## Re: A problem to keep you up at night

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• ... 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
• 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???
• 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???
>
> [Check out great fares at Orbitz!]
>
>
• ... 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

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).
• 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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• 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.
>
> _________________________________________________________________
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> Check out the most exciting women's community on the Web
> http://www.ivillage.com
• ... 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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• ... 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