Posers and Puzzles

Posers and Puzzles

  1. H. T. & E. hte
    Joined
    21 May '04
    Moves
    3510
    09 Jan '05 09:023 edits
    You have a square of side-length a. You select two points A and B , "randomly ",anywhere inside the square. The problem is to find the expectation (average) of the length of the straight line segment AB, averaged over all random selections. For a circle , this can be worked out easily, in terms of the radius of the circle. How about , working out the expectation of the distance between two random points inside a square, in terms of its side-length?
  2. Joined
    08 Jun '04
    Moves
    3351
    10 Jan '05 07:411 edit
    Originally posted by ranjan sinha
    You have a square of side-length a. You select two points A and B , "randomly ",anywhere inside the square. The problem is to find the expectation (average) of the length of the straight line segment AB, ...[text shortened]... ndom points inside a square, in terms of its side-length?
    BTW - what is the expected distance between two randomly chosen points within a circle ? Which , you say , can be worked out
    " easily" in terms of the radius of the circle ?
  3. H. T. & E. hte
    Joined
    21 May '04
    Moves
    3510
    12 Jan '05 11:35
    Originally posted by cheskmate
    BTW - what is the expected distance between two randomly chosen points within a circle ? Which , you say , can be worked out
    " easily" in terms of the radius of the circle ?
    Yes , indeed it can be worked out. But that can be the subject matter of another puzzle thread. Off to the new thread then , for it.
  4. Joined
    30 Oct '04
    Moves
    2295
    16 Jan '05 12:511 edit
    Originally posted by ranjan sinha
    Yes , indeed it can be worked out. But that can be the subject matter of another puzzle thread. Off to the new thread then , for it.
    It look easy BUT Whenn I got down to do it , it turned out that it is not easy at all. May be it can be done numerically by programming the problem and running it on a computer. Analytical solution or expression seems beyond my under-graduate level skills of mathematics.
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