More Magic Squares

The magic square of Leonhard Euler

Leonhard Euler created the following magic square:

The above magic square of order 8 has the following properties:

• Each row and each column has a sum of 260.
• Each half of a row or column has a sum of 130.

It’s called a magic square, although the diagonals don’t sum to 260. It’s also the solution to the chess problem I’ve already posted.

The magic square of Benjamin Franklin

The following magic square of order 8 was constructed by Benjamin Franklin, the famous scientist and writer of the 1700s.

Notice that each row or column of the magic square has a sum of 260. Also , half of each row or column has a sum of 130. In addition, if we take the halves of the diagonals in twos, “arcs” are formed which all have the same sum which also equals 260.

In many layouts of the square the numbers add up to 260.

The magic square of the apocalypse

It is attributed to A.W.Johnson, of which more details are not known, and is known as the magic square of the apocalypse, (of order 6), as the sum that appears in each column, row and diagonal is 666!!!!

The magic square of the mirror

The following magic square of order 4 has a sum of the numbers of each column, row and both diagonals equal to 176. (Picture 1)

Now, if we were to put a mirror on the left and look at its reflection, we would have a new magic square…  (Picture 2)

If we again calculate the sum of the numbers of each column, row and two diagonals, we would again see that it is equal to 176.

If we take the original square again and turn it upside down, we will again have a new magic square, which, if we again calculate the sum of the numbers of each column, row and both diagonals, we will again see that it is equal to 176. (Picture 3)

Now, if we were to put a mirror on the left, and in it, and see its reflection, we would have a new magic square…  (Picture 4)

If we again calculate the sum of the numbers of each column, row and both diagonals, we would again see that it is equal to 176.