Patterns (Miracles of Maths In Meadows)

pineapple.jpgWhen I saw the writing/picture prompt:


I was very excited…as it touched a scientific nerve on my brain!

Have you ever noticed that many plants grow in spiral formations? A pineapple, for example, may have 8 spirals of scales going around one way and 5 or 13 going in the opposite direction.

If you have time, look closely at the seeds in a sunflower, you may be able to see 55 and 89 spirals crossing over each other or perhaps even more.  Start looking at your vegetables…you will notice spirals more and more!

Do you have any idea why plants grow in this way? Does the number of spirals have any significance?  If you are a mathematician or biologist you probably know all about this already.

Why Do Many Plants Grow In Spirals?

Most plants arrange new growths at a unique angle that produces spirals. What angle is it?

Only what has been termed the “golden angle” of approximately 137.5 degrees results in an ideally compact arrangement of growths. What makes this angle so special?

The golden angle is ideal because it cannot be expressed as a simple fraction of a revolution. The fraction 5/8 is close to it, 8/13 is closer, and 13/21 is closer still, but no fraction exactly expresses the golden proportion of a revolution.

Thus, when a new growth develops at this fixed angle with respect to the preceding growth, no two growths will ever develop in exactly the same direction. Consequently, instead of forming radial arms, spirals form.

Remarkably, a computer simulation of growth from a central point produces recognizable spirals only if the angle between new growths is correct to a high degree of accuracy. Straying from the golden angle by even one tenth of a degree causes the effect to be lost.​

How Many Petals on a Flower?

Fibonacci, Golden Ratio, Sacred Geometry, SpiralInterestingly, the number of spirals that result from growth based on “the golden angle of growth” is usually a number from a series called the Fibonacci sequence. This series was first described by the 13th-century Italian mathematician known as Leonardo Fibonacci. In this progression, each number after 1 is equal to the sum of the previous two numbers​—1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.

daisiesThe flowers of many plants that exhibit a spiral growth pattern often have a Fibonacci number of petals. Now…I would like to envision you heading out into local fields and meadows tomorrow morning and putting this to the test – are you ready to go count petals?  Fruit and vegetables often have features that correspond to Fibonacci numbers.

There are fundamental mathematical principles and laws in nature that have been there for millennia, long long before any noggin sat down and worked out they were observing sheer genius!