1.Yang saya temukan konsep matematika, persoalan matematika dan penyelesaian
matematika pada zaman kuno yang sekarang masih dipakai :
Konsep matematika yang saya temukan yaitu mengenai konsep bilangan nol, yang pertama kali ditemukan pada zaman kuno di India dan pertama kali diterapkan oleh Aryabhata. Dia menerapkan bilangan nol dalam sistem perhitungan, bukan sekedar tempat kosong. Kemudian sekarang kita menjumpai bilangan nol itu pada sistem bilangan cacah.
Penyelesaian matematika yang saya temukan yaitu L’hospital yang dikemukakan oleh De L’Hospital, yaitu aturan penggunaan limit fungsi .
2.Yang saya temukan kosep matematika, persoalan matematika, dan penyelesaian
matematika pada zaman kuno yang sekarang sudah tidak dipakai :
• Penyelesaian matematika yang saya temukan yaitu pada zaman Mesir Kuno yang sekarang tidak dipakai adalah mencari π = 3,16, namu pada zaman sekarang dipakai nilai π = 3,14.
3.Yang saya temukan konsep matematika, persoalan matematika dan penyelesaian
matematika pada saat ini yang tidak ada hubungannya dengan matematika zaman kuno :
Penyelesaian matematika yang tidak ada hubungannya dengan zaman kkuno yaitu mengenai pemecahan matematika dengan menggunakan closed problem, open-ended problem, closed problem.
Minggu, 11 Januari 2009
Problem → how to translate history owning soul differentiating history with other science.
Context of Sejarah→ Graphical
→ Time
→ Society
→ Cultural
Methodologies
Bearing with other science.
METHODS HISTORY
Pursuant to:
1. Ide → so far explain that idea.
Example of : artefak, physical evidence, what undetected was when made.
Mathematics relate to science of else → Thales.
Mathematics Egypt
Mathematics of Babilonia
applied sciences and nature of empiris
↓ Observation
↓
Withdrawal of conclusion
Ommission of physical : artefak, idea.
Mathematics Egypt and of Yunani
↓
In Allexandria.
Example of : isn't it Egypt mathematics.
Pythagoras which first time prove induceed.
- Induction
- Teachership → pythagoras.
- Stream pythagorean.
Pythagoras → problem formula c² = a² + b². Emerge history is called→ number of irrasional.
• History is fact.
• Past time to express fact expressed at the present day.
• Many opinions: science of logos/ discourse.
control / psychology.
History of Matematika → make the explanation / explaining/ prediksi forwards needing other science.
Eksplanasi → Can exploited by now → to come → can weared to support job / duty in study of matematics.
Constraint :
old document → but along with the have expanding to of TI ( information
technology / passing internet ).
New document : old document its contents.
Pythagoras : triple pythagoras
number of irrasional.
Aristoteles : no possible number. Because do not find understanding of irrasional.
Euclides : Deductive Science of mathematics. His book content: definition, aksioma/postulat/teorema
Definition: earliest from a theorem. Example of : definition of titik → garis → circle.
idea of jetty / primitif → sintetik apriori that is can find although not yet known people / his object. Aristoteles → Definite REGRESS that is definition rotation which there no ending. According to Aristoteles if us wish to start surely we own elementary assumption. That Elementary assumption precede definition.
Place weared for the start → place tread on / base / fondation → the there is effort to start, there is foundation.
Mathematics world there is owner of is basis build his own world and there is which have no base. But both less precise the statement, correct is the basis him have the character of dinamik, told by Immanuel Khan. Basis mathematics is efistemolog that is science which the was base of asked.
Science Epistemolog → knowledge sources → knowledge reality → object of human → Plato. Browler → matematics have base to intuition (anti fondation).
Franciss Beckhend and David heume → peripatetic metematics.
Aristoteles → Matematics of experience ( external of head ).
Mathematics Gilbert → built with sturdy base ( logical ) or have the character of formally.
Kurt Godel → pupil of Gilbert → make equipment axiom / non axiom.
