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    • Hint for the peg and hole puzzle

      19 March, 2012

      Consider the following picture:

      key

      The tighter fit is the one for which the ratio of peg area to hole area is greater.

      Back to puzzle

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      Anonymous

      19 March 2012

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      Comment

      Is it!?

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      Anonymous

      1 April 2013

      In reply to is it!? by Anonymous

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      It is!

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      Macrocompassion

      26 June 2013

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      Comment

      It is the friction force between the peg and the hole which causes it to offer resistance and to become a relatively tight fit.

      The corners of the square will elastically deflect and create bearing stresses. Depending on the elasticity of these corners and that of the stiffer circular hole some friction force will make the fit a tight one.

      However, in the case of the circular peg the bearing surfaces are determined by what is in effect a stiffer surface due to the non-pointed shape of the peg. Here the surface of the hole is flat offering greater stiffness too. This means less elastic deflection and greater forces. Consequently it is the round peg which is able to cause the tightest situation.

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      Anonymous

      12 December 2013

      In reply to Of pegs and holes by Macrocompassion

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      :-)

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      Anonymous

      10 March 2016

      In reply to Of pegs and holes by Macrocompassion

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      You could have just as easily said more surface area touching equals more friction which equals a tighter fit.
      The illustration depicts this very clearly.

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      Anonymous

      24 September 2014

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      If we assume perfectly round and perfectly square elements, there are four points of contact in each case. Same tightness. The part of the peg that doesn't contact the hole is irrelevant.

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      Larry Barbrow

      10 August 2022

      In reply to pegs and holes by Anonymous

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      Right on the mark. You must have experience with calculus (as x approaches infinity), or just plain old smart. If the shapes are absolutely perfect, an infinitely small portion toiches with the round peg in square hole, or square peg in round hole. However, to be fair, if the two objects are man made, then the odds favor the round peg in the square hole combo!

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