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The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
As a running example, we consider a 10×10 magic square, where we have divided the square into four quarters. The quarter A contains a magic square of numbers from 1 to 25, B a magic square of numbers from 26 to 50, C a magic square of numbers from 51 to 75, and D a magic square of numbers from 76 to 100.
Apart from the trivial case of the first order square, most-perfect magic squares are all of order 4n. In their book, Kathleen Ollerenshaw and David S. Brée give a method of construction and enumeration of all most-perfect magic squares. They also show that there is a one-to-one correspondence between reversible squares and most-perfect magic ...
The Siamese method, or De la Loubère method, is a simple method to construct any size of n-odd magic squares (i.e. number squares in which the sums of all rows, columns and diagonals are identical). The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère , [ 1 ] as he was returning from his 1687 ...
Start by creating a (2n+1)-by-(2n+1) square array consisting of n+1 rows of Ls, 1 row of Us, and; n-1 rows of Xs, and then exchange the U in the middle with the L above it. Each letter represents a 2x2 block of numbers in the finished square.
Since each 2 × 2 subsquare sums to the magic constant, 4 × 4 pandiagonal magic squares are most-perfect magic squares. In addition, the two numbers at the opposite corners of any 3 × 3 square add up to half the magic constant. Consequently, all 4 × 4 pandiagonal magic squares that are associative must have duplicate cells.
A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. [1] A traditional magic square is a square array of numbers (almost always positive integers ) whose sum taken in any row, any column, or in either diagonal is the same target number .
Scott Flansburg (born December 28, 1963) is an American dubbed "The Human Calculator" and listed in the Guinness Book of World Records for speed of mental calculation.He is the annual host and ambassador for The National Counting Bee, a math educator, and media personality.