David Chandler's Journal of Java Web and Mobile Development

  • David M. Chandler

    Web app developer since 1994 and Google Cloud Platform Instructor now residing in Colorado. Besides tech, I enjoy landscape photography and share my work at ColoradoPhoto.gallery.

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Count the spirals...

Count the spirals left and right, Fibonacci

Φ, the Golden number

Φ – 1 = 1 / Φ = φ

Φ, φ = (√5 ± 1) / 2 = 1.618034…, 0.618034…

Somehow I made it through 12 years of public school, an engineering degree, and 15 years of working with scientists and engineers before I learned about the “most irrational number in the universe.” But now that I know, I’m sharing!

Derived from the Fibonacci series (and in fact, any other series that sums the previous two terms, regardless of the initial terms), the golden ratio was known by the Greeks as the “divine proportion”, is found throughout nature, and is commonly used to this day in art and architecture. Phi can be found in the proportions of numerous plants and animals, in the shape of the nautilus shell and the patterning of seeds in daisies, sunflowers, coneflowers, and pinecones, and even in that wonderful Fibonacci fruit, the pineapple. The frequent occurrence of the Fibonacci and Lucas series, Golden ratio, Golden angle, and Golden spiral throughout nature exemplify the magnificent mathematical order in the universe and suggest its origin in a mathematical Mind far more advanced than the mind of man.

“How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”

— Albert Einstein

Dr. Ron Knott of the UK has put together some beautifully illustrated resources on the subject:

Besides the excellent photography, diagrams, and mathematics, be sure to note the Excel spreadsheet model of a sunflower head, which inspired this interactive demo I created using GWT.

“For what can be known about God is plain to them, because God has shown it to them. For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse.”

— Romans 1:20, ESV