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It is given a regular -gon . On its a) incircle b) circumcircle is chosen a random point . For which natural numbers and the following expression is a constant:
It is given a regular -gon that inscribed in cicrcle . On its c) concentric circle is chosen a random point . Than for , .
For odd powers there exist sequence of plus and minus that .
ins-
06.04.2011, 12:05
Thank you very much. How did you got this result? Is it very well known fact?
Dimoniada
06.04.2011, 12:26
Последний раз редактировалось Dimoniada 06.04.2011, 13:03, всего редактировалось 1 раз.
(Оффтоп)
I'm never seen that result, to my mind it's hard problem for schoolchildren. P.S.: Во втором утверждении пропустила, как и должно быть нечётным, иначе "не получится".
ins-
06.04.2011, 12:38
(Оффтоп)
It is not intended for schoolchilren if it is not TST or last round of NOM. What i like/dislike is the problem is not pure geometric. I think i saw similar Vietnamese proposal - the particular case (n=3, m=4) for IMO. I was just curious to see what more skilled mathematicians know about this. When I smoke I wonder such things