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Activity for siric‭

Type On... Excerpt Status Date
Comment Post #287410 https://youtu.be/P3ifP2GpMAo
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over 1 year ago
Comment Post #287419 I think grid is the wrong word. I meant box or square. It’s a continuous distribution so the points can be anywhere in the square (no identical points). I am concerned about the probability distribution of lengths. So, if the points are randomly distributed an arbitrarily large number of times (say, ...
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over 1 year ago
Edit Post #287419 Post edited:
over 1 year ago
Comment Post #287419 I think my explanation was poor. The points do not have to be in a lattice grid; they can be arranged anywhere in the box - so there are infinite arrangements.
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over 1 year ago
Comment Post #287410 Take $d = 1$, $n = 2$ and $a_1 = 500$. We get $500(501)(502)(503)(504)(505) + 1$ which is not a perfect square.
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over 1 year ago
Edit Post #287419 Initial revision over 1 year ago
Question What is the probability that the convex hull of $n$ randomly distributed points has $l$ of the points on its boundary?
Consider a square in which $n$ points are uniformly randomly distributed. Now consider the convex hull of these points. The "length" of the convex hull is defined as the number of points in the perimeter of the convex hull i.e. $n \\; -$ the number of points strictly contained by the convex hull. ...
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over 1 year ago