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Από τα καλλίτερα κανάλια στο yt αυτό, κόσμημα.

sys3x έγραψε: 24 Δεκ 2021, 14:53 Από τα καλλίτερα κανάλια στο yt αυτό, κόσμημα.

Πραγματι, κι απο πολλές απόψεις!
Έκανε διαθέσιμο και τον κόδικα που επινόησε για τα gfx.

It all depends what one means by random chord.
It depends what one means by randomness in general. We go to a street and we make a bet like this: Will the first person who turns the corner be bald or with hair ? After many trials a certain percentage will come up. But what if we go to another place, a place predominantly frequented by men ? Other percentage - bigger.
Could it be that 0.5 is the correct solution in the chord problem ?
Let's suppose that our circle is the circle x^2+y^2 = 1. That is the circle of radius 1 centred at the origin of a system of Cartesian coordinates.
Then we want a random straight line, this will be a line of the form Y = A.X + B.
A is the random tangent of an angle ranging from 0 to π/2 and B is also random but has to satisfy the condition B^2 < = 1 + A^2, so the line intersects the circle and a chord exists.
You can't get more random and unbiased than that.
Maybe I could proceed analyticaly from this point but I did n't. I used random number sampling and the result for the probability of length of chord >= sqr(3) is 0.5.
So that's the correct result and the other methods are biased.