Talk:Frustum

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Should a frustum be classified as a polyhedron?

If a truncated cone is a frustum, then not all frusta are polyhedra.

Am I correct? Please discuss.

-Comment by 128.61.118.174

I don't know any specific policy on category usage. I'd think it can make sense to include a category even if it doesn't apply to all forms or definitions. Tom Ruen 21:04, 10 January 2007 (UTC)

I think that some of the calculations on the page are missing. --Proficient 07:10, 8 April 2007 (UTC)

My Maths teacher said it is a frustrum and not a frustum was this just misprnounciation on her part or can it actually be called a frustrum

Yes, in my opinion you're right. Or maybe the conical frustrum could be considered an infinite-faced polhyedron XD

198.28.92.5 07:43, 24 May 2007 (UTC) David Ashby:

Warning: I think that the equation for surface area may be incorrectly given as:

A = π(R1S1 − R2S2)

Another website gives

A = pi * S * (R1+R2)

This makes more sense. S1 and S2 are not defined in the current wikepedia article, only S.

If I get time, I'll come back and definitively answer this, otherwise perhaps someone else can?

[edit] Answers

A mathematician and linguist replies:

• A polyhedron is a geometric object with flat faces and straight edges (the definition at polyhedron), so yes, a frustum of a pyramid is definitely a polyhedron. The frustum of a cone is therefore definitely not a polyhedron, as its surfaces are not all planar. (Mathematically speaking, the limit as n tends to infinity of a polyhedron with n faces is not itself a polyhedron as it does not fit the definition of a polyhedron. Similarly, a circle can be considered to be the limit as n tends to infinity of a regular n-gon, but that does not make it a polygon.)
• The spelling frustrum is erroneous, according to the Oxford English Dictionary, and they know what they are talking about. This misspelling probably comes about because the other word beginning "frust..." that everyone knows is "frustrate". So, anonymous poster, I'm afraid your maths teacher was incorrect. Teachers can be wrong too, alas. — Paul G 12:10, 17 May 2007 (UTC)