Fibonacci Series Part-II

The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, which plants and nature use to arrange leaves and form growth spirals.

Why leaf angles matter

When new leaves grow above older leaves along a plant stem, they can block sunlight if they overlap directly. Without enough sunlight, the lower leaves cannot make food through photosynthesis (oli serkkai) and may wither. Using an angle of 180 degrees causes the third leaf to block the first leaf completely, while a 120-degree turn causes the fourth leaf to sit directly above the first leaf.

The golden ratio and golden angle

• In the Fibonacci sequence, adding the previous two numbers produces 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55.
• Dividing a larger Fibonacci number by the number right before it gives a value close to 1.618, which is known as the golden ratio.
• Dividing a full turn of 360 degrees by 1.618 gives 222.5 degrees, which leaves an angle of 137.5 degrees, called the golden angle.
• Arranging leaves at this 137.5-degree angle places each new leaf neatly in the gap between older leaves so that every leaf receives maximum sunlight.

Building the Fibonacci spiral

A spiral can be drawn geometrically by creating squares whose side lengths match the Fibonacci numbers. Two adjacent squares of size 1 are placed side by side, followed by attaching a square of size 2, then size 3, size 5, and size 8 along the outer edges. Drawing a curved line, or arc, between the opposite corners of each square connects them into a continuous curve called the Fibonacci spiral.

Where the spiral appears in nature

• Snail shells grow outward following the curved shape of a Fibonacci spiral.
• Satellite images show that massive weather systems like cyclones form this exact spiral.
• Entire galaxies swirl across space in shapes that match the Fibonacci spiral.
• Flowers, fruits, and vegetables also display these Fibonacci patterns in how they grow.