2,839 reputation
2825
bio website arcsecond.wordpress.com
location Baltimore, MD
age 29
visits member for 3 years, 9 months
seen yesterday

I'm a physics graduate student.


Mar
16
awarded  Nice Question
Mar
16
comment What am I doing when I separate the variables of a differential equation?
Thanks for the link, but the description there is not what you said. Differentials as described in Wikipedia are not infinitesimal changes.
Mar
16
comment What am I doing when I separate the variables of a differential equation?
The $dx$ and $dy$ are coming from a single limit. That's what I've been taught in calculus. This answer is logically equivalent to saying "you can do that because you can do that".
Mar
16
asked What am I doing when I separate the variables of a differential equation?
Mar
14
comment What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
Why the down votes?
Mar
14
revised What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
added 87 characters in body
Mar
14
revised What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
added 5 characters in body
Mar
14
comment What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
@Billare Thanks. Should say "I'll use Gauss's..."
Mar
14
comment What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
@kake Right. It's not supposed to be a proof so much as a heuristic to suggest the identity might be true.
Mar
14
answered Non-traditional math concepts for early education
Mar
14
answered What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
Mar
14
comment What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
I like the analogy to a fluid flow, but for the divergence, were you referring to many needles converging to or diverging from a point rather than one needle? That would make more sense to me since one needle cannot change its shape or grow and shrink. I'm also wary of considering a two-dimensional fluid when the curl is defined in three.
Mar
12
awarded  Nice Question
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