Contents
What is the use of magic square?
The use of magic squares is illustrated for balancing out linear trend from main variable effects and lower order interactions in some factorial experiments, and from some Latin and Graeco- Latin square designs. Some devices for assessing the size of the trend are also indicated.
How do you find the magic number in a magic square?
A magic square is a grid containing the numbers 1, 2, 3, and so on, where each row, column and diagonal add up to the same number. An example is shown below, you will see that each row, column and diagonal add up to 34. This number 34 is the “magic number” of the magic square.
How many magic squares are there?
Fact: There are 880 magic squares, counting the symmetric ones only once.
Why is 1729 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.
What kind of numbers are used in semi magic squares?
Jean-Claude Rosa, France, constructed this 3×3 semi-magic square (with 6 correct sums) using only odd numbers. Interesting, because most of the 3×3 semi-magic squares use both odd and even numbers. Strange: in this smallest possible example, all the numbers used are squares of primes.
How to calculate 3×3 magic square of squares?
Using these 3 primitive Pythagorean triangles having the same area: 1380² + 19019² = 19069² 3059² + 8580² = 9109² 4485² + 5852² = 7373² he constructed this 3×3 square (with 7 correct sums) using only odd numbers. 6 of its 9 numbers are squares of primes. 5521² 10337² 19069² 20399² 9109² 1367² 7373² 17639² 11639²
Is there a parametric solution with a non-square magic sum?
The first known example with a non-square magic sum was constructed by Michael Schweitzer(Fig MS4of the M.I. article). It would be very interesting to find a parametric solution with a non-square magic sum, generating an infinite number of 3×3 squares.