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# Magic squares

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### Magic squares

1. 1.  NAME: DHRUV SOLANKI  CLASS:VIII – A  ROLL NO. : 7  SUBJECT: MATHS
2. 2. Magic Squares A 3 x 3 magic Square Put the numbers 1 to 9 into the square so that all rows, columns and diagonals add to the magic number. 1 2 Magic Number = ? 3 6 5 4 7 8 9 4 7 5 3 9
3. 3. 15 ( 1) (1 ) 2 n n Sum n + → = Magic Squares A 3 x 3 magic Square Put the numbers 1 to 9 into the square so that all rows, columns and diagonals add to the magic number. Magic Number = ? 1 2 3 6 5 4 7 8 9 51 9 2 8 6 43 7
4. 4. In the Middle Ages magic squares were believed to give protection against the plague! In the 16th Century, the Italian mathematician, Cardan, made an extensive study of the properties of magic squares. During this century they have been used as amulets in India. Even today they are widespread in Tibet, (appearing in the “Wheel of Life) and in other countries such as Malaysia, that have close connections with China and India.
5. 5. A 4 x 4 Magic Square ( 1) (1 ) 2 n n Sum n + → = Put the numbers 1 to 16 into the square so that all rows, columns and diagonals add to the magic number. 1 Magic Number = ? 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 880 Solutions! 34 10 11 6 7 15 14 8 129 16 1 13 4 5 3 2
6. 6. 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 The Melancholia Magic Square The melancholia magic square is highly symmetrically with regard to its magic constant of 34. Can you find other groups of cells that give the same value? 34
7. 7. An Amazing Magic Square! 7 12 1 14 2 13 8 11 16 3 10 5 9 6 15 4 This magic square originated in India in the 11th or 12th century How many 34’s can you find?
8. 8. Benjamin Franklin’s Magic Square. The American statesman, scientist, philosopher, author and publisher created a magic square full of interesting features. Benjamin was born in Massachusetts and was the 15th child and youngest son of a family of seventeen. In a very full life he investigated the physics of kite flying.
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