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Jun
24
comment Arnold Trivium Problem 39
@Potato since the Gauss integral does not change under deformations, we can deform $A$ into a straight line or (even easier) flatten $B$ into a circle, where we going around twice. Then the integral might be doable by hand. This is line when we integrate complex functions using Cauchy Residue Formula.
Jun
24
comment Arnold Trivium Problem 39
@Potato I wouldn't dream of doing the integrals by hand... unless you truly enjoy long and tedious integrals :-)
Jun
24
awarded  Nice Answer
Jun
24
comment Arnold Trivium Problem 39
I have to step away, but I can do a numerical calculation... just to see!
Jun
24
comment Arnold Trivium Problem 39
e.g. Gauss Linking Number Revisited (Ricca + Nipoti) Journal of Knot Theory and Its Ramifications
Jun
24
revised Arnold Trivium Problem 39
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Jun
23
answered Arnold Trivium Problem 39
Jun
23
revised Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?
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Jun
23
revised Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?
added 259 characters in body
Jun
23
revised Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?
added 407 characters in body
Jun
23
revised Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?
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Jun
23
revised Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?
added 358 characters in body
Jun
23
answered Why does $\cos(x) + \cos(y) - \cos(x + y) = 0$ look like an ellipse?
Jun
23
comment Integral relations in Fricke and Klein
@glebovg i added more details... why didn't you give me the 100?
Jun
22
answered What is the connection between the discriminant of a quadratic and the distance formula?
Jun
21
answered Proving $e^x \sin x$ is not uniformly continuous on $[0,\infty)$
Jun
19
comment Two sets $X,Y \subset [0,1]$ such that $X+Y=[0,2]$
@jack any reason in particular $4$?
Jun
15
revised Expansion coefficients of an orthonormal basis must satisfy $c_n n^{1/2}\to 0$ as $n\to \infty$ for $\sum|c_n|^2$ to converge.
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Jun
15
comment Expansion coefficients of an orthonormal basis must satisfy $c_n n^{1/2}\to 0$ as $n\to \infty$ for $\sum|c_n|^2$ to converge.
@1233dfv I was stuck there too. Either you add all the $n$ which are perfect squares or finally I decided $n = k^2$.
Jun
15
revised Expansion coefficients of an orthonormal basis must satisfy $c_n n^{1/2}\to 0$ as $n\to \infty$ for $\sum|c_n|^2$ to converge.
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