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Re: A problem to keep you up at night

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  • clowenst@ucsd.edu
    ... Are you sure that the triangular hole is equilateral? I don t think you can do that. Isoceles triangle, yes. This is a pretty old problem, except for the
    Message 1 of 11 , May 31, 2001
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      --- In sliderule@y..., "Allen B, Carlisle" <profali5205@h...> wrote:
      > I have a math problem that may confound and/or delight you menza
      > folks out there. Draw an object that if slid through a one inch
      > square hole in a sheet of metal so that there would be a point
      > where no sunlight would seep through. This same abject could do
      > the same thing going through a circle of one inch diameter and
      > an equalateral triangle that measures an inch on each side.
      > Good!.....Now what is the volume of this object???

      Are you sure that the triangular hole is equilateral? I don't
      think you can do that. Isoceles triangle, yes.

      This is a pretty old problem, except for the equilateral part.
      It can be found in _Puzzles Old & New_ by Hoffmann, originally
      published in 1893. Reprinted by Sterling Publishers in 1997.

      To construct the shape, start with a cylindrical cork 1 inch dia.
      Cut it to 1 inch length. You now have a shape that will fit the
      square and circular holes. Draw a line across the diameter of the
      circle at one end. Make a sloping cut from that line down to the
      circle at the other end, on each side. You now have a shape that
      will fit a triangular hole.

      Unfortunately, the triangular profile is one inch high and one inch
      wide, so two sides of the triangle are sqrt(5/4), and it isn't
      equilateral. Tonight my calculus doesn't feel up to finding
      the volume, maybe it will feel better tomorrow.

      carl
    • jporcus@mac.com
      Allen, First, it s Mensa, not menza. Second, it equilateral, not equalateral. Third, are you sure that the triangle portion of the problem statement
      Message 2 of 11 , May 31, 2001
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        Allen,

        First, it's "Mensa," not "menza."

        Second, it "equilateral," not "equalateral."

        Third, are you sure that the triangle portion of the problem
        statement specifies an equilateral triangle rather than a triangle
        of equal base and height of 1 inch? The latter has a fairly simple
        solution, while the former is impossible.

        Fourth, what the hell does this have to do with slide rules?!

        Jimmy P.

        --- In sliderule@y..., "Allen B, Carlisle" <profali5205@h...> wrote:
        > I have a math problem that may confound and/or delight you
        menza folks
        > out there. Draw an object that if slid through a one inch square
        hole in
        > a sheet of metal so that there would be a point where no
        sunlight would
        > seep through. This same abject could do the same thing going
        through a
        > circle of one inch diameter and an equalateral triangle that
        measures an
        > inch on each side. Good!.....Now what is the volume of this
        object???
      • Chris Redding
        Hello, ... snip----- Mr. Porcine, are you a member? ... snip----- It s impolite to correct one s speling. ... snip----- I m afraid that both cases you mention
        Message 3 of 11 , Jun 2, 2001
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          Hello,

          jporcus@... wrote:
          >
          > Allen,
          >
          > First, it's "Mensa," not "menza."
          snip-----
          Mr. Porcine, are you a member?

          > Second, it "equilateral," not "equalateral."
          snip-----
          It's impolite to correct one's speling.

          > Third, are you sure that the triangle portion of the problem
          > statement specifies an equilateral triangle rather than a triangle
          > of equal base and height of 1 inch? The latter has a fairly simple
          > solution, while the former is impossible.
          snip-----
          I'm afraid that both cases you mention are impossible.

          > Fourth, what the hell does this have to do with slide rules?!
          snip-----
          The "h" word!
          > Jimmy P.
          >
          > --- In sliderule@y..., "Allen B, Carlisle" <profali5205@h...> wrote:
          > > I have a math problem that may confound and/or delight you
          > menza folks
          > > out there. Draw an object that if slid through a one inch square
          > hole in
          > > a sheet of metal so that there would be a point where no
          > sunlight would
          > > seep through. This same abject could do the same thing going
          > through a
          > > circle of one inch diameter and an equalateral triangle that
          > measures an
          > > inch on each side. Good!.....Now what is the volume of this
          > object???
          >
          > Yahoo! Groups Sponsor
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        • jporcus@mac.com
          ... Are you willing to make this interesting by putting your money where your mouth is? Jimmy P. PS: Sorry for seeming impolite to Allen. Just wanted to
          Message 4 of 11 , Jun 2, 2001
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            --- jporcus@m... wrote:
            >> Third, are you sure that the triangle portion of the problem
            >> statement specifies an equilateral triangle rather than a
            >> triangle of equal base and height of 1 inch? The latter has a
            >> fairly simple solution, while the former is impossible.
            >
            --- Chris Redding <credding@c...> wrote:
            > I'm afraid that both cases you mention are impossible.

            Are you willing to make this interesting by putting your money
            where your mouth is?

            Jimmy P.

            PS: Sorry for seeming impolite to Allen. Just wanted to correct
            his spelling on behalf of all Mensans (as well as all
            Equilatoratorians).
          • Korny
            I worked out a solution that fills all the parameters of the problem as stated. I will be posting it soon and will post the link here. What does all this have
            Message 5 of 11 , Jun 3, 2001
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              I worked out a solution that fills all the parameters of the problem as stated. I will be posting it soon and will post the link here.

              What does all this have to do with SR? It has to do with math.


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            • Allen B, Carlisle
              YOU FOUND THE SOLUTION???!!!!! FANTASTIC!!! As far as slide rule relationship, when you work out the volume then use only your paper, pencil and slide rule.
              Message 6 of 11 , Jun 3, 2001
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                YOU FOUND THE SOLUTION???!!!!! FANTASTIC!!! As far as slide rule
                relationship, when you work out the volume then use only your paper,
                pencil and slide rule.

                Korny wrote:
                >
                > I worked out a solution that fills all the parameters of the problem as stated. I will be posting it soon and will post the link here.
                >
                > What does all this have to do with SR? It has to do with math.
                >
                > _________________________________________________________________
                > iVillage.com: Solutions for Your Life
                > Check out the most exciting women's community on the Web
                > http://www.ivillage.com
              • Korny
                ... Actually, I think some of the parameters were omitted, so I jumped into the opening. Anyhow, I got the files dressed up for the net. When you see the
                Message 7 of 11 , Jun 3, 2001
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                  On Sun, 03 June 2001, "Allen B, Carlisle" wrote:

                  >
                  > YOU FOUND THE SOLUTION???!!!!! FANTASTIC!!! As far as slide rule
                  > relationship, when you work out the volume then use only your paper,
                  > pencil and slide rule.
                  -----
                  Actually, I think some of the parameters were omitted, so I jumped into the opening.

                  Anyhow, I got the files dressed up for the net.

                  When you see the solution you will understand that the volume is simple.


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                • jporcus@mac.com
                  ... Has this (i.e., the impossible) been posted yet? We re all waiting! Jimmy P. PS: Ron Hudson is indeed correct in his solution (which is the same solution
                  Message 8 of 11 , Jun 6, 2001
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                    --- In sliderule@y..., Korny <raykornele@i...> wrote:
                    > I worked out a solution that fills all the parameters of the
                    > problem as stated. I will be posting it soon and will post the
                    > link here.

                    Has this (i.e., the impossible) been posted yet? We're all
                    waiting!

                    Jimmy P.

                    PS: Ron Hudson is indeed correct in his solution (which is the
                    same solution that many others have also alluded to, but which
                    explains well).
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