Mathland: From Flatland to Hypersurfaces
IT Revolution in Architecture is a series which looks at architecture in the light of the electronic revolution, reflecting on the effects which the virtual dimension is having on architects and architecture in general. Each volume examines a single topic, highlighting the essential aspects and exploring their relevance for the architects of today. How the latest forms of mathematics help us shape the space around us - the fascinating story of a radical transformation. The latest book in our successful series IT Revolution in Architecture provides a concise summary of how our perception of the space around us has radically changed in recent years. We could even go as far as to say that we ourselves shape the space around us according to how our perceptions of the universe alter and develop, and mathematics plays a pivotal role. In this book, the "virtual" protagonist of the journey through the concept of space is the square.
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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
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.