By Christoph J. Scriba, Peter Schreiber, Jana Schreiber
The current quantity offers a desirable review of geometrical principles and perceptions from the earliest cultures to the mathematical and creative options of the 20 th century. it's the English translation of the third version of the well-received German e-book “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, technology and engineering.
Geometry originated within the historic cultures alongside the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in historic Greece. encouraged via the Greek arithmetic, a brand new germ of geometry blossomed within the Islamic civilizations. throughout the Oriental impact on Spain, this information later unfold to Western Europe. the following, as a part of the medieval Quadrivium, the certainty of geometry used to be deepened, resulting in a revival through the Renaissance. including parallel achievements in India, China, Japan and the traditional American cultures, the ecu techniques shaped the tips and branches of geometry we all know within the glossy 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 computing device sciences within the nineteenth and twentieth centuries.
Each bankruptcy of the e-book starts off with a desk of key ancient 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 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'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 booklet i've got ever visible from Springer and the inclusion of such a lot of colour plates rather improves its visual appeal dramatically!
Prof. J.W. Dauben (City collage of latest York)
An first-class ebook in each appreciate. The authors have effectively mixed the background of geometry with the overall improvement of tradition and historical past. …
The photograph layout is additionally excellent.
Prof. Z. Nádenik (Czech Technical college in Prague)
Read or Download 5000 Years of Geometry: Mathematics in History and Culture PDF
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Extra resources for 5000 Years of Geometry: Mathematics in History and Culture
Account of the texts in [Waerden 1962]). Speaking purely geometrically, we can deal with this issue easily when generalising the problem of doubling the square (cf. 1). Speaking algebraically, we are dealing with the extension of extracting the square root to extracting the cubic root, which is an issue that had already been addressed by the Babylonians. 1) This formation of two geometrical means x, y between two given quantities (here: a, 2a) corresponds to a pure cubic equation, as springs to mind easily.
The diagonals of a rectangle are equal and halve each other. 6. The peripheral angle in a semi-circle is a right one. 36 2 Geometry in the Greek-Hellenistic era and late Antiquity The theorem stated last, known as Thales’ theorem, has been passed on by the female historian Pamphile (1st century AD), as reported by Diogenes Laertius (3rd century). In order to express his gratitude for recognising this fundamental fact, Thales is said to have sacriﬁced an ox to honour the gods! As we already know from the paragraphs on pre-Greek mathematics, the line segment and/or the straight line and the circle (next to the point) belong to the oldest geometrical elements.
Hence, it is clear that we must be dealing with a transcendental curve! Yet, we can easily describe it, since it is constructed by two simple movements. Imagine a square, the upper side of which moves parallel to the starting position with constant speed to the lower side. At the same time, the left side of the square turns clockwise around the lower corner point with constant angle speed in a manner such that both movements start and end simultaneously. In this case, the upper end of the turning line segment describes a quadrant within the square.