Wednesday, April 1, 2009

A rose by any other name is just as sweet

Gertrude Stein wrote "Rose is a rose is a rose is a rose." The trick of this phrase is using the law of thricefold repetition, for emphasis of a particular point. However, a spiral is not a spiral is not a spiral.

One of the better known geometric forms is the Archimedean spiral, named after Archimedes, the famous ancient mathematician. This form is found in windup springs in mechanical toys and analog watches.
Another type of spiral, that is more frequent in Nature, is the logarithmic spiral. The best visual example of this type of spiral is the cut away section of the Nautilus Shell. A special type of logarithmic spiral is the Fibonacci spiral, which is based on the golden ratio. Many discussions have been made regarding artists having used in their works an approximation of the golden ratio in order to make it more aesthetically pleasing.

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Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica