2

I am interesting about the geometric properties of 3-D spheres and I know nothing about hyper-spheres. Please can you describe me, what is a hyper-sphere?

Bumblebee
  • 18,220
  • 5
  • 47
  • 87

1 Answers1

4

A hypersphere (or $n$-sphere) is the set of points in $n$-dimensional space such that the distance from the point to the origin is constant: $$ \{ x \in \mathbb R^n : | x | = c \} $$for some constant $c$. The most common use of the word refers to the $n = 4$ case.

Zach
  • 381
  • There is some more information here: http://mathworld.wolfram.com/Hypersphere.html – Zach Jun 18 '14 at 04:16
  • Why special on n=4 case? – Bumblebee Jun 18 '14 at 04:16
  • Just because that is one more dimension then we have in our universe. It is the first "weird" dimension, when we can no longer have a true mental picture of it. Similar to a "hypercube" in four dimensions; note that the picture here cannot possibly be four dimensional, and yet it tries to represent a four dimensional shape: http://en.wikipedia.org/wiki/Hypercube – Zach Jun 18 '14 at 04:24