Rene Descartes → method of reach for mathematics rationalism stream ( epistemolog ). Epistemolog : knowledge theory which deal with knowledge scope and essence, if and the bases of and also responsibility of scientific statement which owned, do we have knowledge regarding natural as it is. This sceptic start appearance of epistemolog.
Is told by Aristoteles and of Franciss Bacon.
Cogito Ergo Sum → doubtfulness method. This famous understanding later, then with
rationalism there is one which cannot be hesitated, that is me
is hesitating. I who is hesitating because of me thinking. If so I
think surely there is and correctness. If thinking exist, meaning
I am there is the thinking cause exist.
o Mind is all important appliance in obtaining and knowledge of experimentknowledge.
elementary
Rene Descartes → Problem in knowledge philosophy is not how soybean cake us, but why
we earn to make by mistake. If us systematically try to doubt of
as many as possible knowledges of us, finally we will reach dot
which cannot be hesitated so that knowledge of us can be woke up of
absolute certainty, this matter was referred as by infinite
universal method.
Context of Sejarah→ Graphical
→ Time
→ Society
→ Cultural
Methodologies
Bearing with other science.
METHODS HISTORY
Pursuant to:
1. Ide → so far explain that idea.
Example of : artefak, physical evidence, what undetected was when made.
Mathematics relate to science of else → Thales.
Mathematics Egypt
Mathematics of Babilonia
applied sciences and nature of empiris
↓ Observation
↓
Withdrawal of conclusion
Ommission of physical : artefak, idea.
Mathematics Egypt and of Yunani
↓
In Allexandria.
Example of : isn't it Egypt mathematics.
Pythagoras which first time prove induceed.
- Induction
- Teachership → pythagoras.
- Stream pythagorean.
Pythagoras → problem formula c² = a² + b². Emerge history is called→ number of irrasional.
• History is fact.
• Past time to express fact expressed at the present day.
• Many opinions: science of logos/ discourse.
control / psychology.
History of Matematika → make the explanation / explaining/ prediksi forwards needing other science.
Eksplanasi → Can exploited by now → to come → can weared to support job / duty in study of matematics.
Constraint :
old document → but along with the have expanding to of TI ( information
technology / passing internet ).
New document : old document its contents.
Pythagoras : triple pythagoras
number of irrasional.
Aristoteles : no possible number. Because do not find understanding of irrasional.
Euclides : Deductive Science of mathematics. His book content: definition, aksioma/postulat/teorema
Definition: earliest from a theorem. Example of : definition of titik → garis → circle.
idea of jetty / primitif → sintetik apriori that is can find although not yet known people / his object. Aristoteles → Definite REGRESS that is definition rotation which there no ending. According to Aristoteles if us wish to start surely we own elementary assumption. That Elementary assumption precede definition.
Place weared for the start → place tread on / base / fondation → the there is effort to start, there is foundation.
Mathematics world there is owner of is basis build his own world and there is which have no base. But both less precise the statement, correct is the basis him have the character of dinamik, told by Immanuel Khan. Basis mathematics is efistemolog that is science which the was base of asked.
Science Epistemolog → knowledge sources → knowledge reality → object of human → Plato. Browler → matematics have base to intuition (anti fondation).
Franciss Beckhend and David heume → peripatetic metematics.
Aristoteles → Matematics of experience ( external of head ).
Mathematics Gilbert → built with sturdy base ( logical ) or have the character of formally.
Kurt Godel → pupil of Gilbert → make equipment axiom / non axiom.
Rene Descartes → method of reach for mathematics rationalism stream ( epistemolog ). Epistemolog : knowledge theory which deal with knowledge scope and essence, if and the bases of and also responsibility of scientific statement which owned, do we have knowledge regarding natural as it is. This sceptic start appearance of epistemolog.
Is told by Aristoteles and of Franciss Bacon.
