### Spirals and the Golden Ratio The Golden Ratio: Phi, 1.618

Aug 25, 20120183;32;The Fibonacci spiral gets closer and closer to a Golden Spiral as it increases in size because of the ratio of each number in the Fibonacci series to the one before it converges on Phi, 1.618, as the series progresses (e.g., 1, 1, 2, 3, 5, 8 and 13 produce ratios

Fibonacci Numbers and Phi Are Related to Spiral Growth in Nature.If you sum the squares of any series of Fibonacci numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci nu...Alternate Spirals in Plants Occur in Fibonacci Numbers.The most common appearances of a Fibonacci numbers in nature are in plants, in the numbers of leaves, the arrangement of leaves around the stem and...Golden Spirals in Sea ShellsGolden ratios are also sometimes found in the160;proportions of successive spirals of a sea shell, as shown below.The Nautilus Shell Spiral Is Not A Golden Spiral but Often Still Has Golden Ratio Proportions.The nautilus shell is often shown as an illustration of the golden ratio in nature, but the spiral of a nautilus shell is NOT a golden spiral, as i...