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Benno Artmann - One of the best experts on this subject based on the ideXlab platform.
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euclid the creation of mathematics
1999Co-Authors: Benno ArtmannAbstract:Preface *Notes to the reader *General historical remarks *The Origins of Mathematics I: The Testimony of Eudemus *Euclid: Book I *Origin of Mathematics 2: Parallels and Axioms *Origins of Mathematics 3: Pythagoras of Samos *Euclid: Book II *Origin of Mathematics 4: Squaring the Circle *Euclid: Book III *Origin of Mathematics 5: Problems and Theories *Euclid: Book IV *Origin of Mathematics 6: The Birth of Rigor *Origin of Mathematics 7: Polygons after Euclid *Euclid: Book V *Euclid: Book VI *Origin of Mathematics 8:Be Wise, Generalize *Euclid: Book VII *Origin of Mathematics 9: Nicomachus and Diophantus *Euclid:Book VIII *Origins of Mathematics 10: Tools and Theorems *Euclid: Book IX *Origin of Mathematics 11: Math is Beautiful *Euclid: Book X *Origins of Mathematics 12: Incommensurability and Irrationality *Euclid: Book XI *Origins of Mathematics 13: The Role of Defiinitions *Euclid: Book XII *Origins of Mathematics 14: The Taming of the Infinite *Euclid: Book XIII *Origin of Mathematics 15: Symmetry Through the Ages *Origin of Mathematics 16: The Origin of the Elements *Notes *Bibliography *Index
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the origin of mathematics 3 Pythagoras of Samos
1999Co-Authors: Benno ArtmannAbstract:Pythagoras lived about 570-490 B.C.E. The only roughly determined date in his life is ≈ 530, when he left Samos to settle in Crotona, in southern Italy. At Crotona he founded a religious and philosophical society that soon came to exert considerable political influence in the Greek cities of southern Italy. He was forced to leave Crotona about 500 and retired to Metapontum, where he died (see Fig. 6.1).
Abraham A Ungar - One of the best experts on this subject based on the ideXlab platform.
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the hyperbolic pythagorean theorem in the poincare disc model of hyperbolic geometry
American Mathematical Monthly, 1999Co-Authors: Abraham A UngarAbstract:Sometime in the sixth century B.C. Pythagoras of Samos discovered the theorem that now bears his name in Euclidean geometry. The extension of the Euclidean Pythagorean theorem to hyperbolic geometry, which is commonly known as the hyperbolic Pythagorean theorem (see [3, 5, 6, 9-11]), does not have a form analogous to the Euclidean Pythagorean theorem, so some authors have concluded that a truly hyperbolic Pythagorean theorem does not exist. For example, Wallace and West assert "the Pythagorean theorem is strictly Euclidean" since "in the hyperbolic [Poincare disc] model the Pythagorean theorem is not valid!" [15]. We show that a natural formulation of the hyperbolic Pythagorean theorem does exist: it expresses the square of the hyperbolic length of the hypotenuse of a hyperbolic right angled triangle as a natural "sum" of the squares of the hyperbolic lengths of the other two sides. The most general M6bius transformation of the complex unit disc D= {z: lzl < 1} in the complex z-plane [2,4,8],
Inta Volodko - One of the best experts on this subject based on the ideXlab platform.
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From Pythagoras to Archimedes
Boundary Field Problems and Computer Simulation, 2017Co-Authors: Aleksandrs Kovancovs, Inta VolodkoAbstract:In the history of mathematics, there are a lot of famous names, and much can be said about them. This paper is dedicated to some outstanding Ancient Greek mathematicians: Thales of Miletus, Pythagoras and Archimedes. Thales of Miletus can be considered the father of today's mathematics. His main achievement in mathematics was his idea about mathematical proof. Today, mathematics is not imaginable without proofs. Today's mathematics has undoubtedly taken a lot from Pythagoras of Samos Island. There are many interesting facts in the biography of Pythagoras. Pythagoras gathered around himself a group of young people, who started doing scientific research in philosophy and mathematics. This group was later named the School of Pythagoras. Under Pythagoras leadership, mathematics became the science in the meaning we understand it today, that is, mathematics started working with abstract numbers and geometrical figures. Here are some of Pythagorean achievements: they strengthened the idea of mathematical proof; they researched relationships between numbers and came to the concept of irrational numbers, without which today's mathematics is impossible; established the base for the regular polygon theory. Archimedes of Syracuse is another great mathematician of the ancient world. Archimedes devoted all his life to science and protecting his home town from attacks of the Roman fleet. Thanks to Archimedes, Syracuse was considered an inaccessible city for a long time. Archimedes discovered the lever law, invented the block system, screws and polyplastics to lift great weigh. He built war throwing machines that were able to throw huge stones to a great distance. Archimedes was not only a great mathematician, but also the greatest technician of the ancient world, under the leadership of whom a small group of people in a long period of time could resist the power of thousands of armed men.
Aleksandrs Kovancovs - One of the best experts on this subject based on the ideXlab platform.
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From Pythagoras to Archimedes
Boundary Field Problems and Computer Simulation, 2017Co-Authors: Aleksandrs Kovancovs, Inta VolodkoAbstract:In the history of mathematics, there are a lot of famous names, and much can be said about them. This paper is dedicated to some outstanding Ancient Greek mathematicians: Thales of Miletus, Pythagoras and Archimedes. Thales of Miletus can be considered the father of today's mathematics. His main achievement in mathematics was his idea about mathematical proof. Today, mathematics is not imaginable without proofs. Today's mathematics has undoubtedly taken a lot from Pythagoras of Samos Island. There are many interesting facts in the biography of Pythagoras. Pythagoras gathered around himself a group of young people, who started doing scientific research in philosophy and mathematics. This group was later named the School of Pythagoras. Under Pythagoras leadership, mathematics became the science in the meaning we understand it today, that is, mathematics started working with abstract numbers and geometrical figures. Here are some of Pythagorean achievements: they strengthened the idea of mathematical proof; they researched relationships between numbers and came to the concept of irrational numbers, without which today's mathematics is impossible; established the base for the regular polygon theory. Archimedes of Syracuse is another great mathematician of the ancient world. Archimedes devoted all his life to science and protecting his home town from attacks of the Roman fleet. Thanks to Archimedes, Syracuse was considered an inaccessible city for a long time. Archimedes discovered the lever law, invented the block system, screws and polyplastics to lift great weigh. He built war throwing machines that were able to throw huge stones to a great distance. Archimedes was not only a great mathematician, but also the greatest technician of the ancient world, under the leadership of whom a small group of people in a long period of time could resist the power of thousands of armed men.
Constantinos Macris - One of the best experts on this subject based on the ideXlab platform.
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approaching Pythagoras of Samos ritual natural philosophy and politics
Riedweg Christoph (2013). Approaching Pythagoras of Samos : Ritual natural philosophy and politics. In: Cornelli Gabriele; McKirahan Richard; Macris C, 2013Co-Authors: Christoph Riedweg, Gabriele Cornelli, Richard Mckirahan, Constantinos MacrisAbstract:The following paper adopts a rather peculiar three-step approach: Starting from general notions about Pythagoreanism and from the impact which Pythagorean ideas have had through the centuries to this day, it then tries to cautiously reconstruct at least some hypothetically authentic traits of the elusive Samian sage and his movement, interpreting the all too scanty evidence against the background of its contemporary Ionian natural philosophy and of modern sociological concepts. Finally, a bold attempt is made to elucidate Pythagoras' bewildering personality from comparable phenomena in today's society which are characterized by a similar blend of rational and irrational elements.
