Geometry

Read e-book online 5000 Years of Geometry: Mathematics in History and Culture PDF

By Christoph J. Scriba, Peter Schreiber, Jana Schreiber

ISBN-10: 3034808976

ISBN-13: 9783034808972

The current quantity presents a desirable evaluate of geometrical principles and perceptions from the earliest cultures to the mathematical and inventive strategies of the 20 th century. it's the English translation of the third variation 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 old 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. during the Oriental impression on Spain, this data later unfold to Western Europe. right here, 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 eu 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 idea with a number of buildings 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 sleek times.

The ebook will entice 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's no similar work.

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

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

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

According to the legend, as a result of revealing the secret, he was banned from the Pythagorean community and perished at sea. A possible trigger could have been studying the ratio of side s and diagonal d of a square: the Pythagorean Theorem immediately results in d2 = 2 · s2 . Hereby, we can quickly derive a contraction, if we assume s and d as numbers and use the natural number properties ‘even’ and ‘uneven’. 1 Ionian era Illus. 7 Memorial of Pythagoras on the isle of Samos [Photo: R. Tobies] 39 40 2 Geometry in the Greek-Hellenistic era and late Antiquity Illus.

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. 6 Regular hexagon inscribed in the circle Every angle at the centre here equals 60◦ or a sixth of four right angles. Since each angle at the centre lies opposite to a triangle side of length r (r = radius), the other two angles also equal 60◦ , thus, 3 × 60◦ = 180◦ = 2R.

11 Plimpton 322; Old Mesopotamian text in cuneiform (Plimpton Library, Columbia University, New York). The text contains a list of right-angled triangles with integer sides h, w and d. A few columns on the left have broken off. The second and third column feature width w and the diagonal (hypotenuse) d in integers. The last column specifies the ongoing row numbering. In rows 11 and 15 values w and d have a common factor; in all other instances they are coprime [Neugebauer/Sachs 1945]. It seemed that this text contained a type of trigonometric table, fitting in the great number of tables which we have from Mesopotamia.

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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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