Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: 11 year olds homework
Replies: 46   Last Post: Nov 26, 2004 6:42 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Angus Rodgers

Posts: 387
Registered: 12/6/04
Re: 11 year olds homework
Posted: Nov 16, 2004 8:04 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


On 14 Nov 2004 06:31:37 GMT, israel@math.ubc.ca
(Robert Israel) wrote:

>Let F be the mapping (a,b,c,d) -> (|a-b|,|b-c|,|c-d|,|d-a|) on R^4.
>Note that F is positively homogeneous (i.e. F(tx) = t F(x) if
>t >= 0), so multiplying a vector by a positive scalar doesn't
>change the number of iterations needed to reach (0,0,0,0).
>[...] this mapping has arbitrarily long orbits (on Z^4 as
>well as R^4).

Even worse:

If k is the unique real solution of k^3 + 2k^2 - 2 = 0,
and u is the vector (1, k + 1, (k + 1)^2, k^2 + 3k + 3),
then F(u) = (k, k(k + 1), k + 2, k^2 + 3k + 2) = ku
(because k(k + 1)^2 = k + 2), therefore F^n(u) = (k^n)u
\neq (0, 0, 0, 0) for all n >= 0.

--
Angus Rodgers
(angus_prune@ eats spam; reply to angusrod@)
Contains mild peril



Date Subject Author
11/13/04
Read 11 year olds homework
Chris
11/13/04
Read Re: 11 year olds homework
Virgil
11/13/04
Read Re: 11 year olds homework
Ryan Reich
11/13/04
Read Re: 11 year olds homework
Virgil
11/14/04
Read Re: 11 year olds homework
Randy Yates
11/14/04
Read Re: 11 year olds homework
G. A. Edgar
11/17/04
Read Re: 11 year olds homework
David Ames
11/17/04
Read Re: 11 year olds homework
Stephen Herschkorn
11/17/04
Read Re: 11 year olds homework
Road Runner News
11/18/04
Read Re: 11 year olds homework
Jeremy Boden
11/18/04
Read Re: 11 year olds homework
Rick Decker
11/18/04
Read Re: 11 year olds homework
Gerry Myerson
11/20/04
Read Re: 11 year olds homework
The Ghost In The Machine
11/18/04
Read Re: 11 year olds homework
Jeremy Boden
11/18/04
Read Re: 11 year olds homework
Dave Seaman
11/18/04
Read Re: 11 year olds homework
Richard Henry
11/19/04
Read Re: 11 year olds homework
jmfbahciv@aol.com
11/19/04
Read Re: 11 year olds homework
Phil Carmody
11/19/04
Read Re: 11 year olds homework
Paul Leyland
11/19/04
Read Re: 11 year olds homework
Keith Ramsay
11/19/04
Read Re: 11 year olds homework
Christian Bau
11/19/04
Read Re: 11 year olds homework
Jeremy Boden
11/19/04
Read Re: 11 year olds homework
Phil Carmody
11/18/04
Read Re: 11 year olds homework
Tom Kirke
11/19/04
Read Re: 11 year olds homework
jmfbahciv@aol.com
11/19/04
Read Re: 11 year olds homework
jmfbahciv@aol.com
11/22/04
Read Re: 11 year olds homework
John Schoenfeld
11/14/04
Read Re: 11 year olds homework
Robert Israel
11/14/04
Read Re: 11 year olds homework
Robert Israel
11/14/04
Read Re: 11 year olds homework
Virgil
11/16/04
Read Re: 11 year olds homework
Angus Rodgers
11/20/04
Read Re: 11 year olds homework
Rouben Rostamian
11/20/04
Read Re: 11 year olds homework
Angus Rodgers
11/20/04
Read Re: 11 year olds homework
Angus Rodgers
11/20/04
Read Re: 11 year olds homework
Angus Rodgers
11/21/04
Read Re: 11 year olds homework
Angus Rodgers
11/21/04
Read Re: 11 year olds homework
Angus Rodgers
11/22/04
Read Re: 11 year olds homework
Angus Rodgers
11/26/04
Read Re: 11 year olds homework
Keith Ramsay
11/26/04
Read Re: 11 year olds homework
Angus Rodgers
11/13/04
Read Re: 11 year olds homework
Richard Henry
11/13/04
Read Re: 11 year olds homework
The Ghost In The Machine
11/13/04
Read Re: 11 year olds homework
Angus Rodgers
11/14/04
Read Re: 11 year olds homework
Phil Carmody
11/14/04
Read Re: 11 year olds homework
Angus Rodgers
11/14/04
Read Re: 11 year olds homework
Ignacio Larrosa Cañestro
11/21/04
Read Re: 11 year olds homework
tinyurl.com/uh3t

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.