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Comment by Asraelite | Hacker News Reader

I never understood the need to distinguish between "ball" and "sphere" in maths. Sure, one is solid and the other hollow, but why is that fact so important that you need to use a completely different word? As I understand it, you could replace every instance of "ball" in this article with "sphere" and it would still be correct.

We don't have special words for the voluminous versions of other 3D shapes, so why do spheres need one?

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> you could replace every instance of "ball" in this article with "sphere" and it would still be correct.

I completely agree. N-ball is maybe more mathematically precise. It might rule out some strange edge case I couldn't think of. I chose it mostly for stylistic reasons. n-ball is shorter than n-sphere, and ball is a more playful term.

I do however understand the need to define the two object classes, and see little issue with giving them distinct names.

> We don't have special words for the voluminous versions of other 3D shapes, so why do spheres need one?

Topologists don't need them because they already have ball and sphere.

In analysis, I can imagine them calling full hyperrectangles "brick", and empty hyperrectangles "box", but both words start with "b", so there is no shorthand for them on paper. I^n and ∂I^n are just fine.

And, indeed, it’s probably in topology where the distinction between sphere and ball is most important.

We do for 2D though - Circle and disc. And in 4D plus we have the 3-sphere and 4-ball, etc.

And for 3D shapes have Torus, and, well, ‘solid-torus’.

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