Aratati ca in orice triunghi are loc inegalitatea :
\( \sum \frac{1}{a+b-c} \geq \frac{ \sqrt3}{2r}. \)
Mihai Opincariu, G.M.B. 10/2000
Inegalitate in triunghi din gazeta matematica
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Inegalitatea de mai sus este echivalenta dupa cateva calcule cu inegalitatea Finsler-Hadwiger, i.e.
\( a^2+b^2+c^2\geq 4S\sqrt{3}+(a-b)^2+(b-c)^2+(c-a)^2. \)
\( a^2+b^2+c^2\geq 4S\sqrt{3}+(a-b)^2+(b-c)^2+(c-a)^2. \)
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.