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Jack,
I'm hoping you will finally reveal (1) why my "impossible stairway" is half
of an arch, and (2) why the location of its CG is not crucial. Surely, if
the CG of each group of blocks extends beyond the edge of the supporting
block the entire stack will fall.
Paul O. Johnson
----- Original Message -----
From: "Jack Uretsky" <jlu@HEP.ANL.GOV>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, January 25, 2002 8:00 PM
Subject: Re: Sum of Infinite Series
Hi all-any of my few physics and math reference books. Since it's based on center
My math resource, who pulled this problem on me 3 years ago,
finally revealed that we're talking about 1/2 of an arch, so the location
of the cg is not crucial.
Regards,
Jack
On Thu, 24 Jan 2002, Paul O. Johnson wrote:
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This is a math question. Please bear with me. I can't find the answer in
of gravity and stability principles, I feel emboldened to ask it here.
eight identical rectangular wooden blocks (about 8 inches long). The object
I am creating a tabletop exhibit at The Science Place. It consists of
is to create an "impossible stairway" by stacking the blocks so that the top
block extends beyond the supporting edge of the bottom block. It looks
unstable but it ain't.
so that the steps get shorter as you work your way down. The top step
The theoretical best solution is to stack the blocks from the top down
(between blocks 1 and 2) is 1/2 block-length, the next step down (between
blocks 2 and 3) is 1/4 block-length, then 1/6, 1/8, 1/10, 1/12, and finally
1/14 block-length between blocks 7 and 8.
extension is. This requires that I sum the infinite series 1/2 + 1/4 + 1/6 +
I want to state in the exhibit's sign what the absolute maximum
1/8 + . . . I'm ashamed to admit that I no longer carry this trivial math
equation in my head (I know I once did). Can anyone help me?
me. I
Paul O. Johnson
Exhibit Developer
The Science Place
Dallas, Texas
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<DIV><FONT face=Arial size=2>This is a math question. Please bear with
Sincecan't find the answer in any of my few physics and math reference books.
emboldened toit's based on center of gravity and stability principles, I feel
Scienceask it here.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I am creating a tabletop exhibit at The
inchesPlace. It consists of eight identical rectangular wooden blocks (about 8
blockslong). The object is to create an "impossible stairway" by stacking the
block. Itso that the top block extends beyond the supporting edge of the bottom
thelooks unstable but it ain't.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The theoretical best solution is to stack
wayblocks from the top down so that the steps get shorter as you work your
next stepdown. The top step (between blocks 1 and 2) is 1/2 block-length, the
1/12,down (between blocks 2 and 3) is 1/4 block-length, then 1/6, 1/8, 1/10,
theand finally 1/14 block-length between blocks 7 and 8.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I want to state in the exhibit's sign what
series 1/2absolute maximum extension is. This requires that I sum the infinite
this+ 1/4 + 1/6 + 1/8 + . . . I'm ashamed to admit that I no longer carry
trivial math equation in my head (I know I once did). Can anyone help
me?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Paul O. Johnson</FONT></DIV>
<DIV><FONT face=Arial size=2>Exhibit Developer</FONT></DIV>
<DIV><FONT face=Arial size=2>The Science Place</FONT></DIV>
<DIV><FONT face=Arial size=2>Dallas, Texas</FONT></DIV></BODY></HTML>
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--
"But as much as I love and respect you, I will beat you and I will kill
you, because that is what I must do. Tonight it is only you and me, fish.
It is your strength against my intelligence. It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
Greg Nagan from "The Old Man and the Sea" in
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