mathematics dalam). Is ( itu) `` fair'' to accept when what correctness a[n computer can verification, even though single nobody? Do experiencing of or jacquards from what human being can find [about/around] their world change with usage of computer when thinking tool sebaai? Computer [is] strength and very sophisticated , but limited will its use idea iperkakas sebaga finally limit? This issue [is] lifted and considered [by] Advertisement of Infinitum: Spectre in Machine of Turing'S by Rotman Brian, and Pi ( 22:7) blue in the sky by Yohanes Barrow.

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history mathematics

mathematics history

in learning mathematics history [is] not possible (to) if us study without resource person ( source of). learning mathematics history without source [is] something that of bullshit, non sens as well as comonsent, hence in description hereunder a lot come from resource person able to be trusted even opinion [all] mathematics philosopher even also [is] the source of from mathematics science. hence without lessening respect in description hereunder, after us read many our others article try to write down again in the form of summary from various resource person which we mention [in] is final [of] description. so that if there are by mistake and or every thing related to that can check to repeat and crossed cheque .

` Mathematics represent one of [the] elementary science which must master by student. Because as according to picture above, in the reality inseparable mathematics of everyday human life. Mathematics always experience of growth comparing diametrical with progress of technology and science. Such matter, most [do] not realize by some of caused [by] student [is] its minim [of] information [regarding/ hit] what and bagimana in fact that mathematics.

And will be more be good if us study something or any if started from its its[his] hence learning mathematics even also earn better if us also study history. so that [is] later expected [by] if we start to learn mathematics science can eliminate the way of ancient in studying [him/ it] like Thereby, hence will cause ugly [at] process learn student, namely they are only learning mathematics by listening clarification a Teacher, learning by heart formula, last multiply problem practice by using formula which have been learned by heart, but have never there [is] effort to comprehend and look for meaning which in fact about target of study of itself mathematics

During the time society have perception ( negative mitos) to mathematics. As which [is] told [by] Frans Susilo in its article [in] Magazine BASES entitling Mathematics of Humanistik, that most negative attitude to mathematics arising from wrong view or misunderstanding [regarding/ hit] mathematics. To comprehend mathematics real correctly and appropriately, first of all require to clarify beforehand some negative myth to mathematics.

Some among myth, for example is: first, ascription that to study mathematics needed [by] special talent which [do] not have each and everyone. Mostly people of berpandangan that to be able to study mathematics needed to have high intellegence, as a result which feel its intellegence lower they [do] not motivat to learn mathematics.

[both/ second] Myth, that mathematics [is] science [count/calculate]. Ability [count/calculate] with numbers (it) is true cannot avoid [by] when learning mathematics. But, [counting/calculating] only representing some of [is] small the than the overall of mathematics content. Besides doing enumerations, people also try to comprehend why that enumeration [is] done with a[n way of is certain .

Third myth, that mathematics only using brain. Mathematics activity (it) is true need logic and intellegence of brain. But, just intellegence and logic fall short. To be able to expand, mathematics very is requiring [of] artistic human being intuition and creativity as does and art. Creativity in mathematics concerning akal-budi, imagination, esthetics, and intuition concerning real correct things. [All] mathematics usually begin on research by using intuition, and later;then try to prove that intuition [is] correctness. Admiration [at] facet of[is beauty [of] and regularity frequently also become the source of motivation to all mathematics to create new breakthroughs for the shake of development of mathematics .

Fourth myth, that most importantly in mathematics [is] real correct answer. important real correct answer (it) is true and have to be laboured. But, more important in fact [is] how to obtain;get real correct answer. Equally, in finishing problem of mathematics, more important [is] process, understanding of, penalaran, and method which [is] used in finishing the the problem to the last yield real correct answer .

Fifth myth, that truth of mathematics [is] truism. Truth of in mathematics in fact have the character of nisbi. Truth of mathematics depend on agreement early mutualy agreed [by] the so-called ' postulate' or ' axiom'. May even exist ascription that [there] no truth ( truth) in mathematics, existing only authenticity ( validity), that is penalaran matching with used [by] logic order [is] human being in general .

Word " mathematics" coming from word ( máthema) in interpreted Greek as " science, science, or learn" also ( interpreted mathematikós) as " liking to learn".

