So, I'm trying to work out the finer points of a science fantasy universe. A big part of it is going to revolve around rod-like, um, rods of a particular material. I need to know what monetary value to set for a given mass of this material to appropriately represent its scarceness/value... which is going to be tied into the volume of an important common artifact made from it. I don't have the final dimensions of the artifact, because I need to know how to figure out the volume of my "ballpark" version of it... because this thing's going to effectively set the value of everything else... so I need to know that my ballpark is somewhat reasonable for everything else I'm thinking of.
If the above is too specific, I can vague it up a bit.
Anyway:
The object I think I'm thinking of is a hexagonal prism. Specifically, I'm envisioning something like a rod (as I said), except not rounded... when viewed from the top or bottom, it looks like a regular hexagon. So, question one... is that, in fact, a hexagonal prism?
Question two, if A is the length of each the hexagon's sides and B is the length of the prism's sides, what's the volume of the prism? Obviously I'm looking for a formula here, though if somebody wants to show me the formula AND solve it for A = 1 and B = 1, and then I can multiply that by whatever the final length of the rods'll be, that'd be helpful.
ID:29942
 Apr 24 2007, 5:48 pm
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Apr 24 2007, 6:00 pm
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Xero-EP
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http://en.wikipedia.org/wiki/Hexagonal_prism
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The area of a hexagon is equal to the area of the six equilateral triangles that make it up, and each of those equilateral triangles has a side in length equal to the distance from the centre of the hexagon to a vertex of the hexagon. Volume is just multiplying in another dimension to the hexagon's area.
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ATW (according to Wikipedia), the volume of that prism would be 3*sqrt(3)/2*A*A*B.
So for A=1, B=1 that's 3*sqrt(3)/2, or approximately 2.5980762113533159402911695122588 according to Windows calculator. (Formula for area of a hexagon obtained from http://en.wikipedia.org/wiki/Hexagon - I haven't actually checked if that's correct.) (Edit: MathWorld confirms the formula, so it's probably correct.) | |
Thanks, that's exactly the sort of break down I need.
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From what I'm hearing, they sound like the quantum refractors from Megaman Legends. Do they serve as a power source? That'd be creepily similar to them.
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Yes, but there's not more than a superficial resemblance to the quantum refractors. While I enjoy old skool Megaman, I'd never heard of them before.
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