Pickett
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Everything posted by Pickett
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It's just like the riddle about an archeologist trying to sell some of his artifacts to a museum, and he claimed he found artifacts from around 500 B.C. including pots, tools, some artwork, and money from the time. The way he knows that it's from around 500 B.C. is because everything was made using materials available at the time, the money was coins that had years 530 B.C. - 490 B.C. on them, and the artwork was of events that happened at the time. The museum curator immediately threw the man out and called him a fraud...why? (Not trying to start a new discussion, just saying that the reasoning is the same)
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Again, i saw this one that has been "dead" for a few years...but no one gave the answer to it...and it's unfortunate that this user hasn't had a post in a year and a half (and this was their only one) and that no one solved it...because that probably means they won't verify the answer, but believe me, it's right...
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So, I learned this one when I was in my Calculus class and thought it was just sort of fun. Basically, there is a shape, called Gabriel's Horn (where you take the curve generated by the function f(x) = 1/x (where x >= 1)) and revolve it around the x-axis to form a horn shape. Using calculus, you can calculate the volume of this shape (it doesn't show up very well, but π is PI: Volume = π 1∫a (1/x2) dx = π (1 – 1/a) So, lima->∞ π (1 – 1/a) = π (1 – 0) = π The surface area can also be calculate as: Surface Area = 2π 1∫a √(1 + 1/x4) / x dx We know that √(1 + 1/x4) > √(1)...so we know that the Surface Area > 2π 1∫a √(1) / x dx = 2π ln a So, lima->∞ 2π ln a = ∞ You might ask why this is a paradox...you can think of it this way: Imagine you are a painter, it would take infinite amount of paint to paint the surface of this figure...however, you could FILL the entire shape with π volume of paint. I like this one (I know WHY it isn't a paradox...but that's no fun to give that away right away...), so I thought I'd post it.
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Sorry, I had changed my answer before you posted this reply...so, maybe my new answer is correct?
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This riddle has been quiet for a few years...but I just saw it.
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Oh, how I miss my non-Euclidean Geometry class...Hope this helped.
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umm... how many windows are in this place? I mean, who cares if the lights go out...since it's lunch time, if there are ANY windows, then SOMEONE must have seen something, right?
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