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 techniques of the 20 th 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 series of advancements in cultural historical past and their interplay with structure, the visible arts, philosophy, technology 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 by means of the Greek arithmetic, a brand new germ of geometry blossomed within the Islamic civilizations. in the course of 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 used to be 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 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 platforms, geometry as a conception with a number of buildings and geometry in desktop 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 historic and sleek times.
The e-book 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 related work.
Prof. J. Grattan-Guinness (Middlesex college London)
"Five Thousand Years of Geometry" - i feel it's the so much good-looking e-book i've got ever noticeable from Springer and the inclusion of such a lot of colour plates rather improves its visual appeal dramatically!
Prof. J.W. Dauben (City college of latest York)
An first-class ebook in each recognize. The authors have effectively mixed the heritage 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
500 BC). Aristotle was already referring to them as “Pythagoreans”; this school of thought died out during the course of the 4th century. (We must not confuse this movement with the so-called NeoPythagoreans, who followed up on the old school of thought from 100 AD onwards. ) Eudemus’s historical report, mentioned above, which unfortunately has been passed on only indirectly, states that Pythagoras is said to have turned geometrical knowledge into ‘free teaching’. 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.
In order to do so, he could have used the method of constructing areas described in Book II of Euclid’s ‘Elements’. Aristaeus knew (approx. 330) the correlation of these curves with the circular cone. He constructed the hyperbola (to be exact: a branch thereof), the parabola and also the ellipse as sections perpendicular to a generating line of an obtuse, a right-angled and an acute (perpendicular) circular cone. He dealt with these curves in a (lost) treatise on such “bodily” loci thus called because they were derived from the solid of a cone.
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 ) .
5000 Years of Geometry: Mathematics in History and Culture by Christoph J. Scriba, Peter Schreiber, Jana Schreiber