Especial discipline in mathematics relied on requirement of calculation in commerce, measurement of and land;ground of memprediksi event in astronomy. Third [of] this requirement in general relate to third the division of mathematics area public: study about structure, change and room.

Iesson about structure started with number, very [common/ public] and first [is] number of natural integer and and operation its its[his], all that formulated in elementary algebra. Nature of more circumstantial integer studied in number theory.

Investigation of methods to solve equation of mathematics studied in abstraction algebra, which for example, studying about field and ring, structure which [is] generalizing of[is nature of which [is] generally owned [by] number.

Science about room early from geometry, that is geometry of Euclid and trig of room three dimension ( what also can be applied to other dimension), latter later;then also generalizing to geometry of Non-Euclid playing central role in [common/ public] theory of relativity. Some complicated problems about compass construction and ruler [is] finally finished in theory of Galois.

modern Science area about geometry of diferensial geometry generalizing algebra geometry and to some direction:: geometry of diferensial emphasize at function concept, buntelan, derivatif, direction and smoothness, whereas in algebra geometry, geometric objects depicted in the form of a group of equation of polinomial.

heory of Grup study symmetry concept abstractionly and provide bearing [among/between] room study and structure. Connective topology [of] room study with change study with focusing [at] concept of kontinuitas.

Understand and change mendeskripsikan [at] amount able to be [counted/calculated] [by] [is] a[n ordinary in natural sciences, and calculus woke up as a means of for tujauan. Especial concept which used to explain change of variable [is] function. Many problems which [is] have back part [to] naturally to [relation/link] [among/between] amount and fast [is] its change, and method to solve problem this [is] the this topic of from equation of differensial. For the merepresentasikan of amount which [is] kontinu used [by] real number, and study of mendetail from nature of him and nature of known as [by] real value function [of] real analysis. For some reason, very precisely to generalize complex number which studied in complex analysis. focussed Functional analysis [of] attention [at] ( characteriscally unlimited dimension) function room, putting down basis for quantum mechanics among many its something else. Many phenomenon [in] nature can dideskripsikan with dynamic system and theory of chaos face fact which many from that systems not yet showed rule road;street which cannot be estimated.

Mathematics [is] in general affirmed as research of pattern of structure, change, and room; do not more formal, a possible tell [is] research of number and number'. In the eyes of formalis, mathematics [is] inspection of aksiom affirming abstraction structure use symbolic logic and mathematics notation; other view drawn in mathematics philosophy. Specific structure which investigated by matematikus often have to come from Natural Sciences, very [common/ public] [in] physics, but mathematics also affirm and investigate structure to because only just in until hematics, because structure possible provide, for the occurence of, unifier generalizing to some sub-bidang, or appliance assist for the calculation of habit. Finally, many matematikus learn area [done/conducted] [by] them to because which only just aesthetic, see hematics as artistic form than as practical science.

Because learning mathematics history in fact also study mathematics science, hence learning mathematics history even also can start from recognizing [all] philosopher of matematika.serta study result of its idea . and following [is] [all] mathematics philosopher and its idea result

Pythagoras ( 580 - 475 SM )

Tender age

Pythagoras born [in] island of Samos, Greek South [about/around] 580 SM ( Pre-Christian). He/She are well-traveled to Babylon Egypt and estimated [by] have reached India. [In] Babylon above all, Pythagoras braid [relation/link] with experts mathematics. After llama explore isle, Pythagoras leaving its birth land;ground and move to Crotona, Italian Estimated [by] Pythagoras have see 7 miracle of world ( ancient where one of them [is] temple of Hera which located in town its birth. Now, temple of Hera have collapsed and only remaining 1 pillar which [do] not far from town of Pythagorian ( its name [is] weared in memory of best putra [of] him). Wading strait and some mile to north [is] Turki, there are other miracle that is Ephesus.

