Almost from the time that people added numbers, someone would have noticed a curious pattern … that 1 + 9 = 2 + 8 = 3 + 7 = 4 + 6. As one number grows, the other decreases by the same amount, so the total remains constant. It would not have taken long before similar sums were drawn across each other, for example, 9 + 5 + 1 vertically and 3 + 5 + 7 horizontally, sharing the five (see the square to the right). From this it would be a short step to a pattern with a fascinating property: a magic square, like the one at right, in which the totals of all columns and rows and both diagonals are the same.
This page will explore these patterns and why they ‘work.’ We will examine different ways of designing such squares, and the surprising variety among those that exist. We will construct squares of increasing size and ask ourselves whether there is a limit to their size. We will see squares that are built from prime numbers, others that look the same when rotated 180°, and magic squares with other strange properties.
We will also learn some of the history of these fascinating squares and how Albrecht Dürer (1471-1528) managed to construct a magic square for his engraving, Melancholia, in which the middle numbers at the bottom give 1514, the year of the engraving!
We were all deeply impressed with Graeme from the very beginning. [Lucas’] confidence radically changed within only 3 weeks of Graeme’s instruction and assistance. I am sure this was largely attributed to Graeme’s infectious passion and love for his subject, and his high personal level of skill, teaching experience and understanding of mathematics. Lucas always found Graeme could explain concepts so knowledgeably and easily, which really did transform Lucas’ appreciation and enjoyment of the subject. Graeme always gave Lucas assistance and time over and above his hour’s tutoring session. Graeme has developed a wonderful relationship and more of a mentoring role which has been of great assistance and value to Lucas as he faces the pressures of his final year of school. I have no hesitation in recommending Graeme as an outstanding tutor and friend, and a very wise, knowledgeable and capable teacher of the highest calibre.
Sally T (parent, 2005)
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