Magic squares – Different direction, same Sum
Introduction
Not every mathematical concept has some magic and fun. This concept of number theory was unique and calculative as well. The famous puzzles of mathematics like sudoku came after the existence of this puzzle and won popularity, but this concept has an extraordinary way to represent itself with arrangements and combinations leading to enjoyment in free time and also rewarding with tons of mathematical knowledge and interest.
What is magical in these squares?
A square array of numbers consisting of positive integers usually are known as magic squares. The digits placed in each row, column, and both main diagonals have their total sum the same. The magic squares in a particular order of the number of integers along one side (n) and the constant sum is termed as magical constant. These can be arranged in thousand ways by just using 1-9 numbers in a three-by-three grid. A magic square is obtained by just 8 digits, where each row, column, and diagonal sum up the magic total.
Ancient origins
The very first known reference to the magic square was in China though the exact origin is unknown. It was known by a Chinese legend of Lo Shu (scroll of river Lo), in the times of 650 BCE. The story of the discovery of magic squares revolves around a turtle who appeared to king Yu in a devastating flood. The turtles back had a pattern with numbers represented on his back by circular dots. Because of this legend, the odd and even numbers are arranged in such a manner that even numbers always lie in the corner and were believed as good luck charm for their magical properties.
This unique idea started floating with the silk routes to various countries and gave rise to interesting exchanges in the culture of mathematics. In the Indian book of divination, the magic squares were discussed and used to measure the quantities of perfume.
An example of a pattern on the turtles back which lead to this discovery
Various size grids
An order is the number of rows and columns in a magic square. This order may vary according to the patterned square. For e.g. a three-by-three magic square is defined as an order of three. An order of two matrices doesn’t exist as they can justify only if all the numbers are identical. The quantities of magic squares increase as the order increases. A magic square of order four gives 880 different arrangements, while the order of five gives a magic total of almost millions of magic squares. The magic squares can be arranged in order of six but no one calculated the number of possibilities.
Conclusion
The most magically magical invention of magic square ever made by a magician. This tells us about how mathematics is serving us with interesting, knowledgeable, and unique concepts. The true essence of these magic squares can be only derived when we actually attempt to make one. Being a fan of mathematical puzzles like sudoku, tangram, etc. this amazing concept forced me to take a detailed look at this. Studies say that a new puzzle game named geomagic squares came into existence in the modern era where instead of numbers, the use of various geometrical shapes was tried. Lastly, mathematics is a compact of fun, knowledge, etc., and taking a tour of the history of mathematics is undoubtfully magical.