Pythagoras [is] child of Mnesarchus, a merchant which coming from Tyre. [At] age 18 year he/she come in contact with Thales Thales, a old grandfather, defining mathematics to Pythagoras pass its so called pupil [of] Anaximander, but confessed by Pythagoras as teacher [is] Pherekydes Pythagoras leave Samos in the year 518 SM. [Do] not llama later;then he/she open school [in] Croton accepting pupil without differentiating gender. That school become very famous even Pythagoras finally menikah wrongly one its pupil. Picture detailed aboutPythagoras [do] not too clear Told afterwards, he/she go to Delos in the year 513 SM to take care of benefactor at the same time its teacher, Pherekydes. Pythagoras remain to over there until he/she die in the year 475 SM Its, go to school Croton walk terseok-seok and many internal conflict, but can continue to walk until 500 SM before becoming political appliance.

How Pythagoras create cult to number Number [is] “ deity Mathematics and myths” spurious about number cannot be dissociated. Each;Every number [is] symbol or symbolise something that related to metaphysics [is] matter of lumrah [in] Chinese Pythagoras even also [do] not miss from “ trap” myth about number He/She 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 secret [so that/ to be] healthy always, figure of eight [is] marriage secret. Number even [is] anomalous number and woman / odd [is] man “ Bless us, deity number,” [is] citation from [all] follower Pythagoras which giving special treatment to number empat,”yang create human being and deitys, Tetraktys O pregnant holy [of] creation source and root coming from outside human being.

Worship of number like within reason sorcerer with ball its crystal perhaps – later on day, constitutoing [all] mathematics after Pythagoras. Utterance of Plato “ God comprehending geometry” or citation of Galileo “ Biggest Book about nature written with mathematics symbols.” [Whether/ what] that including mathematics or sorcery. clear [of] mathematics more difficult to comprehend Mathematics [relation/link] with near by music once. Is not surprising if Pythagoras also can become a musicians. Number myth of Pythagoras consist in to pass “ keajabiban pentagram. Form segi-lima which small more and more until takterhingga.

Pythagoras as musician

Pythagoras [is] also known as talented musicians, a player Iira;lyre. Invention of related/relevant music with mathematics early when Pythagoras play at monokord a box unfolded strings above one of [the] its side By moving finger go up and go down [at] lines which intend to be made, Pythagoras recognize that yielded voice can be estimated. When middle shares depressed, each;every string tabletop and under string yield tone [is] same: correct tone 1 octave *

pythagoras perhaps can be conceived of [by] thinker of ages new his day. He/She also a excellent orator, famous intellectual at the same time teacher that kharismatik. All make many people wish to learn from him. It is not a wonder if [do] not llama later;then he/she have many follower and caught up by founding school top-drawer Elementary philosophy to Pythagoras [is] number. Greek inherit the understanding of about number of Egypt geometrik. Its Result, Greek mathematician cannot differentiate [among/between] form ( shapes) with number ( numbers At the moment to prove ordinary mathematics theorema used [by] [of] drawn pictures by using of a kind made ruler of stone or metal and compass Ratios [is] key to comprehend nature, Pythagorean and mathematics more modern finish many energi by diging is deeper [of] their theorys. Finally they [is] proportion memilah into ten category differ the so-called with harmonious middle dot ( harmonic [of] means). One of the this middle dot contain most is number “ beautiful” [in] world: ratio gold ( ratio golden). Nothing that [is] special the than this gold ratio but inspiration something that by gold ratio seems representing very beautiful obyek-obyek. Even until moment this, architect and artist intuitively know that obyek-obyek pregnant [of] gold ratio look artisticly. And this ratio influencing many work [at] artistic area and architecture Parthenon, temple of Athena biggest, woke up with ratio method gold [is] on each;every its aspect [of] him. In mind Pythagorean, ratio control universe and mean sahih for all West world also.

Handicap [at] doctrine of Pythagorean

Number zero [do] not get space in framework Pythagorean. Number zero [there] no or unknown to in dictionary Greek. Using number zero in a[n ratio seems impinge natural law. A[N ratio becoming not there [is] its meaning because “ interference” number zero. Number zero divided a[n number or number can break logic. Zero making “ hole [at] version universe method of Pythagorean, to the reason of this is attendance of number zero cannot be tolerated. Pythagorean nor can solve “ problem” of mathematics concept – number irrasional, what in fact also represent peripheral product ( product by) formula: a + b = c². This concept also attack angle;corner their approach, but hotly brotherhood remain to be taken care of [by] as a secret. This secret have to remain to be taken care of don't leak or their cult fall to pieces. They [do] not know that number of irrasional [is] “ time bomb” to framework think Greek mathematics Ratio [among/between] two number at the most compare two line with length differ. Elementary ascription [of] Pythagorean [is] sensible everything in universe relate to accuration ( neatness), proportion without handicap or is rational.

