By Christoph J. Scriba, Peter Schreiber, Jana Schreiber

ISBN-10: 3034808976

ISBN-13: 9783034808972

The current quantity presents a desirable review of geometrical principles and perceptions from the earliest cultures to the mathematical and inventive suggestions of the twentieth century. it's the English translation of the third variation of the well-received German e-book “5000 Jahre Geometrie,” during which geometry is gifted as a sequence 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 historic Greece. encouraged by means of the Greek arithmetic, a brand new germ of geometry blossomed within the Islamic civilizations. during the Oriental impression 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 throughout the Renaissance. including parallel achievements in India, China, Japan and the traditional American cultures, the ecu techniques shaped the information and branches of geometry we all know within the sleek age: coordinate tools, analytical geometry, descriptive and projective geometry within the seventeenth an 18th centuries, axiom structures, geometry as a thought with a number of buildings and geometry in laptop sciences within the nineteenth and twentieth centuries.

Each bankruptcy of the e-book 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 extra discover the issues of geometry in historical and smooth times.

The e-book will attract mathematicians attracted 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 isn't any similar work.

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

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

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

An very good publication in each recognize. The authors have effectively mixed the historical past of geometry with the final improvement of tradition and historical past. …

The image layout can be 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

Sample text

Alten] First, he mentions the art of counting and calculating; we will skip its justification here. Then, the dialogue partners agree on geometry as the second science. Again, its use for commanders of war is cited first: “Clearly, he said, we are concerned with that part of geometry which relates to war; for in pitching a camp, or taking up a position, or closing or extending the lines of an army, or any other military manoeuvre, whether in actual battle or on a march, it will make all the difference whether a general is or is not a geometrician.

This supposedly means that geometry was studied for its own sake, in contrast to acting according to rules given by necessities, practical life or sacred purposes. Hence, here lies the beginning of the development of pure mathematics. The number was at the core of Pythagoras’s religious-philosophical teaching. , the Pythagoreans developed the first foundations of number theory as well as a musical theory based on simple numeric ratios. When dealing with mathematical questions, they had the devastating cognition that irrational ratios exist.

Each of the four corner squares has the outer half (along a diagonal) cut off, which gives you an octagon approximated to the circle. Calculate its area and approximate it to the most proximate square root, from which you extract the root! Accordingly, this root is the side length of a square, which together with the circle of diameter d = 9 are almost of equal area. To what extent does the Egyptian formula result from that? b) In order to judge the quality of this approximation formula, calculate the resulting value for n with two digits after the comma!

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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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