Difference between k-simplex and affine k-simplex

ehrenfest · May 15, 2008

1. The problem statement, all variables and given/known data
http://en.wikipedia.org/wiki/Affine_simplex

Can someone please explain the difference between a k-simplex and an affine k-simplex? Is the difference just that in a k-simplex, the points do not have to be affinely independent? On the wikipedia page, they say in the introduction that the points need to be affinely independent even for a k-simplex.

2. Relevant equations

3. The attempt at a solution

cristo · May 15, 2008

I was say, judging on that Wikipedia page, that a simplex and an affine simplex are the same thing. Of course, Wiki isn't entirely correct. Have you seen the terms used in different ways? Could you tell us where you have used the terms used?

Vid · May 15, 2008

A regular simplex is one with vertices at the standard basis vectors. An affine simplex is an affine transformation (linear transform + a translation) of the standard simplex. Affine transformations preserve colinearity and ratios of line segments of the same line. An affine simplex is a k-simplex.

ehrenfest · May 15, 2008

cristo said: ↑

I was say, judging on that Wikipedia page, that a simplex and an affine simplex are the same thing.

OK good, that would resolve my confusion.

cristo said: ↑

Of course, Wiki isn't entirely correct. Have you seen the terms used in different ways? Could you tell us where you have used the terms used?

No I haven't seen them used in different ways.

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Difference between k-simplex and affine k-simplex

ehrenfest

cristo

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