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Aug
27
comment How can I describe the area between two ellipses?
@BenCrowell I agree with Lubin - most likely, the term $(1-\frac{(x_0-c_2)^2}{x_1^2})$ in $y_0=\sqrt{y_2^2(1-\frac{(x_0-c_2)^2}{x_1^2})}$ becomes negative, causing the smaller $x$ values to become imaginary. Therefore, the $x$ that we're looking at has to be the larger one. I guess that answers that. I don't think we need to go through a numerical case if my explanation sounds convincing enough. That still only gets me down to where I ended in my question, though.
Aug
27
asked How can I describe the area between two ellipses?
Aug
26
comment Numerical Analysis
There was no complex conjugate. Just saying.
Aug
26
answered Can you approximate a vector field?
Aug
26
revised Calculate the area on a sphere of the intersection of two spherical caps
added 173 characters in body
Aug
26
revised Calculate the area on a sphere of the intersection of two spherical caps
Minor LaTeX corrections, grammar
Aug
26
revised Calculate the area on a sphere of the intersection of two spherical caps
Minor LaTeX corrections
Aug
26
answered Calculate the area on a sphere of the intersection of two spherical caps
Aug
25
comment Divisibility of consecutive natural numbers
@dato yes but what anon is trying to convey here is that there doesn't have to be a prime every 2012 consecutive numbers.
Aug
25
accepted Solving the DE for a two-body system
Aug
24
comment Pre-Calculus - Solving for $x^3$
When you used the quadratic formula and got the two roots $a=\frac{-1+i\sqrt{3}}{2}$ and $b=\frac{-1-i\sqrt{3}}{2}$ you should be replacing $x^2+x+1$ with $(x-a)(x-b)$, not what you did.
Aug
24
revised Green's theorem for conservative fields - are partials equal?
Minor math error (forgot dA)
Aug
24
comment Green's theorem for conservative fields - are partials equal?
No problem. Glad to help. FYI, subscripts, in this context, mean partials - $\frac{\partial f}{\partial x}=f_x$.
Aug
24
comment Integer combination
Will the formula always be less than or equal to? And that simple? (i.e., in the form $a x + b y \le c$ for integers a, b, and c)?
Aug
24
comment Green's theorem for conservative fields - are partials equal?
There. I hope my edit was what you were looking for.
Aug
24
revised Green's theorem for conservative fields - are partials equal?
Missed a period, added a proof, put more LaTeX in.
Aug
24
comment Green's theorem for conservative fields - are partials equal?
@alkamid $P_y$ and $f_{xy}$ are the same thing (if $f$ exists). The actual Young's Theorem says $f_{xy}=f{yx}$. As for the typo, it was just a missing period, right?
Aug
24
revised Green's theorem for conservative fields - are partials equal?
Missed a period.
Aug
24
answered Green's theorem for conservative fields - are partials equal?
Aug
24
comment Is the vector cross product only defined for 3D?
Why don't you get a vector in the end? Using Mathematica's Cross[] function is allowed over any number of vectors, so long as there's one more dimension than the number of vectors. Playing around with using matrices to find the cross product and using Cross[], I found the result only differed by factors of -1 occasionally.