A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry) by Chris McMullen

Author:Chris McMullen
Language: eng
Format: azw3, epub
Publisher: Topher Books
Published: 2012-12-30T16:00:00+00:00

The two obvious cubes in the tesseract drawn above (filled with monkeys, but you have to imagine the monkeys yourself) are the inner and outer cubes. The large outside cube and small inside cube look like ordinary 3D cubes drawn in 2D in perspective. These two cubes lie in the usual xyz hyperplane; these diagonal lines are along z, corresponding to the usual 3D depth. These z edges converge to a depth vanishing point that is above and to the right of the tesseract. That leaves 6 more cubes to find. Where are they?

The last 6 cubes are top/bottom, right/left, and front/back. The first 2, inside/outside, correspond to the ana and kata cubes. The top/bottom, right/left, and front/back cubes don't look like ordinary 3D cubes drawn on a 2D sheet of paper. They appear to be shaped more like pyramids, but this is only an illusion created by hyperperspective. The w edges are all parallel, but don't look it; we see these w edges as if we're looking down a hyperhallway (compare with the 3D hallway picture from earlier in this chapter). The hyperdepth vanishing point, corresponding to the w edges, lies inside of the interior cube (where all of the w edges converge). All 4 pairs of parallel cubes that bound the above tesseract are shown below.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.