ALL ABOut mathematic...
In this page, i will introduce some opinion about ancient mathematich and mathematich in now period. Time and place in the past and present have relationship with history of mathematic.
1. I found that mathematic concept, mathematic problem and solving in ancient period that in now :
a. Phytagoras Theorm
Phytagoras theorm was found by babilonians at 1000 BC ago. But Phytagoras proved the best of pythagoras theorm mathematically. The theorem called “the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle)”.
b. Logic
Aristoteles is the first finding logic. Logic use to explanation sentense. Although, some times used to give conclusion.
c. algebra from al khawarizmi, calculus from newton and lebneiz, derivate, probability, etc.
2. I found mathematic concept, Problem and solving mathematic in old period whom don’t use in this period :That is π = 3,125 from babilonia, he tables of square root, tables of rank three and rank two. The traditional equipment not use in today.
3. I found mathematic concept, Problem and solving mathematic not relationship with ancient period. :
The modern technology. For example computer use to 2 digits for operation it`s 1 and zero. Calculating with finger, sempoa, etc.
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Sunday, January 11, 2009
Foundations of mathematics
The foundation mathematich very important. This is used to some field of mathematich. Such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
The foundation give much assumption from philosophy of mathematich. For example the the assumstion from plato, aristoteles, brouwer, immanuel kant, etc .
The main of Foundation of mathematich it is :
1. Platonism..
Platonism is from plato. Platonism is veru important for mathematich method. He is the son of Ariston and Perictione, was born in Athens. The foundational philosophy of Platonist mathematical realism, as give by mathematician Kurt Gödel. The platonism is term of plato cave. The Follow of plato mathematic as ideal’s. This mathematic are be found in your idea.
2. Intuitionism
Intuitionism is from LEJ Brouwer, it is contends the primary objects of mathematical discourse are mental constructions governed by self-evident laws. Intuitionists have challenged many of the oldest principles of mathematics as being nonconstructive and hence mathematically meaningless. intuitionism is a program of methodological reform whose motto is that "there are no non-experienced mathematical truths. In intuitionism, the term "explicit construction" is not cleanly defined, and that has led to criticisms
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The foundation mathematich very important. This is used to some field of mathematich. Such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
The foundation give much assumption from philosophy of mathematich. For example the the assumstion from plato, aristoteles, brouwer, immanuel kant, etc .
The main of Foundation of mathematich it is :
1. Platonism..
Platonism is from plato. Platonism is veru important for mathematich method. He is the son of Ariston and Perictione, was born in Athens. The foundational philosophy of Platonist mathematical realism, as give by mathematician Kurt Gödel. The platonism is term of plato cave. The Follow of plato mathematic as ideal’s. This mathematic are be found in your idea.
2. Intuitionism
Intuitionism is from LEJ Brouwer, it is contends the primary objects of mathematical discourse are mental constructions governed by self-evident laws. Intuitionists have challenged many of the oldest principles of mathematics as being nonconstructive and hence mathematically meaningless. intuitionism is a program of methodological reform whose motto is that "there are no non-experienced mathematical truths. In intuitionism, the term "explicit construction" is not cleanly defined, and that has led to criticisms
____^_^_the end____
Saturday, January 10, 2009
History of Mathematics according to Figures
History of Mathematics according to Figures
1. THALES (624 BC - 550 BC)
( Greek mathematician)
- The first mathematician found theorem.
- Finding the comparison sides of triangle is 3 : 4 : 5
- Finding the diameter radian theorem
- Finding the congruent triangle theorem
- Geometry and Astronomy expert
2. PYTHAGORAS (569 BC-500 BC)
( Greek mathematician)
- Dissenter of irrational magnitude and zero
- Discovering axioms and postulats
- Proved the best of pythagoras theorm mathematically
- Finding of interval tone And the ratio of number
- Proved Sulbasutra’s theorem
- Presentation of numeral and explain the meaning of dot (.)
3. ARCHYTAS (428 BC-347 BC)
( Greek mathematician)
- sought to combine empirical observation with Pythagorean theory
- applied the theory of proportions to musical harmony
- solved the problem of doubling the cube by an ingenious construction in solid geometry using the intersection of a cone, a sphere, and a cylinder.
4. EUDOXUS (408 BC-355 BC)
( Greek mathematician)
- contributions to the early theory of proportions (equal ratios) forms the basis for the general account of proportions found in Book V of Euclid's Elements .
- contributed a solution to the problem of doubling the cube. that is, the construction of a cube with twice the volume of a given cube
- Eudoxus's proof of the latter began by assuming that the cone and cylinder are commensurable, before reducing the case of the cone and cylinder being incommensurable to the commensurable case.
- proved that the areas of circles are proportional to the squares of their diameters.
5. EUCLIDES (408 BC-355 BC)
( Greek mathematician)
- He is “ Geometry Father”
- A writer of “ The Elements ” , it contains 13 books :
I. Geometry bases
II. Geometry algebraic
III. Circle theories
IV. Make lines and curves
V. Abstract proportion theory
VI. Proportion geometry
VII. Numeral theory bases
VIII. Numeral theory proportion
IX. Numeral theory
X. Classification
XI. Three dimension of geometry
XII. Measuring of shapes
XIII. Three dimension shapes
- The Euclidean corpus falls into two groups: elementary geometry and general mathematics.
6. ARISTOTELES ( 384 - 322 BC)
( Greek mathematician)
- Aristotle's writings show that even he realized that there is more to logic than syllogistic.
- Aristotle's claim to be the founder of logic rests primarily on the Categories, the De interpretatione, and the Prior Analytics, which deal respectively with words, propositions, and syllogisms
7. ARCHIMEDES (287 BC-212 BC)
( Greek mathematician)
- discovering of the relation between the surface and volume of a sphere and its circumscribing cyclinder. The surface area of a sphere is 4πr2 and the surface area of the circumscribing cylinder is 6πr2
- have three masterpiece which studying area flat geometry measurement of circle, kuadratur of and spiral parabola.
- contribution was rather to extend these concepts to conic sections.
- Earlier using big calculating method
8. APOLLONIUS (260 BC-200 BC)
( Greek mathematician)
- known by his contemporaries as “the Great Geometer,” whose treatise Conics is one of the greatest scientific works from the ancient world.
- inspired much of the advancement of geometry in the Islamic world in medieval times, and the rediscovery of his Conics in Renaissance Europe formed a good part of the mathematical basis for the scientific revolution.
- defining terms like parabola, elliptical, and hyperbola.
- Giving instruction concerning enumeration technique quickly.
9. DIOPHANTUS (200BC- 250BC)
( Greek mathematician)
- large and extremely influential treatise upon which all the ancient and modern fame of Diophantus reposes, is his Arithmetica.
- the first known work to employ algebra in a modern style
- inspiring the rebirth of number theory.
- Finding equation of quadrate which has two roots
10. MUHAMAD IBN Mūsā AL-Khwārizmī (780 C-850 C)
(Irak mathematician)
- He is “ Father Algebra”
- working on elementary algebra, al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr waʾl-muqābala was translated into Latin in the 12th century, from which the title and term Algebra derives.
- working by al-Khwārizmī introduced Hindu-Arabic numerals (see numerals and numeral systems) and their arithmetic to the West.
- Compiling a set of astronomical tables (Zīj), based on a variety of Hindu and Greek sources. This work included a table of sines, evidently for a circle of radius 150 units
11. RENE DESCARTES (1596-1650 C)
(French mathematician)
- the first to abandon scholastic Aristotelianism.
- Expressing in the dictum “I think, therefore I am” (best known in its Latin formulation, “Cogito, ergo sum,” though originally written in French, “Je pense, donc je suis”).
- developing a metaphysical dualism.
- investigating reports of esoteric knowledge
- Inventing analytic geometry, a method of solving geometric problems algebraically and algebraic problems geometrically
12. PIERRE DE FERMAT (1601-1665 C)
(French mathematician)
- the founder of the modern theory of numbers.
- Discovering the fundamental principle of analytic geometry
- finding tangents to curves and their maximum and minimum points led him to be regarded as the inventor of the differential calculus.
- co-founder of the theory of probability.
