Mathematician Arthur Benjamin said, "Mathematics is the science of patterns, and we study it to learn how to think logically, critically, and creatively." Not only do patterns exist in nature, they are clearly ubiquitous. Mandelbrot's fractals (often called the thumbprint of God) are but one example of a mathematical pattern repeated on a scale ranging from the micro world to the cosmos. Another extraordinary pattern is known as the Fibonacci sequence, which graphically translates into Fibonacci's spirals (often referred to as the fingerprints of God.) Leonardo Bonacci (a.k.a. Leonardo of Pisa and Fibonacci) was an Italian mathematician most famous for his discovery of what has been called the "golden sequence" of numbers. The famous Fibonacci sequence is simply the following, repeated to infinity. The next number in the sequence is always the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181... This reasonably short video demonstrates how the pattern can be found everywhere from DNA to clouds in the sky. This slightly longer documentary claims to find the golden sequence everywhere in nature, art, music, and even the Mandelbrot set. Of course, not everyone agrees with mathematicians who claim the Fibonacci sequence can be found in virtually everything in the universe. For example, physicist Donald Simanek offers harsh criticism of Fibonacci on a page at his website called the "Fibonacci Flim-Flam." Professor Simanek described people (like me) who found the pro-Fibonacci video interesting as … [Read more...]