Download e-book for iPad: 5000 Years of Geometry: Mathematics in History and Culture by Christoph J. Scriba, Peter Schreiber, Jana Schreiber

By Christoph J. Scriba, Peter Schreiber, Jana Schreiber

ISBN-10: 3034808976

ISBN-13: 9783034808972

The current quantity presents a desirable evaluation of geometrical principles and perceptions from the earliest cultures to the mathematical and inventive options of the 20 th century. it's the English translation of the third version of the well-received German ebook “5000 Jahre Geometrie,” during 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 historic cultures alongside the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in old Greece. encouraged by means of the Greek arithmetic, a brand new germ of geometry blossomed within the Islamic civilizations. throughout the Oriental effect on Spain, this data later unfold to Western Europe. right here, 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 eu techniques shaped the tips and branches of geometry we all know within the smooth age: coordinate tools, analytical geometry, descriptive and projective geometry within the seventeenth an 18th centuries, axiom platforms, geometry as a conception with a number of constructions and geometry in machine sciences within the nineteenth and twentieth centuries.

Each bankruptcy of the booklet begins with a desk of key historic and cultural dates and ends with a precis of crucial contents of geometry within the respective period. Compelling examples invite the reader to additional discover the issues of geometry in old and smooth times.

The e-book will attract 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 desire it will get a translation, as there isn't any similar work.

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

"Five Thousand Years of Geometry" - i believe it's the such a lot good-looking e-book i've got ever visible 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 latest York)

An very good e-book in each appreciate. The authors have effectively mixed the historical past of geometry with the final improvement of tradition and heritage. …

The picture layout is usually excellent.

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


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

Example text

11) The chord or segment base c was calculated according to c= d2 − (d − 2s)2 . 6). We are dealing here with the first steps of chord geometry, which was further developed by Hipparchus later on. Ptolemy placed this subject at the beginning of his great astronomic textbook (called “Almagest” by the Arabs; cf. 4). However, a notion of angle in general had not yet been developed in Babylonian mathematics; only the right angle occurs implicitly 22 1 The beginnings of geometrical representations and calculations Illus.

Then we connect DK and extend it until intersection Q with the cissoid. We draw the ordinate LM through Q perpendicularly to DC. Then LM and M C are the two mean proportionals for DO and OK: DM : LM = LM : M C = M C : M Q In addition, DM : M Q = DO : OK = a : b If we want to obtain the mean proportionals belonging to both given line segments a, b, we have to extend (or shorten) similarly the line segments DM, LM, M CandM Q according to level of measurement DM : a. Angle trisection The classical problem of dividing any angle into three equal parts kept many Greek mathematicians busy.

450–300 462–429 431–404 387 From 338 335 334–323 311 Approx. 0 Introduction Generally speaking, the Greeks are accepted to be the founders of the natural sciences, in other words, of rational explanations of natural phenomena based on principles and systems. At the same time, it was they who systemised and accounted for rules and instructions passed on (partially by the Oriental cultures) for counting, measuring and solving equations by means of a selfdeveloped logic. These were summarised into a system of theories, which made them the founders of scientific mathematics.

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

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