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Results tagged with linear-algebra
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user 4298
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
27
votes
The number $\pi$ and summation by $SL(2,\mathbb Z)$
I add our explanation and the origin of the problem.
To obtain the formula we just need to verify the following lemma (by a straightforward computation).
Magic Lemma. Let $(a,b),(c,d)$ be as in …
- 5,043
115
votes
3
answers
5k
views
The number $\pi$ and summation by $SL(2,\mathbb Z)$
Let $f(a,b,c,d)=\sqrt{a^2+b^2}+\sqrt{c^2+d^2}-\sqrt{(a+c)^2+(b+d)^2}$. (it is the defect in the triangle inequality)
Then, we discovered by heuristic arguments and then verified by computer that
$$\ …
- 5,043