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Mar
11
comment Find maximum divisors of a number in range
@Chan Think of the constraint as a surface in some high-dimensional space. You want to find the spot on the surface where some function is maximized. Then the directional derivative of the function along the surface must be zero in all directions of the surface. The directional derivative is the dot product of the gradient with the tangent to the surface, so the gradient of the function must be normal to the surface. The gradient of the constraint function is also normal to the surface, so these two gradients must differ by only a constant multiplier, called the Lagrange multiplier.
Mar
11
answered Find maximum divisors of a number in range
Mar
10
awarded  Teacher
Mar
10
answered Why Circle encloses largest Area?
Mar
5
comment Good Physical Demonstrations of Abstract Mathematics
Here's a blog post I wrote a while ago about proving Vieta's formula with basic physics: arcsecond.wordpress.com/2010/09/17/…
Feb
24
accepted Why is Euclidean geometry scale-invariant?
Feb
23
comment Prove that Honeycomb Structures are the Most Geometrically Efficient Structure
not really physics that I can tell. probably belongs in math.stackexchange
Feb
23
awarded  Commentator
Feb
22
awarded  Nice Question
Feb
21
comment Why is Euclidean geometry scale-invariant?
Interesting point. Then all I need to do is understand how why the Pythagorean theorem is special to Euclidean geometry. The most famous proofs that pop to mind for me involve things like similar triangles, though, and so using them would be circular reasoning.
Feb
21
comment Why is Euclidean geometry scale-invariant?
@Qiaochu I know some linear algebra and a little abstract algebra from studying physics, so yes a more modern treatment would be interesting, but depending on what tools it uses I might need a reference to understand the background.
Feb
21
asked Why is Euclidean geometry scale-invariant?
Feb
21
awarded  Editor
Feb
21
revised How to find the distance between a point and line joining two points on a sphere?
changed "C" to "X" to fit with picture
Feb
21
suggested approved edit on How to find the distance between a point and line joining two points on a sphere?
Feb
17
comment Derivation of Fourier Series?
This isn't really a physics question. I'll flag for the mods to migrate it to math.stackexchange.
Feb
3
accepted How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers?
Feb
3
comment How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers?
@wok, @Moron Thank you for the links. I saw that post before asking the question, but once I realized it was answering a slightly different question, I didn't read it in detail. I guess I should have.
Feb
3
comment How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers?
Yes, I get in now. The answer is just ${}_{n-r+1}C_r$. Thank you encouraging me rather than giving it away.
Feb
2
comment How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers?
Nice and simple. Thank you.