Peter Loly
Department of Physics & Astronomy and Winnipeg Institute for Theoretical Physics . University of Manitoba
Peter Loly with Ian Cameron, Eigenvalues of an Algebraic Family of Compound Magic Squares of Order n=3^l, l=2,3,..., and Construction and Enumeration of their Fundamental Numerical Forms.
Peter Loly, Ian Cameron, Walter Trump and Daniel Schindel, "Magic square spectra", Linear Algebra and its Applications, 430 (2009) 2659-2680.
Eigenvalues
in the Universe of Matrix Elements 1..n-squared. Keynote
talk at 16th International Workshop on Matrices and Statistics, Windsor, June
1-3.
(This is an update of the main part of the lead keynote talk at IWMS16, June 1-3, 2007, Windsor, Ontario.)
Enumerating the bent diagonal squares of Dr
Benjamin Franklin FRS , Proceedings of the Royal Society A: //dx.doi.org/10.1098/rspa.2006.1684 - volume 462 (2072),
2271-2279, August 2006 - Feb. 26, 2007 :
2nd of top 10 downloads for past 3 months! Covered in 2006 book "Magische vierkanten - van Lo Shu
tot Sudoku" by Arno
van den Essen (www.wiskundemeisjes.nl/wp-content/uploads/2006/12/kaft.jpg).
Count verifed by Miguel Amela (http://www.region.com.ar/amela/franklinsquares/) and
by FormulaOne
(http://www.f1compiler.com/samples/Franklin%27s%208x8%20Magic%20Square.f1.html)
Second book covers our Franklin work:
Eigenvalues in the Universe of Matrix Elements 1..n-squared. Keynote talk at 16th International Workshop on Matrices and Statistics, Windsor, June 1-3.
Paul C. Pasles: “Benjamin
Franklin’s Numbers – A Unsung Mathematical Odyssey”,
Princeton University Press 2008 – see 228, 241.
12th order Franklin Squares? - A Question
Posed by Loly in the Franklin paper April 2007 - Since the publication of Arno van den Essen's book Christian Eggermont
reports that there has been a mini-media storm in the Netherlands.
Arno van den Essen, Magische vierkanten - Van Lo-Shu tot sudoku, Veen Magazines, 2006 - see 11, 148, 152.
Franklin
Squares - A Chapter in the Scientific Studies of Magical Squares
, transcript for poster talk at NKS2006
(New Kind of Science), Washington, D.C., June 2006. [Complex Systems, vol. 17 (2007) 143-161]
Counting Franklin's Magic Squares -
Math Trek article in Science News by Ivars Peterson
about the Franklin paper and other magical square work by The Manitoba
Magicians. Chosen 3rd of the top 10 weekly MathTrek columns of 2006.
Magic
Square Physics - second Math Trek article by Ivars
Peterson about moments of inertia and the multipole expansion with Adam Rogers.
See also http://www.research.att.com/~njas/sequences/A126275.
Review of
our "Franklin Squares" paper - Math in the Media (AMS), April 2006, by Tony Phillips.
Peter Loly's
Scientific Genealogy (Physics in Canada
ARTWORK from research work .
Cover of article on using Gray code for Chinese
patterns in The Oracle .
REPRINTS . PUBLICATIONS . Magic Squares . Magic Cubes
"The Expanding World of
Physics at Manitoba", by R.D.Connor (a partial
index by P.D.Loly)
Google link for Physics/History .
"What is
Science?" . "What is Physics?" . "physics.org" . "Eric Weisstein's
World of Physics" .
loly at cc dot umanitoba dot ca
A Magic Cube
where the radius of the spheres goes as the cube root of the corresponding
integer element (for another picture see: squareBalls6.bmp
on this site)
ARTWORK from research work . Cover of article on using Gray code for Chinese patterns in The Oracle .
REPRINTS . PUBLICATIONS . Magic Squares . Magic Cubes
"The Expanding World of Physics at Manitoba", by R.D.Connor (a partial index by P.D.Loly)
Google link for Physics/History .
A Magic Cube
where the radius of the spheres goes as the cube root of the corresponding
integer element (for another picture see: squareBalls6.bmp
on this site)