On Thu, 03 Jul 2008 17:04:19 -0400, Jeff Wisnia
wrote:

John Martin wrote:

On Jul 3, 10:53 am, Jeff Wisnia wrote:

Well, the way it was explained to me is:

The stool's four legs are located on the corners of a square.

Label the legs A, B, C, and D.

With A, B and C touching the wavy floor and D not, start rotating the
stool about its central axis, constraining it so that legs A, B and C
remain in contact with the floor.

If you were to rotate the stool through a full 90 degrees leg A could
replace leg D as being the one not touching the floor and leg D would be
in contact with the floor.

Ergo, at some point in less than 90 degrees of rotation leg D must have
made contact with the floor, and if you'd stopped rotating the stool at
that point all four legs would be contacting the floor.

QED

Try it yourself....

Jeff



I don't think it's quite that simple, Jeff - you've got an
inconsistency there.

On the one hand, you say to constrain it while rotating, so that A, B
and C remain in contact with the floor. You can do that. But you
then say that after 90 degrees D will be contacting the floor and A
will be off it. A can't be off it if the chair is constrained so that
A remains in contact.

John Martin


My curious mind got to wondering when I first got involved with this
whole silly musing about four legged stools and wavy floors.

Looks like it was over 12 years ago, and this link provides a grandios
explanation of why what I said really does work:

http://mathforum.org/kb/message.jspa...83862&tstart=0

Happy Independance Day to all.

Jeff (Who can't recall any other US holidays referred to by their dates
instead of their given names. He doesn't think that the shipment of
mayonaise on the Titantic Cinco de Mayo is a US holiday yet.)

And a happy Fourth to you too although it's a shame that, in all those
years at the 'tute you didn't learn to spell independence.

Marv

--
Brass Rat, '63, Course VIII

Marv wrote:

On Thu, 03 Jul 2008 17:04:19 -0400, Jeff Wisnia
wrote:


John Martin wrote:


On Jul 3, 10:53 am, Jeff Wisnia wrote:


Well, the way it was explained to me is:

The stool's four legs are located on the corners of a square.

Label the legs A, B, C, and D.

With A, B and C touching the wavy floor and D not, start rotating the
stool about its central axis, constraining it so that legs A, B and C
remain in contact with the floor.

If you were to rotate the stool through a full 90 degrees leg A could
replace leg D as being the one not touching the floor and leg D would be
in contact with the floor.

Ergo, at some point in less than 90 degrees of rotation leg D must have
made contact with the floor, and if you'd stopped rotating the stool at
that point all four legs would be contacting the floor.

QED

Try it yourself....

Jeff



I don't think it's quite that simple, Jeff - you've got an
inconsistency there.

On the one hand, you say to constrain it while rotating, so that A, B
and C remain in contact with the floor. You can do that. But you
then say that after 90 degrees D will be contacting the floor and A
will be off it. A can't be off it if the chair is constrained so that
A remains in contact.

John Martin


My curious mind got to wondering when I first got involved with this
whole silly musing about four legged stools and wavy floors.

Looks like it was over 12 years ago, and this link provides a grandios
explanation of why what I said really does work:

http://mathforum.org/kb/message.jspa...83862&tstart=0

Happy Independance Day to all.

Jeff (Who can't recall any other US holidays referred to by their dates
instead of their given names. He doesn't think that the shipment of
mayonaise on the Titantic Cinco de Mayo is a US holiday yet.)


And a happy Fourth to you too although it's a shame that, in all those
years at the 'tute you didn't learn to spell independence.

Marv


Guilty as charged, but YOU may have missed my incorrect spelling of
Titanic. G

Jeff

--
Jeffry Wisnia
(W1BSV + Brass Rat '57 EE)
The speed of light is 1.98*10^14 fathoms per fortnight.