4th dimension

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four dimensional shapes are shown with the text, understand and draw three dimensional cubes

People tell me they have trouble understanding the concept of multiple dimensions. We supposedly live in a 4 dimensional world (the 4th being time). Dimension as mathematicians use the term means orthogonal. Each orthogonal means 90 degrees away. Each higher dimension is orthogonal to the lower dimension. A line is one dimension a square is two dimensions and a cube...

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Shadow of a rotating cube The animations below accompany an introductory talk on high-dimensional geometry. Mathematically, the second was made by putting a "light source" at a point (0,0,0,h)(0,0,0,h) (with h>0h>0) and sending each point (x,y,z,w)(x,y,z,w) (with w<hw<h) to hh−w(x,y,z)hh−w(x,y,z).

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three dimensional cubes are shown in the diagram

Living in a 3-dimensional world, we can easily visualize objects in 2 and 3 dimensions. But as a mathematician, playing with only 3 dimensions is limiting, Dr. Henry Segerman laments. An Assistant Professor in Mathematics at Oklahoma State University, Segerman spoke to Duke students and faculty on visualizing 4-dimensional space as part of the PLUM lecture series on […]

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