Cogito Ergo Sum → doubtfulness method. This famous understanding later, then with
rationalism there is one which cannot be hesitated, that is me
is hesitating. I who is hesitating because of me thinking. If so I
think surely there is and correctness. If thinking exist, meaning
I am there is the thinking cause exist.
o Mind is all important appliance in obtaining and knowledge of experimentknowledge.
elementary
Rene Descartes → Problem in knowledge philosophy is not how soybean cake us, but why
we earn to make by mistake. If us systematically try to doubt of
as many as possible knowledges of us, finally we will reach dot
which cannot be hesitated so that knowledge of us can be woke up of
absolute certainty, this matter was referred as by infinite
universal method.
HISTORY MATHEMATICS PURSUANT TO FIGURE
THALES
attributed to First person inventions of mathematics
Mathematics which first time formulating theorema / proposition
Applied sciences in the reality have been put down by Thales before
Pythagoras making number
Using geometry to solve problem like pyramid counting pursuant to shadow
length and ship distance of coast
Because his him, he is known as by statesman, adviser, engineer,mathematics,
and astral expert.
PYTHAGORAS
• Is not inventor of theorems/ theorem of pythagoras, but him considered to be
from the theorems because first verification of this theorem is best which
have been given by Pythagoras
• Brotherhood of Pythagoras number menemukan √ 2 as of irrasional.
• Joining between mathematics and music to make something becoming regular and
do not in confusion, music sharpen feeling while mathematics give order how
this world can walk regularly
• Philosophy of Pythagoras pursuant to ascription that integer is denominator
from all kinds of nature of from Iihat vitamin
• Assumed by Neoplatonis as inventor of brotherly numbers / amicabel.
SOKRATES
A philosophy
Philosophy teaching of have never been written down, was but conducted by
him with deed namely with way of living
If observed truly, he also do not teach philosophy, but live to have
philosophy. Is not knowledge expert, but thinker .
Target of the philosophy of to look for truth applying forever and ever
Rendering midwifery technique ( tekhne maieutika ) in philosophizing
Isn't it ideology concerning perception of cosmology
Teaching of flange at naturalism where form of such organization is
individualis with democracy as organizational principle of him
A filusuf owning understanding that life of solar system supposing, mean
seen planets encircling sun, hence becoming a conclusion that strong
determine the weakness.
PLATO
1. Is pupil of Sokrates and teacher of Aristoteles
2. Plato is creator of teaching completely goal, in consequence the philosophy
of named by idealism. Teaching of delivering birth because the interaction
of with clan of sofis
3. Plato is expert think first which accept understanding of is existence of
nature is not object
4. All important Facet in philosophy of Plato is idea of concerning Utopia is
earliest theme in the network of length idea of him, both of theory of
concerning ideas where studying concerning universal problem, later;then the
conception of more coming scientific from memory than perception.
EUKLIDES
a) Learn mathematics at Plato academy and in place this is also lifted as
instructor of mathematics
b) Biggest masterpiece of him is book " The Element " what consist of 13 book
c) Known as by geometry father because telling number theory and geometry
d) Finding appliances of for example meter and ruler
Mistar→to make straight line which do not limited
Jangka→to make circle of the size different radius
e) Subjects the studied is forms, equation pythagoras theorema in algebra,
radian, tangent, geometry of room,theory of proposition, and others.
APPOLONIUS
o A mathematics which expert in geometry
o Theorem of connecting some element in trilateral
o Appolonius divide curve become 3 category :
• Plane loci → straight line dan circle
• Solid loci → trapeze shares or cutting
• Linear loci → aliance mark with lines and area form.
o Writing way quickly which comprising instruction of enumeration concepts or
tips-tips quickly
o Conception parabola, ellipse and hyperbolas giving many contributions for
modern astronomy.
DIOPHANTUS
Known as by algebra father because the masterpiece of entitling aritmetika
is masterpiece in the field of algebra and also develop algebra concepts
A Greek mathematics which living in Iskandaria
Biggest Masterpiece of him in the form of book of aritmetika, first book
concerning algebra system
Looked after shares of Diophantus aritmetika contain resolving of problem
about 130 problem yielding equations of first storey;level and second.
attributed to First person inventions of mathematics
Mathematics which first time formulating theorema / proposition
Applied sciences in the reality have been put down by Thales before
Pythagoras making number
Using geometry to solve problem like pyramid counting pursuant to shadow
length and ship distance of coast
Because his him, he is known as by statesman, adviser, engineer,mathematics,
and astral expert.
