In the forest lived Hermit, Robber and Bear. People build three highways across the forest, but all of them choose to stay in the wood between roads. Hermit is looking for place with [i]minimum noise, [/i] Robber - with [i]the same distance to every road [/i]and Bear wish to live in the[i] very center of wood.[/i] Randomize triangles and try to find best place for every character!
[list] [*]Robber's problem has simple and exact solution. [*]I suppose Bear dream about [i] baricenter[/i] but it's just hypothesis. [*]The level of noise from each highway inversely proportional to distance, so best place for Hermit is [math]\frac 1 r_1 + \frac 1 r_2 + \frac 1 r_3 \; = \; min[/math] [/list] Hermit's problem has no simple geometric solution (?)