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Magic Squares

In: Ramanujan’s Notebooks

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  • Bruce C. Berndt

    (University of Illinois, Department of Mathematics)

Abstract

The origin of Chapter 1 probably is found in Ramanujan’s early school days and is therefore much earlier than the remainder of the notebooks. Rules for constructing certain rectangular arrays of natural numbers are given. Most of Ramanujan’s attention is devoted to constructing magic squares. A magic square is a square array of (usually distinct) natural numbers so that the sum of the numbers in each row, column, or diagonal is the same. In some instances, the requirement on the two diagonal sums is dropped. In the notebooks, Ramanujan uses the word “corner” for “diagonal.” We emphasize that the theory of magic squares is barely begun by Ramanujan in Chapter 1. Considerably more extensive developments are contained in the books of W. S. Andrews [1] and Stark [1], for example.

Suggested Citation

  • Bruce C. Berndt, 1985. "Magic Squares," Springer Books, in: Ramanujan’s Notebooks, chapter 0, pages 16-24, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1088-7_2
    DOI: 10.1007/978-1-4612-1088-7_2
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