PYTHAGORAS
• Is not inventor of theorems/ theorem of pythagoras, but him considered to be
from the theorems because first verification of this theorem is best which
have been given by Pythagoras
• Brotherhood of Pythagoras number menemukan √ 2 as of irrasional.
• Joining between mathematics and music to make something becoming regular and
do not in confusion, music sharpen feeling while mathematics give order how
this world can walk regularly
• Philosophy of Pythagoras pursuant to ascription that integer is denominator
from all kinds of nature of from Iihat vitamin
• Assumed by Neoplatonis as inventor of brotherly numbers / amicabel.
SOKRATES
A philosophy
Philosophy teaching of have never been written down, was but conducted by
him with deed namely with way of living
If observed truly, he also do not teach philosophy, but live to have
philosophy. Is not knowledge expert, but thinker .
Target of the philosophy of to look for truth applying forever and ever
Rendering midwifery technique ( tekhne maieutika ) in philosophizing
Isn't it ideology concerning perception of cosmology
Teaching of flange at naturalism where form of such organization is
individualis with democracy as organizational principle of him
A filusuf owning understanding that life of solar system supposing, mean
seen planets encircling sun, hence becoming a conclusion that strong
determine the weakness.
PLATO
1. Is pupil of Sokrates and teacher of Aristoteles
2. Plato is creator of teaching completely goal, in consequence the philosophy
of named by idealism. Teaching of delivering birth because the interaction
of with clan of sofis
3. Plato is expert think first which accept understanding of is existence of
nature is not object
4. All important Facet in philosophy of Plato is idea of concerning Utopia is
earliest theme in the network of length idea of him, both of theory of
concerning ideas where studying concerning universal problem, later;then the
conception of more coming scientific from memory than perception.
EUKLIDES
a) Learn mathematics at Plato academy and in place this is also lifted as
instructor of mathematics
b) Biggest masterpiece of him is book " The Element " what consist of 13 book
c) Known as by geometry father because telling number theory and geometry
d) Finding appliances of for example meter and ruler
Mistar→to make straight line which do not limited
Jangka→to make circle of the size different radius
e) Subjects the studied is forms, equation pythagoras theorema in algebra,
radian, tangent, geometry of room,theory of proposition, and others.
APPOLONIUS
o A mathematics which expert in geometry
o Theorem of connecting some element in trilateral
o Appolonius divide curve become 3 category :
• Plane loci → straight line dan circle
• Solid loci → trapeze shares or cutting
• Linear loci → aliance mark with lines and area form.
o Writing way quickly which comprising instruction of enumeration concepts or
tips-tips quickly
o Conception parabola, ellipse and hyperbolas giving many contributions for
modern astronomy.
DIOPHANTUS
Known as by algebra father because the masterpiece of entitling aritmetika
is masterpiece in the field of algebra and also develop algebra concepts
A Greek mathematics which living in Iskandaria
Biggest Masterpiece of him in the form of book of aritmetika, first book
concerning algebra system
Looked after shares of Diophantus aritmetika contain resolving of problem
about 130 problem yielding equations of first storey;level and second.
HISTORY MATHEMATICS GEOGRAPHICALLY
MESOPOTAMIA
- Finding number system first time.
- Finding heavy system and measure system.
- Number initially symbolised with rib printing;mould or seagegrass at clay.
- Number 1-10 symbolised with ribs level off while tens of and the fold of
symbolised with straightening rib.
- Year 2500 SM system denary shall no longger be used and rib changed by
notation in form of wedge.