- Solving the related problem of finding the surface area of a segment of a paraboloid of revolutio
13. ISAAC NEWTON (1642-1727 C)
(English mathematician)
- he was the original discoverer of the infinitesimal calculus
- A writer of Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)
14. LEONHARD EULER (1707-1783 C)
(Swiss mathematician)
- The founders of pure mathematics
- The made decisive and formative contributions to the subjects of geometry, calculus, mechanics, and number theory
- Developing methods for solving problems in observational astronomy and demonstrated useful applications of mathematics in technology and public affairs.
- carried integral calculus to a higher degree of perfection, developed the theory of trigonometric and logarithmic functions, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics
- developing the concept of function in mathematical analysis
15. CARL FRIEDRICH GAUSS (1777-1855 C)
( German mathematician)
- contributing to number theory, geometry, probability theory, geodesy, planetary astronomy, the theory of functions, and potential theory (including electromagnetism)
- discovering a regular polygon of 17 sides can be constructed by ruler and compass alone.
- publishing works on number theory, the mathematical theory of map construction, and many other subjects.
16. AUGUSTUS DE MORGAN (1806-1871 C)
(English mathematician)
- Contributing to the study of logic include the formulation of De Morgan's laws
- Developing of the theory of relations and the rise of modern symbolic, or mathematical, logic
- recognizing the purely symbolic nature of algebra, and he was aware of the possibility of algebras that differ from ordinary algebra
17. GEORGE CANTOR (1845-1918 C)
(German historian of mathematics)
- A writer of “Mathematische Beiträge zum Kulturleben der Völker “(1863; “Mathematical Contributions to the Cultural Life of the People”)
- Considering one of the finest published histories of mathematics
¬¬¬¬___^_^__the end_____
1. THALES (624 BC - 550 BC)
( Greek mathematician)
- The first mathematician found theorem.
- Finding the comparison sides of triangle is 3 : 4 : 5
- Finding the diameter radian theorem
- Finding the congruent triangle theorem
- Geometry and Astronomy expert
2. PYTHAGORAS (569 BC-500 BC)
( Greek mathematician)
- Dissenter of irrational magnitude and zero
- Discovering axioms and postulats
- Proved the best of pythagoras theorm mathematically
- Finding of interval tone And the ratio of number
- Proved Sulbasutra’s theorem
- Presentation of numeral and explain the meaning of dot (.)
3. ARCHYTAS (428 BC-347 BC)
( Greek mathematician)
- sought to combine empirical observation with Pythagorean theory
- applied the theory of proportions to musical harmony
- solved the problem of doubling the cube by an ingenious construction in solid geometry using the intersection of a cone, a sphere, and a cylinder.
4. EUDOXUS (408 BC-355 BC)
( Greek mathematician)
- contributions to the early theory of proportions (equal ratios) forms the basis for the general account of proportions found in Book V of Euclid's Elements .
- contributed a solution to the problem of doubling the cube. that is, the construction of a cube with twice the volume of a given cube
- Eudoxus's proof of the latter began by assuming that the cone and cylinder are commensurable, before reducing the case of the cone and cylinder being incommensurable to the commensurable case.
- proved that the areas of circles are proportional to the squares of their diameters.
5. EUCLIDES (408 BC-355 BC)
( Greek mathematician)
- He is “ Geometry Father”
- A writer of “ The Elements ” , it contains 13 books :
I. Geometry bases
II. Geometry algebraic
III. Circle theories
IV. Make lines and curves
V. Abstract proportion theory
VI. Proportion geometry
VII. Numeral theory bases
VIII. Numeral theory proportion
IX. Numeral theory
X. Classification
XI. Three dimension of geometry
XII. Measuring of shapes
XIII. Three dimension shapes
- The Euclidean corpus falls into two groups: elementary geometry and general mathematics.
6. ARISTOTELES ( 384 - 322 BC)
( Greek mathematician)
- Aristotle's writings show that even he realized that there is more to logic than syllogistic.
- Aristotle's claim to be the founder of logic rests primarily on the Categories, the De interpretatione, and the Prior Analytics, which deal respectively with words, propositions, and syllogisms
7. ARCHIMEDES (287 BC-212 BC)
( Greek mathematician)
- discovering of the relation between the surface and volume of a sphere and its circumscribing cyclinder. The surface area of a sphere is 4πr2 and the surface area of the circumscribing cylinder is 6πr2
- have three masterpiece which studying area flat geometry measurement of circle, kuadratur of and spiral parabola.
