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Article #2367Re: expected distance between points in a sphere
From: Nairo Aparicio
Date: Sun, 22 Nov 1992 14:27
Date: Sun, 22 Nov 1992 14:27
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In article <1992Nov20.072501.16998@nsisrv.gsfc.nasa.gov>, fgg@gemini.gsfc.nasa.gov (Frank G. Gomez) writes: |> Two small problems: |> |> Given two random points within a sphere of unit radius, what is |> the expected straight-line distance between them ? |> I only know basic things about theory of probability, so I am going to try to guess the answer. Given a random point within a sphere (such that the probability that the point is in a volume V is 3V/(4 pi)), the expected straight -line distance between the point and the centre of the sphere is 0.75 (I mean, the average of a continuous distribution with density 3x^2, 0<x<1). If we add another point, the expected relative position of that point with respect to the former is that when both points are on the same diameter (this is because of the symmetry). so I would say that the answer might be 2*0.75 = 1.5. (but I am not sure). |> Given a square sheet of paper, make three folds (nothing fancy, just a normal |> fold). At the end you will get a polygon. What is the maximum number of sides |> this polygon can have ? Can you generalize to n folds (assuming the paper has |> no thickness) ? |> I am going to guess again. How about 4+5*n where "n" is the number of times you fold the square sheet? Nairo Aparicio
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Path: arc1-ca.pugleaf.net!sparky!uunet!pipex!warwick!uknet!doc.ic.ac.uk!cc.ic.ac.uk!umahf69 From: umahf69@ma.ic.ac.uk (Nairo Aparicio) Newsgroups: rec.puzzles Subject: Re: expected distance between points in a sphere Message-ID: <1992Nov22.142731.10100@cc.ic.ac.uk> Date: 22 Nov 92 14:27:31 GMT References: <1992Nov20.072501.16998@nsisrv.gsfc.nasa.gov> Sender: umahf69@ic.ac.uk (?/20000) Organization: Imperial College Mathematics Department Lines: 29 Nntp-Posting-Host: macaw.ma