auszerordentl. Mathkoll. am 23.4.07/Prof. McGill

[Institut für Mathematik]

Auszerordentliches Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. G.P.H. Styan McGill (University, Montreal)

mit dem Thema: ''An illustrated introduction to magic squares''

Abstract:
Frederick Augustus Porter Barnard (1809--1889), the tenth president of
Columbia College (now Columbia University) and after whom Barnard College is
named, observed that ``The construction of magic squares has been practiced
earlier than the period of authentic history and it has preoccupied the
attention of the curious in every age, among them men of high scientific
eminence.'' In this talk we focus on magic square matrices that are fully
magic, i.e., the rows, columns, and the two main diagonals all sum to the
same ``magic sum''. We concentrate on magic square matrices with 3 nonzero
eigenvalues and with rank equal to 3, and on some associated postage stamps.
As examples we consider the 'Luoshu matrix'

(4   9   2)
(3   5   7)
(8   1   6)
and the 'Dürer matrix'
 (16  3  2  13)
(5  10  11  8)
(9  6  7  12)
(4  15  14  1)

The magic square associated with the Luoshu matrix was apparently first
considered by the (mythical) Chinese engineer-emperor Yü the Great (fl. c.
21st century BC), while the magic square associated with the Dürer matrix
appears in Albrecht Dürer's well-known copper-plate engraving 'Melencolia
I', which dates from 1514 AD.
This engraving is depicted on a stamp issued by Aitutaki--Cook Islands and
on a stamp from Mongolia.
We present some (apparently new) closed-form matrix formulas for the odd and
even powers of a magic matrix A with rank equal to 3 and with 3 nonzero
eigenvalues, such as the Luoshu and Dürer matrices, and over six hundred
essentially different 4x4 magic square matrices.

Zeit: Montag, 23. April 2007, 16.45 Uhr (Kaffeejause), 17.15 Uhr Vortrag

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
Seminarraum C 2.09

Harald Rindler
Klaus Schmidt