Amazing Maths – The Golden Spiral in Nature

At Gallagher School in Midrand we are obsessed with maths and science. And so are our learners! Why? Well, because maths and science are all around us everyday. And the more we teach our children about it, the more they will see and experience the wonderful world of science and mathematics around them.

What is the Golden Spiral?

The Golden Spiral is formed in a progressive sequence of rectangles, each about 1.61803 bigger then the last. Goldenspiral

Because the ratio remains the same every time the rectangle is divided, the spiral goes on forever. The sequence of numbers known as the Fibonacci sequence is 0,1,1,2,3,5,8,13,21,34,55,89 and so on. You get it by making each number the sum of the two preceding it. It’s easy to build this in Excel. Put 0 in A1, and 1 in A2, then in A3 put =SUM(A1,A2), then copy A3 down the page. The numbers get very big, very quickly. Now in B3 put =A3/A2, make sure you’ve got plenty of decimal places and copy that formula down column B. The result rapidly approaches the Golden Ratio, then, at 102 334 155 divided by 63 245 986 = 1,618 033 988 749 89, Excel runs out of power and it stops changing.

Already fascinating, but it gets even stranger… In nature, the ratio and the golden spiral crop up all over the place. Here are some examples (images from Google).

The Nautilus shell


The Nautilus shell


Spiral galaxies






Don’t you just love mathematics and nature?!



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