n-Dimensional geometry.

Discussion in 'Physics & Math' started by Dinosaur, Oct 22, 2017.

  1. Dinosaur Rational Skeptic Valued Senior Member

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    When time is used as a 4th dimension, the mathematics describes a static universe. This can be useful because there are well developed mathematical disciplines (most notably Differential or Metric geometry) which deal with geometry in more than 3 dimensions, providing some insights into the laws of physics which are not intuitively obvious.

    There are formulas for the volume & surface area of spheres & other objects in spaces of more than 3 dimensions. Google will provide formulas. Some of the results are counter intuitive. The following is one example.

    Visualize a 3D sphere embedded in a cube with a 3D sphere in each corner. The spheres in the corners are much smaller than the central sphere. For higher dimensional spaces, the spheres in the corners can be larger that the central sphere.​
     

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