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Re: Sum of Infinite Series

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-
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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--Boundary_(ID_08JiN333mfqKc4MD0GO6HA)
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This is a math question. Please bear with me. I can't find the answer in
any of my few physics and math reference books. Since it's based on center
of gravity and stability principles, I feel emboldened to ask it here.

I am creating a tabletop exhibit at The Science Place. It consists of
eight identical rectangular wooden blocks (about 8 inches long). The object
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.

The theoretical best solution is to stack the blocks from the top down
so that the steps get shorter as you work your way down. The top step
(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.

I want to state in the exhibit's sign what the absolute maximum
extension is. This requires that I sum the infinite series 1/2 + 1/4 + 1/6 +
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?

Paul O. Johnson
Exhibit Developer
The Science Place
Dallas, Texas

--Boundary_(ID_08JiN333mfqKc4MD0GO6HA)
Content-type: text/html; charset=iso-8859-1
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<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="MSHTML 6.00.2712.300" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face=Arial size=2>This is a math question. Please bear with
me. I
can't find the answer in any of my few physics and math reference books.
Since
it's based on center of gravity and stability principles, I feel
emboldened to
ask it here.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>I am creating a tabletop exhibit at The
Science
Place. It consists of eight identical rectangular wooden blocks (about 8
inches
long). The object 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.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>The theoretical best solution is to stack
the
blocks from the top down so that the steps get shorter as you work your
way
down. The top step (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.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Arial size=2>I want to state in the exhibit's sign what
the
absolute maximum extension is. This requires that I sum the infinite
series 1/2
+ 1/4 + 1/6 + 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?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT>&nbsp;</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>

--Boundary_(ID_08JiN333mfqKc4MD0GO6HA)--


--
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