Euclid (325 – 265 SM)

History

Is not old Pythagoras die, born Euclid. [At] this era mathematics more knowledgeable as science and less mystique Theorema-Theorema just is enhanced: curves, circle’s and other forms studied [by] [is] the same as like straight line and of bidang–bidang level off. Year of[is so-called above only predicting for no him of[is source of which is competent to be trusted. There [is] source of mentioning Euclid live [among/between] year 330 - 275 SM Institute shading study of that moment [is] academy Plato. A period of/to is golden [of] Greek and freedom of have expression making new thinkers pop out. To be founded [by] [at] 380 SM, get away from incoming invasions [of] silih change, live in suksesi many tiran and become avalanche eyewitness two big culture – Greek and of Romawi – before finally closed [by] [at] sixth century by emperor of Justinian Euclid estimated to learn [at] academy of Plato this before ifted to become instructor of [is] same mathematics in place. There [is] story of Euclid still teach [in] this academy when Alexander Glorious express its mission to conquer world. Greek with Egypt and of Mediterian and nations [in] archipelago Greek conquered by armed forces of Macedonian. [At] year 332 SM, Glorious Alexander specify state's capital [in] Alexandria, Egypt and nine year later;then he die [at] age 33 year. Throne giving of to general of Ptolemy or Claudius Ptolemaeus.

University of Ptolemy

Ptolemy - egghead *, developing not only a[n dynasty including one of [the] its very is famous clan Kleopatra, but also found larger ones university of academy of Plato and invite Euclid to teach over there. [In] this new place, Euclid blaze the way instruction of mathematics and remain over there to the death. As a teacher, he/she perhaps one of [the] Archimedes menthol There [is] legend narrating that child of Ptolemy enquire to Euclid if there is a way of easy to learn geometry by studying all preposisi. “ [There] no way of smoothly study geometry,” [is] answer of Euclid at the same time order prince again read geometry book. This answer become citation ( famous quotation) of Euclid Euclid die but university of Ptolemy [in] Alexandria continue walk. One of [the] biggest pupil [of] him – without overruling student humanity friend, [is] Archimedes. Greece of Syracuse bailing science [in] university, where one of [the] its instructor [is] Euclid Personal [of] Euclid.

Euclid can be conceived of [by] especial mathematics. He/She [is] recognized

because its ommission in the form of mathematics masterpiece which [is] decanted

in book of The Elements very monumental. Fruit think which [is] infused [by] the the book make Euclid assumed as mathematics teacher during the time and matematikawaan biggest [of] Greek Personal [of] Euclid described as one who [is] kindhearted, downright patient and always ready to assist and work along with people other. Many formulated theorema-theorema [it] represent esult of previous thinkers masterpiece [is] including Thales Hippokrates and of Pythagoras Many wrong information about Euclid. There [is] mentioning that he [is] child of Naucrates which born [in] Tyre. Other Information please tell that [in] delivering birth [in] Megara. (Itstructured book pursuant to topic and theme Each;Every book early with difinisi, postulate ( just for book of I preposisi, theorema before covered with verification by using postulate and difinisi which have been mentioned. Book this out Greek year 1482, translated to Latin and Arab, and also become geometry textbook and logic [at] early year 1700-an. Outline fill the each book.

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

Book of II : Algebra Geometry

Book of III : Theorys about circle

Book of IV : Way of making tortous picture and line

Book of V : Theory about abstraction proportions

Book of VI : [is] same Form and proportions in geometry

Book of VII : Elementary [of] number theory

Book of VIII : Proportions Continuation in number theory

Book of IX : Theory Number

Book of X : Classification

Book of XI : Geometry three dimension

Book of XII : Measuring forms

Book of XIII : Forms of Tri-Matra ( three dimension)

made [by] format [is] Euclid assist happened standarisasi Greek mathematics. Subyek-Subyek studied by Euclid including forms, Pythagoras theorema, equation in algebra, radian, tangent, room geometry, proportion theory prime number, perfect number, positive integer, number irrasional, draw tri-matra ( three dimension). Euclid leave heritage which good for development of mathematics previous Pickings mathematics masterpiece Kompilasi pass book of Elements, showing “ red yarn” that development of mathematics [do] not get out of role of thinker of Greek Criticize to Euclid exactly trigger appearance of non-Euclidian equiping discussion of Euclid. Form Parabola, and hyperbola ellipse start to get attention from [all] mathematics

