By Christoph J. Scriba, Peter Schreiber, Jana Schreiber

The current quantity offers a desirable evaluation of geometrical principles and perceptions from the earliest cultures to the mathematical and creative recommendations of the 20 th century. it's the English translation of the third variation of the well-received German ebook “5000 Jahre Geometrie,” during which geometry is gifted as a series of advancements in cultural historical past and their interplay with structure, the visible arts, philosophy, technology and engineering.

Geometry originated within the old cultures alongside the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in old Greece. encouraged by way of the Greek arithmetic, a brand new germ of geometry blossomed within the Islamic civilizations. in the course of the Oriental impact on Spain, this data later unfold to Western Europe. the following, as a part of the medieval Quadrivium, the certainty of geometry was once deepened, resulting in a revival through the Renaissance. including parallel achievements in India, China, Japan and the traditional American cultures, the ecu methods 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 thought with a number of constructions and geometry in laptop sciences within the nineteenth and twentieth centuries.

Each bankruptcy of the booklet starts off with a desk of key old 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 ebook 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 related 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 obvious from Springer and the inclusion of such a lot of colour plates fairly improves its visual appeal dramatically!

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

An very good e-book in each admire. The authors have effectively mixed the background of geometry with the overall improvement of tradition and background. …

The image layout is usually excellent.

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

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

**Example text**

The analysis of structures found in nature led repeatedly to new mathematical theories, which were then used to explain or visualise further natural (later also economic, social and other) phenomena. The mutual interlocking of empirical observation and scientiﬁc theoretical formation is not just characteristic for natural sciences, but also for the historical development of mathematical thinking. Thereby, we do not want to deny that there were repeated phases, in which inspiration for developing mathematical theories originated from mathematics itself.

Other researchers attempted a number-theoretic interpretation based on reciprocal number pairs. In both cases, we would be dealing with a highly abstract text, which until then had not been demonstrable in Mesopotamian mathematics. Besides, our knowledge of the Babylonian angle concept contradicts a trigonometric interpretation. Since the view had been accepted during the last decades that such texts should not be analysed in isolation but under consideration of the entire cultural environment, both interpretations were doubted, especially the one by Eleanor Robson [Robson 2001].

Alten] 20 1 The beginnings of geometrical representations and calculations Illus. 9 Babylonian polygons. [Kurt Vogel: Vorgriechische Mathematik (Pre-Greek Mathematics), part II. Illus. 69: M´emoires de la Mission Arch´eologique fran¸caise en Iran, Tome XXXIV p. 12] [Bruins and Rutten, published by Paul Geuthner, Paris 1961] length (x). 4). The widespread division problems also form a part of geometry. For instance, if we want to divide any four-sided ﬁeld with the sides a, b, c, d into two parts of equal area by means of a transversal x, which runs from b to d, we follow the instruction below: x= (a2 + c2 ) .

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