History Of Magic Squares

The earliest known Magic Square dates back as far as 2,800BC and, as is often the case, it was the Chinese who devised this very first example.

It’s known as the Lo Shu Magic Square (which roughly translates as “scroll of the River Loh”) and is the one of the most well-known 3 x 3 Magic Squares.

lo shu magic squares,chinese magic squares

The Loh-Shu was reputedly invented by a person named Fuh-Hi, who is regarded as the founder of Chinese civilization.

Although this is the earliest recorded Magic Square, there were undoubtedly others who found instances of these fascinating mathematical curiosities.

For example, the ancient Greeks documented similar squares in 1,300BC or so.

Now, the Loh-Shu square embodies the oriental concept of Yin and Yang, where the odd numbers are represented by white dots, which are Yang, while the even numbers are represented by black dots, which are Yin.

To the Chinese, Yang, or odd numbers, are the emblem of heaven, while Yin, or even numbers, are the emblem of earth.

What’s interesting, therefore, is that, many thousands of miles to the west of China, the Greeks also associated odd numbers with heaven, and even numbers with earth.

Magic Squares were later used by Arabian astrologers, around the ninth century AD, when drawing up horoscopes, although little more is known about these.

woodcut durer,durer melancolia,melancholia durer

It wasn’t until the year 1514AD that the Magic Square became well known, when the German artist and engraver, Albrecht Dürer, created a work called “Melencolia”.

In Melencolia, Durer was very clever as he managed to infuse the date he created this work, i.e. 1514AD, in the centre two squares of the bottom row.

However, this isn’t the first 4 x 4 Magic Square to be found.

The first fourth order Magic Square was actually discovered in Khajuraho, in India, some time around the eleventh or twelfth century.

In more recent years, mathematicians the world over have been creating ever more complex Magic Squares (and other shapes too, such as Magic Cubes), with perhaps the most famous such person being Benjamin Franklin.

Benjamin Franklin is perhaps better known for his other prodigious works, which include being a founding father of the USA, and inventor of devices such as the lightning rod and bifocal glasses, but he was also a talented mathematician too, and his Franklin Squares are some of the most intricate squares ever devised.

Today, they are as popular as ever, even though they have little practical use: they are used as a form of entertainment, within the world of both speed maths and magic, as an educational tool, and, on the darker side, within the black arts, but we’ll leave that particular topic alone as that is well outside the scope of this website.

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