Art Meets Mathematics in the Fourth Dimension
Autor: | Lipscomb, Stephen Leon |
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EAN: | 9783319062532 |
Auflage: | 002 |
Sachgruppe: | Mathematik |
Sprache: | Englisch |
Seitenzahl: | 204 |
Produktart: | Gebunden |
Veröffentlichungsdatum: | 03.11.2014 |
Schlagworte: | Mathematik Mathematik / Philosophie, Geisteswissenschaften Topologie - Differenzialtopologie |
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To see objects that live in the fourth dimension we humans would need to add a fourth dimension to our three-dimensional vision. An example of such an object that lives in the fourth dimension is a hyper-sphere or ¿3-sphere.¿ The quest to imagine the elusive 3-sphere has deep historical roots: medieval poet Dante Alighieri used a 3-sphere to convey his allegorical vision of the Christian afterlife in his Divine Comedy. In 1917, Albert Einstein visualized the universe as a 3-sphere, describing this imagery as ¿the place where the reader¿s imagination boggles. Nobody can imagine this thing.¿ Over time, however, understanding of the concept of a dimension evolved. By 2003, a researcher had successfully rendered into human vision the structure of a 4-web (think of an ever increasingly-dense spider¿s web). In this text, Stephen Lipscomb takes his innovative dimension theory research a step further, using the 4-web to reveal a new partial image of a 3-sphere. Illustrations support the reader¿s understanding of the mathematics behind this process. Lipscomb describes a computer program that can produce partial images of a 3-sphere and suggests methods of discerning other fourth-dimensional objects that may serve as the basis for future artwork.