- contribution was rather to extend these concepts to conic sections.
- Earlier using big calculating method
8. APOLLONIUS (260 BC-200 BC)
( Greek mathematician)
- known by his contemporaries as “the Great Geometer,” whose treatise Conics is one of the greatest scientific works from the ancient world.
- inspired much of the advancement of geometry in the Islamic world in medieval times, and the rediscovery of his Conics in Renaissance Europe formed a good part of the mathematical basis for the scientific revolution.
- defining terms like parabola, elliptical, and hyperbola.
- Giving instruction concerning enumeration technique quickly.
9. DIOPHANTUS (200BC- 250BC)
( Greek mathematician)
- large and extremely influential treatise upon which all the ancient and modern fame of Diophantus reposes, is his Arithmetica.
- the first known work to employ algebra in a modern style
- inspiring the rebirth of number theory.
- Finding equation of quadrate which has two roots
10. MUHAMAD IBN Mūsā AL-Khwārizmī (780 C-850 C)
(Irak mathematician)
- He is “ Father Algebra”
- working on elementary algebra, al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr waʾl-muqābala was translated into Latin in the 12th century, from which the title and term Algebra derives.
- working by al-Khwārizmī introduced Hindu-Arabic numerals (see numerals and numeral systems) and their arithmetic to the West.
- Compiling a set of astronomical tables (Zīj), based on a variety of Hindu and Greek sources. This work included a table of sines, evidently for a circle of radius 150 units
11. RENE DESCARTES (1596-1650 C)
(French mathematician)
- the first to abandon scholastic Aristotelianism.
- Expressing in the dictum “I think, therefore I am” (best known in its Latin formulation, “Cogito, ergo sum,” though originally written in French, “Je pense, donc je suis”).
- developing a metaphysical dualism.
- investigating reports of esoteric knowledge
- Inventing analytic geometry, a method of solving geometric problems algebraically and algebraic problems geometrically
12. PIERRE DE FERMAT (1601-1665 C)
(French mathematician)
- the founder of the modern theory of numbers.
- Discovering the fundamental principle of analytic geometry
- finding tangents to curves and their maximum and minimum points led him to be regarded as the inventor of the differential calculus.
- co-founder of the theory of probability.
- Solving the related problem of finding the surface area of a segment of a paraboloid of revolutio
13. ISAAC NEWTON (1642-1727 C)
(English mathematician)
- he was the original discoverer of the infinitesimal calculus
- A writer of Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)
14. LEONHARD EULER (1707-1783 C)
(Swiss mathematician)
- The founders of pure mathematics
- The made decisive and formative contributions to the subjects of geometry, calculus, mechanics, and number theory
- Developing methods for solving problems in observational astronomy and demonstrated useful applications of mathematics in technology and public affairs.
- carried integral calculus to a higher degree of perfection, developed the theory of trigonometric and logarithmic functions, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics
- developing the concept of function in mathematical analysis
15. CARL FRIEDRICH GAUSS (1777-1855 C)
( German mathematician)
- contributing to number theory, geometry, probability theory, geodesy, planetary astronomy, the theory of functions, and potential theory (including electromagnetism)
- discovering a regular polygon of 17 sides can be constructed by ruler and compass alone.
- publishing works on number theory, the mathematical theory of map construction, and many other subjects.
16. AUGUSTUS DE MORGAN (1806-1871 C)
(English mathematician)
- Contributing to the study of logic include the formulation of De Morgan's laws
- Developing of the theory of relations and the rise of modern symbolic, or mathematical, logic
- recognizing the purely symbolic nature of algebra, and he was aware of the possibility of algebras that differ from ordinary algebra
17. GEORGE CANTOR (1845-1918 C)
(German historian of mathematics)
- A writer of “Mathematische Beiträge zum Kulturleben der Völker “(1863; “Mathematical Contributions to the Cultural Life of the People”)
- Considering one of the finest published histories of mathematics
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