Download 5000 Years of Geometry: Mathematics in History and Culture by Christoph J. Scriba, Peter Schreiber, Jana Schreiber PDF

By Christoph J. Scriba, Peter Schreiber, Jana Schreiber

The current quantity presents a desirable evaluation of geometrical principles and perceptions from the earliest cultures to the mathematical and inventive ideas of the twentieth century. it's the English translation of the third version of the well-received German e-book “5000 Jahre Geometrie,” within which geometry is gifted as a series of advancements in cultural heritage and their interplay with structure, the visible arts, philosophy, technological know-how and engineering.

Geometry originated within the historical cultures alongside the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in historical Greece. encouraged via the Greek arithmetic, a brand new germ of geometry blossomed within the Islamic civilizations. throughout the Oriental impact on Spain, this information later unfold to Western Europe. the following, as a part of the medieval Quadrivium, the knowledge of geometry was once deepened, resulting in a revival in the course of the Renaissance. including parallel achievements in India, China, Japan and the traditional American cultures, the ecu techniques shaped the tips and branches of geometry we all know within the glossy age: coordinate equipment, analytical geometry, descriptive and projective geometry within the seventeenth an 18th centuries, axiom platforms, geometry as a conception with a number of buildings and geometry in computing device sciences within the nineteenth and twentieth centuries.

Each bankruptcy of the publication starts off with a desk of key ancient and cultural dates and ends with a precis of crucial contents of geometry within the respective period. Compelling examples invite the reader to extra discover the issues of geometry in historical and sleek times.

The booklet will entice mathematicians drawn to Geometry and to all readers with an curiosity in cultural history.

From letters to the authors for the German language edition

I wish it will get a translation, as there is not any similar work.

Prof. J. Grattan-Guinness (Middlesex collage London)

"Five Thousand Years of Geometry" - i feel it's the so much good-looking ebook i've got ever noticeable from Springer and the inclusion of such a lot of colour plates fairly improves its visual appeal dramatically!

Prof. J.W. Dauben (City collage of recent York)

An first-class ebook in each recognize. The authors have effectively mixed the background of geometry with the overall improvement of tradition and historical past. …

The photograph layout can be excellent.

Prof. Z. Nádenik (Czech Technical college in Prague)

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Additional resources for 5000 Years of Geometry: Mathematics in History and Culture

Example text

In this case, we would be dealing with a collection of problems on Pythagorean triples, for which in the second column preferably simple numeric values were chosen, whose geometrical relation is yet unclear. This interpretation eliminates the special position, which tablet Plimpton 322 had been assigned by the previous description of Mesopotamian mathematics. The belief that trigonometry already existed approx. 4000 years ago has been reduced to a mere myth. However, this tablet remains a unique compilation of Pythagorean triples to date, which are connected to each other by a quadratic relation.

1 Ionian era 37 Illus. 5 Rectangle with circumcircle Thus, we can derive the theorem immediately by looking at the shape: “The sum of angles in a triangle equals two right angles” (first, for all right-angled triangles, then also for any triangle in which we still need to draw a height h). , probably the subsequent generation. Besides, the theorem was proved independently for both the equilateral and the isosceles triangle. Concerning the latter, the rectangular shape in the circle could have served again as the basis of evidence and the isosceles triangle itself suggests consideration of the hexagon inscribed in the circle, which can be viewed as one of the original geometrical shapes: Illus.

See Illus. 4: Applying the binomial formula In the text from the Seleucids’ era (BM 34568), obviously composed for teaching purposes, occurs a rectangle with the sides a = 4, b = 3, for whose diagonals d we are given the terms d = a/2 + b and d = b/3 + a. Then we are supposed to calculate the three pieces a, b and d by means of the quantities a + d and b or b + d and a. Other than that, we can use a − b = 1 and A = a · b = 12, or a + b = 7 and A = a · b = 12. a) Solve these problems according to the modern method!

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