Lipscomb S. Art Meets Mathematics in the Fourth Dimension

Springer, 2014. — 204 p. 147 illus., 28 illus. in color. — 2nd ed. — ISBN: 3319062530, 9783319062549To 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.
Keywords » 3-sphere - 4-web - art and mathematics - fourth dimension - fractals - hypersphereContents: