Math CentralQuandaries & Queries


Question from Dan:

I am not a mathematician. This seems to me an intuitively simple enough problem that I very much need an answer to from someone who's mathematics are better than mine. Please help.

The question is: for a tesseract of side length = 1
what is the distance of the center of each cube from the center of the tesseract ?

I think I have calculated the distance of each vertex from the center, and of the center of each edge from the center, but the question above baffles me.

(anyone not having a clue what I am talking about can brush up here )

Thanks in advance

We'll use coordinates with the center at (0,0,0,0) and the vertices at


and use Pythagoras' theorem in its 4-dimensional version

\[d^2 = w^2 + x^2 + y^2 + z^2\]

to get distances.

For a vertex of the tesseract, all four coordinates differ from the center's by 1/2:

\[d = \sqrt{\left[(1/2)^2 + (1/2)^2 + (1/2)^2 + (1/2)^2\right]} = 1\]

(did you get that?)

For edge centers, three coordinates differ:

\[d = \sqrt{\left[(1/2)^2 + (1/2)^2 + (1/2)^2 \right]} = \frac{\sqrt 3}{2}\]

I think you can solve now for square-face centers and cube-face centers!

Good Hunting!

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS