Hippiekinkster -> RE: I Don't Think I've Met Any of You (9/8/2008 2:19:20 PM)
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Me: "Why are the donut holes one buys round and not cylindrical-shaped? (think about it) Bear:They are round so people can fit several on a finger. I knew this would cause some confusion. A plain, glazed donut is shaped like a bagel, yes? It's a torus. The donut holes one buys in a box are spherical, yes? But the space in the center of a plain donut.bagel isn't spherical; it's closer to two inverted funnels. Think of it as a solid composed of a stack of circles which have their maximim radii at each end of the solid, and the mimimum radius in the center. Each circle has a thickness of Lim X, x --> 0. We'll call this dx. The area of each circle is, of course, piR^2, and the volume of each circle is piR^2dx. The height of this stack of circles is 2x. If we were to graph R as a function of x (x,y coordinate system where R=y), it would be a parabola with the shape y=ax^2 + bx from -x to x. The space in the center of the bagle would be described as the integral, from -x to x, of pi(y^2)dx, if I remember my calculus properly. Follow me?
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