Some 25 centuries ago Pythagoras developed a semi-mystical philosophy that attempted to approach the divine through mathematics and music (the two weren’t—and aren’t—totally separate). Besides the rather well known theorem for finding the lengths of the sides of right triangles, Pythagoras and his school developed the Golden Section.

If you draw 3 diagonals in a regular pentagon, the intersection divides the lines in a ratio of 0.5(1+5**1/2) (for the mathematically challenged that’s one plus the square root of five all divided by 2) or 1.61803…. Pythagoras and his followers found this ratio aesthetically pleasing and said that it was one of the most important numbers in nature. Phidias adopted this ratio and designed the Parthenon so that the sides of the pediments had it. Many neo-classical buildings throughout the world still use the Golden Section thanks to the influence of the Parthenon.

The Italian mathematician Fibonacci developed a series in which each term is the sum of the two previous terms (0, 1, 1, 2, 3, 5, 8, 13, 21....). This series is found all over the place in nature; the branching of trees, the distribution of the florets of pinecones and pineapples and the petals of many flowers. What does this have to do with the Golden Section? Divide any term of the Fibonacci series by it’s predecessor and you get an approximation of the Golden Section. The larger the two terms the closer the approximation.

The Golden Section also appears in spirals. By drawing perpendicular lines to different parts of the curve, the two lines will have a ratio that is close to 1.6180... (If that’s confusing, well. I don’t quite get it myself.) The shell of the chambered nautilus, the curving of animal horns all use this sort of spiral in their growth. Apparently as a spiral grows in this way, the center of gravity doesn’t change. Galaxies spiral in the same way, but for different reasons.

It seems as though Pythagoras and his followers were really on to something. The Golden Section appears everywhere in nature and does seem to have some relation to whatever underlies the universe.



*Most of this was taken from "A Scientist’s Notebook: Vaults in Vacuum" by Gregory Benford in the August, 1998 issue of The Magazine of Fantasy and Science Fiction.