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Mar
15
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.)
Jan
16
awarded  Notable Question
Mar
29
awarded  Nice Answer
Mar
28
awarded  Yearling
Mar
28
answered Can a piece of A4 paper be folded so that it's thick enough to reach the moon?
Jan
22
awarded  Popular Question
Sep
12
awarded  Critic
Sep
12
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.
Mar
12
revised Congruent Modulo $n$: definition
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Mar
12
suggested approved edit on Congruent Modulo $n$: definition
Mar
4
awarded  Scholar
Mar
4
accepted What is dimensional consistency, mathematically?
Mar
3
revised What is dimensional consistency, mathematically?
added 50 characters in body
Mar
3
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.
Mar
3
awarded  Student
Mar
3
asked What is dimensional consistency, mathematically?
Jan
14
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.
Jan
14
awarded  Teacher
Jan
14
awarded  Editor
Jan
14
revised approximating a discrete function with a continuous one
added differentiability; added 27 characters in body