Mathland: From Flatland to Hypersurfaces

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Springer Science & Business Media, 2004 - Architecture - 93 pages
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"Space "mutates" and is strictly dependent on our scientific concepts. The mutation of these concepts is important because even architecture mutates over time, changing with the various periods and variations in the tools that allow its realization. We can be certain of some of these relationships between the scientific concepts of space and architecture, the relationship between perspective, the architecture of Humanism and the Ptolemaic universe, or that of Cartesian space, of the Mongean projection system and the progressive birth of an architecture that was first a perspective and then more abstract and analytical. But what is happening today? Because if the concept of space has been mutated (and how!) and if the computer technology of this mutation is an agent to at least two or three different powers, then we are in a field of research as rich as it is difficult. We begin to understand the laws and see several possibilities. We are in a "topological" concept of space (we are not interested in the construction of geometric "absolutes" but in systems of families and possible relationships between forms) and are also working to create form in architecture and make spaces actually explorable in more dimensions than just the Cartesian ones."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
 

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Contents

from Euclid to The Death Star
18
What is Mathematics?
19
The Creation of Mathematics
22
The Infinite Space
31
The Fourth Dimension
36
Mathematics Cubism and Futurism
41
The Hypercube
46
3 The Enigma of Mathematics
58
Computers and Submarines
61
4 Topology
66
Final Observations
88
Further Reading
89
Copyright

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Page 7 - AN UNSPEAKABLE horror seized me. There was a darkness; then a dizzy, sickening sensation of sight that was not like seeing; I saw a Line that was no Line; Space that was not Space: I was myself, and not myself. When I could find voice, I shrieked aloud in agony, "Either this is madness or it is Hell.
Page 8 - Les lignes perpendiculaires à cet horizon donnent la profondeur. Or, la nature pour nous hommes est plus en profondeur qu'en surface, d'où la nécessité d'introduire dans nos vibrations de lumière, représentées par les rouges et les jaunes, une somme suffisante de bleutés, pour faire sentir l'air.
Page 8 - ... the characters in which it is written. It is written in mathematical language, and the characters are triangles, circles, and other geometric figures.

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About the author (2004)

Michele Emmer is Professor of Mathematics at Rome University "La Sapienza.

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