Archimedes ( 287 – 212 SM )

History

Archimedes [is] a arsitokrat. Archimedes [is] child Pheidias astronom which born [in] Syracuse, Greek colony which [is] now recognized by the name of Sisilia. He/She have [relation/link] family with tiran ( top kick Hieron II raja) [in] Syracuse in those days. Archimedes berteman dengan of Gelon, child of Hieron II, where both [is] king pledge mathematics Discussing complete Archimedes is not without incident story its invention [of] moment he/she take a bath. Moment that is finding that loss of body weight [is] equal to removed water weight He/She hop from place take a bath and run terlanjang [in] public road Syracuse at the same time scream “ Eureka, eureka!” ( I have found, I have found). Moment that's Archimedes finding first law [of] hidrostatik. Story above early by disingenuous goldsmith by mixing silver to in crown order of Hieron. Suspicious Hieron and order Archimedes to solve the the problem or [do/conduct] examination without destroying crown. Seemingly bath moment Archimedes think of the problem. About worker chance itself gold nothing that knowing [him/ it] A period of/to school.

A period of/to school

Young moment [of] age he/she study [in] Alexandria, Egypt. At the (time) of that is braiding friendship with two people “ special First friend, Conon [is] talented mathematics which very respected [by] Archimedes either through person and also is ntellectual. Friend both, Eratosthenes *), also a mathematics at the same time astronom, even have “ disparity that is: liking to dress up. both this friend, above all [of] Conon Archimedes can shar idea and discuse. Finally Conon die and correspondence between both replaced by Dositheus, pupil of Conon Year 1906, J.L. Heiberg, making dramatic invention [in] Konstantinopel that is: “ letter” Archimedes to Erastosthenes Theorema Mekanikal, a[n method. In its letter this Archimedes measure weight, in imagination, utilize to [count/calculate] wide [of] or know volume ( unknown something that isi) pass something that known, he/she blaze the way science based on dig of fact; this fact [is] used as comparator to [is] later;then proved mathematically There [is] other version which mention that Archimedes estimated sitting under pupil of Euclid. Archimedes can be conceived of mathematics at the same time first physics, where besides finding “ war machine”, mechanical appliances and also water pump to lift river water of Nil utilize to irrigate ( tanahtanah irigasi) in all country.

Nature of is eccentric [of] Archimedes

In the case of is eccentric [of] Archimedes [is] often compared to Weierstrass ( 1815 – 1897). According to its sister saying Weierstrass – when school, have never been given trust to hold pinsil. If holding pinsil hence he/she will draw any which [is] assumed [it] still is empty. Of wallpaper return to conscript clothes. On the contrary Archimedes - not yet recognized paper, always draw [in] sand or flabby land;ground instead of function “ blackboard.” He/She will draw relishly [of] him. If siting at elbow fireplace, he/she will take combustion remains or charcoal and used to draw. After bath, usually he/she will smear entire/all its body with olive, which is inveterate to be weared in those days, than dress, he/she will draw diagrams by using nail finger with “ blackboard” [is] entire/all its oily body There [is] nature of inveterate [of] diidap by [all] mathematics like: forgetting eat. Nature of forgetting to eat Archimedes, moment elaborate problem mathematics

