3 ms·

Looking at the other comments, it seems like most people really like the cheat. I admit it's very cute, and you're absolutely right that this sort of thinking c

Looking at the other comments, it seems like most people really like the cheat. I admit it's very cute, and you're absolutely right that this sort of thinking can be helpful in artificial situations like exams and games --- I've used it myself. That artificiality is why I don't really like that approach, though. It's a brand of thinking that generally works only on artificial problems, because the key component ("you wouldn't be asking me this if it didn't have a well-defined answer") doesn't exist on most problems. Proving that it's constant and then using the r -> 0 trick to calculate the constant is much more satisfactory to me.

baddox 12y ago
Of course, the key components of the analytic solution (knowing the volume formula for spherical caps, spheres, and cylinders) also don't exist on most problems.
vorg 12y ago
> that approach is a brand of thinking that generally works only on artificial problems, because the key component ("you wouldn't be asking me this if it didn't have a well-defined answer") doesn't exist on most problems Perhaps changing the footnote hint "no more information is given" to an integral part of the problem spec, and saying "no more information is required", would make the problem less artificial. There would then be a self-referencial component in the problem definition, self-referentiality being fairly common in nature and engineering.