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MathGroup Archive 2004

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Re: ArcCos[x] with x > 1

  • To: mathgroup at
  • Subject: [mg49343] Re: ArcCos[x] with x > 1
  • From: koopman at (Ray Koopman)
  • Date: Thu, 15 Jul 2004 07:00:06 -0400 (EDT)
  • References: <cd35vb$qd5$>
  • Sender: owner-wri-mathgroup at

jaegerm at wrote in message news:<cd35vb$qd5$1 at>...
> [...] Given is a cube of side length a (or, let's say, 1). What is
> the mean distance of the cube's centre point to its surface.
> Obviously, the result is between a / 2 (the distance to any of the six
> centres of the six faces) and a / Sqrt[2] (the distance to any of the
> eight corners). Sure, that problem can easily be reduced. Think that
> sounds like a simple integration on kindergarden level? So did I. But
> I soon got the impression I was wrong.
Maybe because the distance from the centre to any corner is
Sqrt[(a/2)^2 + (a/2)^2 + (a/2)^2] = (a/2)*Sqrt[3]? :)

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