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 Mar15 comment Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers @Mitch - The statement $3 + 5 = 4 + 4$ definitely isn't sufficient on its own, else I could make up something like $3.2 + 5 = 4.1 + 4.1$. We need to combine this constraint with the right triangle constraint. After getting those two constraints, I think OP is suggesting you might guess that 3/4/5 meets the constraints. (I personally wouldn't have jumped to this, though perhaps it's easier to guess if you just learned about Pythagorean triples.) Sep12 comment which is bigger $I_{1}=\int_{0}^{\frac{\pi}{2}}\cos{(\sin{x})}dx,I_{2}=\int_{0}^{\frac{\pi}{2}}\sin{(\sin{x})}dx$ I don't think this adds much above a direct calculator computation, unless there's something about J_0 and H_0 that leads to a cleaner non-calculator solution. Mar3 comment What is dimensional consistency, mathematically? Thanks for the great link! I haven't finished, but that seems to be what I'm looking for. Jan14 comment approximating a discrete function with a continuous one Right, as long as $f$ is sufficiently well-behaved. If $f$ looks like a smooth interpolation of the discrete $f$, you should be fine. You might run into an off-by-one error where, for example, $f(0.1)$ is the maximum with $h = 0.1$, but $f(0.151)$ is the continuous maximum. Then you might round $0.151$ to $0.2$ and incorrectly conclude that $f(0.2)$ is the discrete maximum. Jan1 comment A complex equation You may be interested in the notion of zero divisors: en.wikipedia.org/wiki/Zero_divisors