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Feb
2
awarded  Supporter
Jan
19
comment How to show $\frac{1}{2\sqrt{2} + \sqrt{3}} = \frac{2\sqrt{2} - \sqrt{3}}{5}$?
For $\frac{a}{b}=\frac{c}{d}$ with b,d non-zero, we have it being equivalent to $ad=bc$, visually the product of 'diagonal'(a,d) and 'anti-diagonal'(c,b) elements. And here you can use this with $(x+y)(x-y)=x^2-y^2$.
Jan
19
comment the solution of a system of nonlinear differential equations
Assuming cross is matrix product, The solution should be time-ordered if $\mu(t)$ does not commute at different times, i.e. $\mu(t_2)\mu(t_1)\neq \mu(t_1)\mu(t_2)$, you can look up Magnus expansion, etc. It's very common for Schroedinger equation in quantum mechanics.
Sep
23
comment How many triangles are there in the picture?
@halirutan no, it's not Binomial[8,3]: you can choose 3 out of all intersections that has connecting lines and make a triangle so the number should be much larger.
Feb
20
awarded  Autobiographer