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In the mathematical field of topology, a homeomorphism or topological isomorphism or bicontinuous function (from the Greek words ?????? (homoios) = similar and ????? (morph?) = shape, form) is a continuous function between two topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces ? that is, they are the mappings which preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. Roughly speaking, a topological space is a geometric object, and the homeomorphism is a continuous stretching and bending of the object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not. An often-repeated joke is that topologists can't tell the coffee cup from which they are drinking from the donut they are eating, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle. ... Read more

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Publisher: Oxford At The Clarendon Press.Publication date: 1921Subjects: NATURAL SCIENCESAstronomy. Astrophysics. Space research.GeodesyAstronomical instruments and techniquesNotes: This is an OCR reprint. There may be numerous typos or missing text. There are no illustrations or indexes.When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. ... Read more

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Sir Thomas Heath (1861 – 1940) was a British civil servant, mathematician, scholar, historian, translator, and mountaineer.He translated the works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes into English.It is primarily through Heath’s translations that modern English-speaking readers are aware of Archimedes’ work.A history of Greek Mathematics was published in 1921. ... Read more

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The book has no illustrations or index. It may have numerous typos or missing text. However, purchasers can download a free scanned copy of the original rare book from the publisher's website (GeneralBooksClub.com). You can also preview excerpts of the book there. Purchasers are also entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Original Publisher: Oxford, The Clarendon press; Publication date: 1921; Subjects: Mathematics, Greek; Mathematics, Greek; Science / General; Mathematics / History ... Read more

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Reprint of Cambridge University press edition of 1910. Paperback. 387 pp. Diophantus of Alexandria, sometimes called "the father of algebra", was an Alexandrian mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations, many of which are now lost. In studying Arithmetica, Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of diophantine equations ("diophantine geometry") and of diophantine approximations remain important areas of mathematical research. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation. Heath's work is one of the standard books in the field. ... Read more

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Originally published in 1877-84.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

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In The Visual Poetics of Power, Nassos Papalexandrou illuminates the early history of the tripod cauldron, the most sacred symbol of the Greeks. He also explores the performative dimensions of the figurative arts in the preliterate contexts of early Greek sanctuaries. ... Read more

Customer Reviews (2)

Very interesting but could be more helpful
This in an opinionated and confident history of Greek mathematics. On issues of interpretation and historiography, a few sections are original and many are based on the classical German literature, not readily available to the modern reader. The problem is with the mathematics, where van der Waerden is very unhelpful. He follows the standard practice of simply reproducing or lightly paraphrasing the original sources. A typical section on Archimedes, which almost entirely lacks commentary, simply reproduces a number of proof and ends "All this is found in Archimedes, in essentially the same words" (p. 220). This is especially ironic since van der Waerden himself portrays as a main reason for the demise of Greek geometry "the difficulty of the written tradition" (p. 266): "An oral explanation makes it possible to indicate the line segments with the fingers; one can emphasize essentials and point out how the proof was found. All of this disappears in the written formulation of the strictly classical style. The proofs are logically sound, but they are not suggestive. One feels caught in a logical mousetrap, but one fails to see the guiding line of thought. As long as there were no interruption, as long as each generation could hand over its method to the next, everything went well and science flourished. But as soon as some external cause brought about an interruption in the oral tradition, and only books remained, it became extremely difficult to assimilate the work of the great precursors and next to impossible to pass beyond it." (p. 266). This is exactly how we feel. It seems obvious, then, that a good history of Greek mathematics will aspire to recreate the qualities here ascribed to the oral traditions. Unfortunately, van der Waerden is generally happy to reproduce the "logical mousetraps" and leave it at that. One further point is important to remember in this context. Today's mathematics tends to be congenial to "logical mousetraps" and shun intuition and applications. In Antiquity it was probably the other way around: it was precisely the mathematicians who were striving for more intuition and applications, while philosophical and other prejudices were exactly opposed to such a development. This inversion of the current roles is indicated in Plutarch: "Plato himself censured those ... who wanted to reduce the duplication of the cube to mechanical constructions, because [it is based on] a non-theoretical method; for in this manner the good in geometry is destroyed and brought to naught, because geometry reverts to observation instead of raising itself above this and adhering to the eternal, immaterial images in which the immanent God is the eternal God." (p. 163). In other words: the surviving mathematical texts are "censured" by non-mathematicans on non-mathematical grounds, whereas the subject matter screams out for a less formalistic treatment.

Make no mistake, this is a math book -
A comparable book might be an Introduction to Algebra book.Complete with descriptions and examples of usage (and of course history).Ifyou're interested in knowing more about Babylonian sexagesimal notation, Egyptian fractions, poetic numbers, Pythagoras, Plato or Hellenistic science interest you then this is a good source for the material and thankfully it has been translated into English.While I believe the translation was accurate, this can be a sleeper if you're not fond of numbers or their manipulation. ... Read more