BABILONIA
• In the field of geometry have known that each;every trilateral painted at
semicircle have right angle
• Geometry of using algebra characters which the was writing method of
indicating that nation of Babilonia know some algebra general laws
• Have recognized theorem of pythagoras
• Number of using number system of sexagesimal
• Aritmetika do not have algorithm of to long division because they use method
base on which practically that a/b = a x 1/b
• Using system denary and phi=3,125
• Inventor of calculator first time
• Recognizing geometry as bases of
is calculation astronomy.
• Using approach for the root of number and square of[is non square
• Geometry of having the character of aljabaris.
ANCIENT MESIR
- Recognizing number system ( number ) that is Hierogliphs and digital.
- Recognizing number system and symbol in year 3100 SM
- Recognizing Triple Pythagoras
- System Number is additive pattern of aritmetika
- Have recognized comparison of is joints line because formulating cotangens from
the aspect of area two between pyramid pallet with his side area
- Mathematics Egypt mount the attainment of lower than nation of Babilonia
- Owning value of π = 256 / 81
- They are only can finish equation of linear and not yet owned knowledge of is
nature of right triangle.
- Year 300 SM use number system base on 10.
ANCIENT YUNANI
- Proving theorem of pythagoras
- Recognizing prime numbers
- Recognizing astronomical science
- Born ball trig him
- Triggering the name of parabola with the meaning right angle;corner shareses of
trapeze →( Archimedes)
- Triggering enumeration technique quickly → ( Appolonius)
- Triggering concept early 0 →( Al Khawarizmi)
- Studying area geometry level off → ( Archimedes ) and also find formula
L = √ s( s-a )( s-b )( s-c )
- Giving important contribution for idea concerning theory number, mathematics
analysis, and integral of calculus.
INDIA
- Mathematics appear in Asia South, that is in civilization of Dale of Indus (
2600-1900 SM)
- Recognizing system denary, negative number and zero
- Inventor of formula early a² +b² = c² → ( Sulbasutra)
- Finding gunam stanam-stanam that is modern decimal notation base →( Aryabatha ).
- Finding relation around a circle →( Brahmagupta)
- Geometri → Recognizing Triple Pythagoras, pythagoras theorema, transformasi and
trilateral of pascal
- Aljabar → Mengenal equation of rank square
- Trigonometri → have recognized sine trig function, and cosinus of versin ( sine
versed / A version= 1-cos A )
CHINA
- Recognizing the nature of year right triangle 3000 SM
- Developing negative number, number denary, binary system, algebra, geometry, trig,
and calculus
- Have found method to solve some equation types that is equation of square, cubic
and qualitik
- Algebra of using system of horner to finish equation of square ( tribe many ).
- Finding number system first time.
- Finding heavy system and measure system.
- Number initially symbolised with rib printing;mould or seagegrass at clay.
- Number 1-10 symbolised with ribs level off while tens of and the fold of
symbolised with straightening rib.
- Year 2500 SM system denary shall no longger be used and rib changed by
notation in form of wedge.
BABILONIA
• In the field of geometry have known that each;every trilateral painted at
semicircle have right angle
• Geometry of using algebra characters which the was writing method of
indicating that nation of Babilonia know some algebra general laws
• Have recognized theorem of pythagoras
• Number of using number system of sexagesimal
• Aritmetika do not have algorithm of to long division because they use method
base on which practically that a/b = a x 1/b
• Using system denary and phi=3,125
• Inventor of calculator first time
• Recognizing geometry as bases of
is calculation astronomy.
• Using approach for the root of number and square of[is non square
• Geometry of having the character of aljabaris.
ANCIENT MESIR
- Recognizing number system ( number ) that is Hierogliphs and digital.
- Recognizing number system and symbol in year 3100 SM
- Recognizing Triple Pythagoras
- System Number is additive pattern of aritmetika
- Have recognized comparison of is joints line because formulating cotangens from
the aspect of area two between pyramid pallet with his side area
- Mathematics Egypt mount the attainment of lower than nation of Babilonia
- Owning value of π = 256 / 81
- They are only can finish equation of linear and not yet owned knowledge of is
nature of right triangle.