Inventions Of Archimedes

Enthusiasm Archimedes [is] pure mathematics: number, geometry [counting/calculating] wide [of] geometry forms. Archimedes recognized because its greatness [of] mathematics application. Greatness this will be elaborated hereunder Meritorious archimedes find Archimedes thread, appliance to lifting water by way of turning around this appliance hilt with hand. Usage early this appliance is to pass what come into ship or boat. But in its growth [is] used for water pump of plain lower to the ground which [is] high lebi. This appliance until now still weared by [all] farmer in all the world Usage of burner mirror, giving indication that some geometry form have been known [by] Archimedes, above all [of] form hyperbola. Radian form, hyperbola and ellipse formed only we how to slice a[n area. Parabola [is] special form: can “ take” sunshine, of direction, and focussed at one particular dot, and concentration all light energi [at] narrow;tight area to be re-transmitted in binding very hot [light/ray] Archimedes have tried to [count/calculate] wide [of] parabola, elliptical hyperbola and determine center of gravity dot [at] half radian and radian. Unknown surely how much/many many masterpieces of Achimedes missing or not yet been found one all important, Method ( The Method, mostly have been found in the year 1906), but other masterpiece [is] including: On Spiral On The Measuremant Circle the of, Quadrature Of Parabola the, on Conoids & Spheroids, Sphere the on & Cylinder, Books Of Lemmas etc. disagree with everything which [is] yielded Archimedes [at] era of Romawi.

) is true there [is] name [is] same, Euclid and born [in] Megara, but that thing happened 100 year before birth of Euclid and profession of Euclid of Megara [is] philosopher. Euclid alone born [in] Alexandria. Mistake of this name plural happened because during the period so called many people [of] Euclid Masterwork of Euclid.

The Element can be told masterpiece of fenomenal in those days Consist

Fibonacci ( 1170 – 1250 )

History

Signifikansi growth of mathematics [at] middle ages [in] Europe along with delivering birth of Leonardo of more Pisa recognized with epithet of Fibonacci ( its meaning [of] child of Bonaccio Bonaccio alone its meaning [of] stupid child, but he/she is non fool ex officio [of] him [is] a consul which [is] Pisa wewakili holded [Position/Occupation] make him often travel With its child, Leonardo, what always follow to state [which/such] even also he/she [do/conduct] lawatan. Fibonacci write book of Liber Abaci after inspiration [at] its visit to Bugia, a[n town what [is] growing [in] Algier. When its father undertake over there Arab mathematics expert show miracle of system number of Hindu-Arab. System which start to be recognized [by] after era Crusader. Calculation which not possible (to) be [done/conducted] by using notation ( Romawi bilangan). After Fibonacci perceiving all conducive calculation by this system he/she set mind on to learn [at] Arab mathematics which live in [about/around] Mediterranean. Spirit [of] learning of is very spirit make he/she [do/conduct] journey to Egypt Syria, Greek, Sisilia.

Composing book

Year 1202 him publish book of Liber Abaci by using – what [is] now referred [as] with algebra by using Hindu-Arabik numeral. This Book give big impact because emerging new world with numbers what can replace Jew system, Greek and of Romawi with letter and number to [count/calculate] and calculation Antecedent of book contain with how to determine amount digit in set of duplication tables or numeral ( read multiplication) with number ten, with number one hundred and further. Calculate by using entire/all and number division, fraction, root, even the solving of equation of line diametrical ( linier) and equation of square. That book [is] provided with application and practice so that excite its reader. Base merchant, illustrate in the world obusiness with numbers also presented. Including here [is] bookkeeping of business ( double enter), depiction about advantage marjin, change ( currency konversi), heavy conversion and size measure ( kalibrasi)

Hare Problem

Meeting with Frederick and questions aised by experts, booked and published [do] not llama later;then. Year 1225 him [release] book of Liber Quadrotorum ( book about Square) dedicated [it] to the The king. In that book [is] contained [by] problem capable to disturb “ common sense” mathematics that is about problem hare of beranak-pinak simple Question [is] but needed brooding think “ How much/many hare tide to beranak-pinak during one year. Early by a couple of hare, if each month a couple of leveret become productive in [both/ second] is - Final [of] [both/ second] month;moon, they marry and female hare [of] I bear a couple of different leveret [of] gender - Final [of] month;moon both, female hare bear a coupleof child new, so that there [is] 2 hare tide - Final [of] third month;moon, female hare [of] I bearhare couple [both/ second], so that there [is] 3 hare tide - Final [of] fourth month;moon, female hare [of] I bear a couple of child new and female hare [of] II bear a couple of leveret so that there [is] 5 hare tide Will be obtained by] answer: 55 hare tide. How if/when that process continue to take place centenary? Its result ( contek just)354.224.848.179.261.915.075 Do there is a way of quickly to [counting/calculating] [him/ it]? Here Fibonacci giving number formula which [is] later;then recognized by the name of Fibonacci deret.

