## Mathland: From Flatland to Hypersurfaces"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 |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

89 | |

### Common terms and phrases

19th century Abbott abstract Alan Turing Alicia Imperiale analogy architects artists avant-garde Banchoff beautiful Berkel calculations completely computer graphics concept configuration construction created Cubism Cubist cultural Definition deformation Digital dimensional Divine Cube Elements Enigma machine esthetic Euclid Euclidean geometry Euclidean space example fact famous film Hypercube four four-dimensional object four-dimensional space fourth dimension Futurists GCCS geometric figures Greek hyperspace Hypersphere hypersurface idea of space images imagine important infinite inhabitants of Flatland interesting intuition invented ISBN Jouffret Klein Bottle leap logic mathe mathematicians mathematics Mathland Max Bill Michele Emmer Mobius House Mobius Strip mutation nature non-Euclidean geometry numbers Osserman painting perspective plane Poincare possible problems projections Robert Musil rotors scientific sional solid space-time spatial Sphere Square story straight line structure surface theory thought three dimensions three-dimensional space tion tool topology transformation true understand universe virtual visual words writes wrote

### Popular passages

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.