- Year 300 SM use number system base on 10.
ANCIENT YUNANI
- Proving theorem of pythagoras
- Recognizing prime numbers
- Recognizing astronomical science
- Born ball trig him
- Triggering the name of parabola with the meaning right angle;corner shareses of
trapeze →( Archimedes)
- Triggering enumeration technique quickly → ( Appolonius)
- Triggering concept early 0 →( Al Khawarizmi)
- Studying area geometry level off → ( Archimedes ) and also find formula
L = √ s( s-a )( s-b )( s-c )
- Giving important contribution for idea concerning theory number, mathematics
analysis, and integral of calculus.
INDIA
- Mathematics appear in Asia South, that is in civilization of Dale of Indus (
2600-1900 SM)
- Recognizing system denary, negative number and zero
- Inventor of formula early a² +b² = c² → ( Sulbasutra)
- Finding gunam stanam-stanam that is modern decimal notation base →( Aryabatha ).
- Finding relation around a circle →( Brahmagupta)
- Geometri → Recognizing Triple Pythagoras, pythagoras theorema, transformasi and
trilateral of pascal
- Aljabar → Mengenal equation of rank square
- Trigonometri → have recognized sine trig function, and cosinus of versin ( sine
versed / A version= 1-cos A )
CHINA
- Recognizing the nature of year right triangle 3000 SM
- Developing negative number, number denary, binary system, algebra, geometry, trig,
and calculus
- Have found method to solve some equation types that is equation of square, cubic
and qualitik
- Algebra of using system of horner to finish equation of square ( tribe many ).
Report Activity And My Result In Searching, Collecting, Studying, Analyzing, Discuse, Concerning History Mathematics Antecedent Of
Word " mathematics" coming from word of mathema in interpreted Greek as " science, science, or learn " also interpreted mathematikos as " liking to learn". In studying mathematics science can be obtained from various media source . For example internet, guide-book, teacher tuition / lecturer, also everyday life dai.
RESULT
Result which I earn and I perceive that is in our mathematics science recognize pythagoras triple. Real of the theorem have been recognized by people of Babylonia since year 1600 SM. Knowledge concerning this is theorem very him in tukar-menukar ( land barter) at that epoch. Someone example of having fairish a pice of land 50 x 50 square meters can convert him by 2 fairish land;ground area 30 x 30 square m and 40 x 40 square m. Besides, mathematics science also used many in other sciences. moment example of first time milk computer, some theory concepts which is is important to be formed by mathematics.
CONCLUSION
Of description, I conclude that in the reality people at former epoch which have applied theory which still apply hitherto and mathematics are the source of from various science.
RESULT
Result which I earn and I perceive that is in our mathematics science recognize pythagoras triple. Real of the theorem have been recognized by people of Babylonia since year 1600 SM. Knowledge concerning this is theorem very him in tukar-menukar ( land barter) at that epoch. Someone example of having fairish a pice of land 50 x 50 square meters can convert him by 2 fairish land;ground area 30 x 30 square m and 40 x 40 square m. Besides, mathematics science also used many in other sciences. moment example of first time milk computer, some theory concepts which is is important to be formed by mathematics.
CONCLUSION
Of description, I conclude that in the reality people at former epoch which have applied theory which still apply hitherto and mathematics are the source of from various science.
Is Why Referred As Theorem of Pythagoras?
Theorem of Pythagoras or is often referred as Pythagoras triple is positive integer triple of a, b, and c fulfilling equation of a² +b² = c². Name of Triple Pythagoras given because the Pythagoras or pupil of believed as a which first time prove that the equation real apply in general at any right triangle with sides straighten and a of b hypotenusa and of c ( here a,b, and c do not have to is integer, but any number of real positive)
When Pythagoras Found
Theorem of Pythagoras express that hypotenuse square from right triangle is equal to amount of his foot/feet squares ( his elbow side ). This theorem is found at century of 6 SM by a so called Greek philosopher and mathematics of recognized Pythagoras also as " Father Number".
Langganan:
Postingan (Atom)
