Minggu, 30 November 2008
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
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]
Pythagoras [is] child of Mnesarchus, a merchant which coming from
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
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.
History
Is not old Pythagoras die, born
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
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
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]
Archimedes ( 287 – 212 SM )
History
Archimedes [is] a arsitokrat. Archimedes [is] child Pheidias astronom which born [in]
A period of/to school
Young moment [of] age he/she study [in]
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.
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
Isaac Newton ( 1642 - 1727
Tender age
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
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]
[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
