Lecture 5 : Latin Squares and Magic
نویسنده
چکیده
Today's application is to magic! Not the friendship kind, though 1 ; instead, we're going to talk about magic squares, an incredibly old piece of mathematics that we can study using Latin squares. Definition. A magic square is a n × n grid filled with the integers {0, 1,. .. n 2 − 1}, such that • each number is used exactly once in our entire grid, and • the sum of all of the entries along any row, column, the main diagonal 2 or the main antidiagonal all come out to the same constant value. Here's an example for order 3: 1 6 5 8 4 0 3 2 7 Magic squares have been studied for a fairly ridiculously long time. Mathematicians and philosophers were aware of them since about 650 BC; since their discovery, people have used them both as the basis for magic tricks (when your population is largely numerically illiterate, magic squares were a neat way to perform seemingly impossible feats) and religious/spiritual/cultural icons. (A zoomed-in portion of an engraving by Albrecht Dürer, titled Melencolia I. Note how he hid the year of his engraving, 1514, in the last row.) 1 Fluttershy is best pony. 2 The main diagonal of a n × n grid is simply the set of cells connecting the top-left to the bottom
منابع مشابه
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The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of the Singular Value sets, here named SV clans, are a powerful way of comparing different integer squares. Several complete sets of magic and Latin sq...
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