# Thread: multi sides figure dependence to ray

1. ## multi sides figure dependence to ray

picture presentation :

http://skrypty24.com.pl/11.JPG

ctg alfa = h / 1/2 * a
alfa will be descrease with angle, dependence ctg alfa will be incease
example for figure where alfa angle is 30 degrees
ctg alfa = sqrt(3) = h / 1/2 a

h = sqrt(3) / 1/2 * a

with increase the number of sides of same side figure, side 'a' going to zero, ctg alfa going to higher and higher value, and reach 'H', like in the h = ctg alfa * 1/2a, h will be increase, so xa / 2h ( dependence the diameter to ray ) will be going to infinity value of sides to H * ctg 0 degrees, no value for it, so to 'H'

2. ## Re: multi sides figure dependence to ray

Okay, if your figure has n sides then alfa= (360/n)/2= 180/n degrees and so goes to 0 as n goes to infinity. Yes, cot(alfa) = h/(a/2)= 2h/a. And since cot(alpha) goes to infinity as alpha goes to 0, it follows that a goes to 0. You say "h will increase" but that depends on what is being held constant. If "d" is held constant, then, yes, h increases toward d in the limit. I am not clear what you are saying will go o 'H' (I assume you mean 'h').

ok thanks