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[Virex]

There's this problem I've been working on for the past... while.  Don't laugh, I'm panicking a bit because it's due tomorrow and I didn't start it soon enough.  Also because it's a pain to use the ancient Greek methods.  Also because I'm nearly certain that this is more than trivial.


Anyway, we've got a cylinder with base C and an inscribed prism inside it, Q--i.e. the base P of Q is inscribed in C.  Both of these figures have height h.

I need to prove that the volume V of the cylinder is not greater than the height of h times the area of C

I don't think I understand the question. You have to prove that a V <= C*h? If so, I suppose that you can not use the common definition of the volume of a cylinder? In that case I'd abuse Q: let the base of Q be B. B is inscribed in C, so area(B) =< area(C) for any prism Q and thus area(B)*h <= V  (assuming you can use the definition of the volume of a prism. Else you'll need to derive the volume of a prism as well, but that should be doable by chopping it up in triangles and generalizing the result).
Let Vert be the amount of vertices of B. Note that for Vert -> inf, area(B) -> area(C). Since for any B area(B)*h <= V, area(C)*h <= V.


Edit: this only works if B is a regular polygon though, so I'm not sure if you're able to use this.

[Vector]

I love you.  You have saved me from shame.

I hate that I thought of that once or twice and went "... Nah..," but more than that, I love you.

But I'm not having your children, and you can't have my house or my car or any of my books or, really, any of my worldly possessions.

Get me the proof to Riemann's first.

[ZetaX]

Normal Riemann or Extended Riemann or Generalised Riemann or Artin-Riemann or...¿ 

[Vector]

Whatever is most beautiful and least likely to result in internet-babies.

[MaximumZero]

See, this proves a hypothesis of mine. Vector-lust is like Dwarf Fortress. You can't win the game, but it's still fun to try once in a while.

[Vector]

See, this proves a hypothesis of mine. Vector-lust is like Dwarf Fortress. You can't win the game, but it's still fun to try once in a while.

Actually, the real reason why Virex will not be bearing my children is because he as wrong, as I realized on the way to school.  He proved the same direction that I'd already proven.

The limit of the circumscribing prisms approaches V as well.  We bound by both ends and then we're good.

[Zrk2]

See, this proves a hypothesis of mine. Vector-lust is like Dwarf Fortress. You can't win the game, but it's still fun to try once in a while.

Dammit! /jk

[Virex]

See, this proves a hypothesis of mine. Vector-lust is like Dwarf Fortress. You can't win the game, but it's still fun to try once in a while.

Actually, the real reason why Virex will not be bearing my children is because he as wrong, as I realized on the way to school.  He proved the same direction that I'd already proven.

The limit of the circumscribing prisms approaches V as well.  We bound by both ends and then we're good.

Whelp there go my chances...

[Leafsnail]

I shouldn't've read the last sentence first.  Gave me totally the wrong impression.

[Heron TSG]

Actually, the real reason why Virex will not be bearing my children is because he as wrong, as I realized on the way to school.

Somehow I think that's not the only reason.

[Vector]

Actually, the real reason why Virex will not be bearing my children is because he as wrong, as I realized on the way to school.

Somehow I think that's not the only reason.

... Wanna bet?

[Heron TSG]

I don't even want to know where you're going with that.

[Christes]

Vector and Virex are seahorses?  I knew it!

[Tellemurius]

note to self: stick to science, keep math low-profile.

[Leafsnail]

Vector and Virex are seahorses?  I knew it!

Nah... I did see a hospital offering buy one get one free on sex changes, though.