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The Golden Mean, Albrecht Durer, and Magic Squares

 On the wall of their tower, the Camelback Dogs have illustrated some very intriguing discoveries involving geometry, mathematics, and nature.

First off in this diagram we have the golden mean. It is a ratio called phi found in all of nature from the very large to the very small. Its numerical expression is 1.6180339887… and just like pi, it goes on and on and on never ending; adding to its mystery. But we can just call it 1.61 for now.

If you were to draw a rectangle with the sides in a 1.61 relationship and then draw in a vertical line to create a square to one side (A), the surprising thing is that the area which is left is once again the golden mean.(B)

If you continued this process of making smaller and smaller squares and rectangles (C) you would discover that if you were to connect geometric points on these figures you would create a spiral (D) which is found in all of nature in everything from seashells, to ocean waves, to the formation of galaxies and even the structure of the your body.

Because of this all inclusive nature of the golden mean, we are therefore drawn, often unknowingly, to any form which makes use of it as an underlying pattern or design. We appreciate these forms because they contain a ratio which has a presence in the foundations of nature and who we are. That is why the Camelback Dogs insisted that their book be designed and printed in a shape which is based on the golden mean ratio. So you would be attracted to it! Jasper’s book, Catwalk also uses the same shape. For more information go to www.goldennumber.net


In the main square of the illustration, the Camelback Dogs have placed a grid of 16 numbers – from 1 to 16. This happens to be a magic square. Why? First off notice the two numbers in the center of the bottom row. They give the date of 1514. This is the year that the great German woodcut artist, Albrecht Durer created an engraving called Melancolia.

There is a woman surrounded by mysteries and curiosities. On the wall behind her is this extraordinary magic square. Add up the numbers in any column or row and you will always get the same total: 34. Not only that; if you add up the four numbers in each corner or the four numbers in the center or even the four individual corner squares you still get the number 34. Here (E) are other patterns which also add up to 34.

How remarkable it is that Durer was able to create this marvelous piece of magic way back in 1514. Did he have some assistance from the Camelback Dogs?

For more information take a look at the book; The Zen of Magic Squares, Circles, and Stars by Clifford A. Pickover. Also, go to www.grogono.com . Click on magic squares.

Copyright © 2005 Jasper Tomkins All rights reserved.