Creates magic squares
Creates normal magic squares of any order >2. Uses the appropriate method depending on n modulo 4.
magic(n)
n |
Order of magic square. If a vector, return a list whose
i-th element is a magic square of order |
Calls either magic.2np1(), magic.4n(),
or magic.4np2() depending on the value of n. Returns a
magic square in standard format (compare the magic.2np1() et seq,
which return the square as generated by the direct algorithm).
Robin K. S. Hankin
William H. Benson and Oswald Jacoby. New recreations with magic squares. Dover 1976.
magic(6) all(is.magic(magic(3:10))) ## The first eigenvalue of a magic square is equal to the magic constant: eigen(magic(10),FALSE,TRUE)$values[1] - magic.constant(10) ## The sum of the eigenvalues of a magic square after the first is zero: sum(eigen(magic(10),FALSE,TRUE)$values[2:10])
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