Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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idiot boxes ?
Also they didn't have idiot boxes back then. Now people waste all their time staring slack jawed at some chicks bottom in high def.
You must remember that people back then had very few alternatives to spending their time compared to what we now live like.
Yeah, but whats most odd is no one can come up with anything new like that anymore. How come people were so much smarter a thousand years ago?
Yes, the concept of solids of revolution will always be etched in my mind. There was such a WOW factor to them in my mind when I was first introduced to them. I always find if amazing that many of the foundations for this type of computation were derived from individuals working by candlelight in an age which now seems eons ago. The imagination of the human mind is truly incredible.
And the wonderfull thing about calculus, now that we have the formula, differentiating allows us to calculate the rate at which the height is changing as the volume increases at a given rate and vice versa.
:-D No problem! But I have to decline the rank of "GOD". My real name, michael, means "who is like God?"
Nice, mikau, you have earned the rank of GOD in my opinion. I missed the substitution for R when I was going around in circles a few days ago. I kept seeing that x and, instead of substituting, I was banging my head trying to use related rates for x and y.
If we work it out with the base of the sphere centered at the origin we don't have to worry about negative integrals, and can do it in one piece. If I integrate it for you...
oops! messed up there, its r^2 not just R. There we go!
woah! How could h be 2 if radius is 1?
I don't know why I typed that. What I was trying to say was that the shell method revolves around the opposite axis of the variable while the disk method revolves around the same axis as the variable.
forgive me if I'm wrong but isn't the disk method integrated in terms of x when rotating about the x axis?
This is what I mean.