Isaac Newton ( 1642 - 1727

Tender age

Newton born premature [at] end of year 1642 * at the same time with year die [him/it] of Galileo. this [is] Body Baby very small ( prematue) so that have to enter tube. Father Newton, a farmer, even have died 3 months before him borne Its mother wish Newton to become farmer, but walke its life change after continuing school [in] Grantham and kost at home a apothecary. HereNewton have opportunity read book and [do/conduct] experiment Invention of water wheel, windmill, sand glass and [hour/clock] irrigate happened [at] this period, before called to [go/come] home to manage land;ground agriculture and desist school. But year 1658, Newton return to apothecary house and back go to school June 1661, Newton enter University of Cambridge Trinity with subsidy program – changing the expense of school by cleaning room and serve requirement of lecturer. Initially he/she study “ Light science ( optics)” Kepler, reading “ Theory elementary [of] geometry” Euclid and also “ Way of and guide of geometry” Tycho Brahe. Below/Under tuition of Isaac Barrow, Newton start studying optics and mathematics. Early year 1665, Newton graduate from Cambridge but after a few times emerge epidemic ( plague bubonic) so that university closed and he/she [go/come] home to its countryside ( Woolsthorpe). In the reality bright many people which becoming supporter at the same time competitor of Newton, dying, because this epidemic.

Sejaman with [all] other area jenius

One day [in] year 1664, [at] a cafe [in] London happened discussion three notable man of science [of] that era, that is: Robert Hooke ( 1635 – 1703), inventor of Hooke law **; Christopher Wren ( 1632 – 1723), man of science at the same time architect developing St Paulus [in] London and astronomical lecturer and also Edmund Halley ( 1656 – 1742 *** in the year 1682 This trio [is] discussing and trying to formulate orbit planet, but always fail. Halley come to Cambridge and asking for Newton advice. In the reality formula “ deposit” Newton what [is] later;then publicized at the instance of Halley, can solve the the problem even later;then there [is] accusation of Hooke that Newton masterpiece [is] plagiarism masterpiece. This matter make Newton completely broken, but for the shake of laying open truth mindful of dying [him/ it] of Copernicus and of Galileo for truth, hence Newton continue to [do/conduct] research and formulating its law until third law Year 1687 publishing Newton masterpiece which [is] monemental, Principia Conflict with this Hooke still going on when Newton also finding theory about colour and light – beforehand early by invention of microscope in the year 1678 by Antony Van of Leewenhoek ( 1632 – 1723) which [is] berkewarganegaan Dutch. At the (time) of [is] same, Christiaan Huygens ( 1629 1695) physics expert, but also elaborate horology ( science about measurement of time) and pencetus of theory about light at the same time a mathematics.

Role of Huygens of vital importance in altering enthusiasm band Liebniz of philosophy and law to later;then to elaborate mathematics ( read: Leibniz). Pierre De Fermat – live during that also, [is] trying to formulate mathematics which incircuit with rate of change, henceforth this mathematics [is] recognized with “ epithet” calculus. Race of this calculus, like we have know with, won by Newton and Leibniz Year 1666, Newton have found calculus but newly ten years later;then, proposed by is Prodigal [of] Society to making report - utilize to be checked - to Johann Bernoulli ( 1646 – 1716). At the (time) of which at the same time, mathematician Germany, Leibniz also check calculus after reading report Newton when there [is] opportunity visit Bernoulli Both [is] alleging each other who first time find calculus. Finally both confirmed that calculus [is] invention of both of them. In its growth, later version calculus of Leibniz more used because more is simple, but calculus we will not recognize, if [do] not there [is] Newton.

[is] taken and rewritten from source- suimber following .

Matematika, Mitos Masyarakat, dan Implikasinya terhadap Pendidikan Matematika di Sekolah Oleh: Abdul Halim Fathoni

“the foundations of mathematics” taken from www.google.com

Paradigma Baru Pendidikan MatematikaOleh Dr. Sutarto Hadi, M.Si., M.Sc.

http://mate-mati-kaku.com/matematikawan/pappus