Magic squares have been known for many centuries. The standard or normal magic square is defined as an arrangement of the first n2 natural numbers (or positive integers) into a square matrix so that the sum of the numbers in each column, row and diagonal is the same magic number.
What is the logic behind magic square?
A magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A magic square contains the integers from 1 to n2.
What is a magic square and how do they work?
A magic square is an n x n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. This number is called the magic number. The main diagonals are those that stretch from corner to corner.
What is the method of magic square?
A magic square will remain magic if two rows, or columns, equidistant from the centre are interchanged. An even order magic square ( n x n where n is even) will remain magic if the quadrants are interchanged. An odd order magic square will remain magic if the partial quadrants and the row is interchanged.
What is unique about Ramanujan magic square?
He died at age 32. Ramanujan created a super magic square. The top row is his birthdate (December 22, 1887). I then started playing around with the numbers row by row and I was then able to get every row and column to add to the same number (133), but not the diagonals.
Why are magic squares Magic?
Magic Squares: When Art is Squared With Mathematics The magic arises because the sum of the numbers present in each row, in each column and in each main diagonal, give the same result, called the “magic constant” or the “magic sum.”
Why 1729 is a magic number?
It is 1729. Discovered by mathemagician Srinivas Ramanujan, 1729 is said to be the magic number because it is the sole number which can be expressed as the sum of the cubes of two different sets of numbers.
Why is 1729 a special number?
1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is also the sum of the cubes of 12 and 1- cube of 12 is 1728 and cube of 1 is 1; adding the two results in 1729.
What do you need to know about magic square?
M = magic(n) returns an n-by-n matrix constructed from the integers 1 through n 2 with equal row and column sums. The order n must be a scalar greater than or equal to 3.
What do you call a magic square of order n?
A magic square of order n is an arrangement of n^2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A magic square contains the integers from 1 to n^2. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M.
How to create magic square in MATLAB magic MathWorks?
M = magic (n) returns an n -by- n matrix constructed from the integers 1 through n2 with equal row and column sums. The order n must be a scalar greater than or equal to 3 in order to create a valid magic square. The sum of the elements in each column and the sum of the elements in each row are the same.
What happens when you divide the magic square by the magic constant?
Dividing each number of the magic square by the magic constant will yield a doubly stochastic matrix, whose row sums and column sums equal to unity. However, unlike the doubly stochastic matrix, the diagonal sums of such matrices will also equal to unity.
