What Is the Geometric Term for the Cartesian Product of n Unit Intervals?

In summary, the cartesian product of n unit intervals is known as the geometric unit n-hypercube or unit n-cube. It is also referred to as an orthogonal unit and is considered an important geometric object.
  • #1
Tac-Tics
816
7
The unit interval is [0, 1].

Is there a name for the cartesian product of n unit intervals? So, [0, 1] x [0, 1] is the unit square, [0, 1] x [0, 1] x [0, 1] is the unit cute. What would you call [0, 1] x ... x [0, 1] with n factors?

I'm guessing there is such a term, because it's a pretty useful geometric object. It's at least as important as an n-torus, which is [tex]S^1 \times \cdots \times S^1[/tex]
 
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  • #2
symmetric k-cell?

n-dimensional symmetric k-cell?

I guess you could call it anything so long as there is at least somewhat of a use for it. How about "yourlastname"-Space?
 
  • #3
Newtime said:
How about "yourlastname"-Space?

Sweet!

If I were to write a paper on it, I'd probably call it an orthogonal unit. Orthogonal is just a cool sounding word.

But I'd still like to hear if there's a name in common use!
 
  • #4
It's the geometric unit n-hypercube, or just unit n-cube for short.
 
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FAQ: What Is the Geometric Term for the Cartesian Product of n Unit Intervals?

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