Introduction

A pinecone has 8 scales in spirals when counting clockwise and 5 scales when counting anticlockwise. A pineapple has 8 fruitlets when counting clockwise and 13 fruitlets when counting anticlockwise.as shown.

The number petals on different flowers

3 Petals: Lilies, Irises.

5 Petals: Buttercups, Wild Roses, Hibiscus, Pansies, Phlox.

8 Petals: Some Delphiniums, Cineraria.

13 Petals: Some Asters, Cineraria.

And of course, all clovers have 3 leaves except for the rare mutated four leaf clover.

Sunflower

The spirals of seeds (parastiches) in the sunflower head number 34 when they are counted in one direction and 55, sometimes 89 for larger sunflowers, when counted in the other direction as shown in the image. This pattern efficiently packs the maximum number of seeds into the head while providing each with optimal space, light, and nutrients.

The DNA molecule

The DNA molecule measures 34 angstroms long and 21 angstroms wide for a full cycle of its double helix.

Image credit; Reddit https://www.reddit.com/r/sciences/comments/d9hli3/the_dna_molecule_is_based_on_the_golden_section

The Fibonacci Series

These numbers of 3, 5, 8, 13, 21, 34, 55 and 89 are not random numbers but are significant because they fit into a sequence precisely. This sequence is generated by each number being the sum of the previous two numbers. So, starting with 0 and 1, the next number will be 0 plus 1 which is 1. The next number will be the sum of the two preceding numbers, 1 plus1 which is 2. In like manner, the next number will be 1 plus 2 to give 3, the next numbers will be 5, then 8, then 13 and so forth. So, the sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144….

This sequence was named after Italian mathematician Leonardo of Pisa. Later he became known as Fibonacci, and the sequence is named after him. He introduced it to Western Europe in his 1202 book Liber Abraci. He originally developed the series by considering the increase in a rabbit population starting from two rabbits which could reproduce after two months, and subsequent rabbits could likewise reproduce after two months. For a detailed explanation, go to Wikipedia: https://en.wikipedia.org/wiki/Fibonacci_sequence.

These numbers turn up, quite often unexpectantly, and they pervade all of nature. In fact, there is a journal dedicated to them, the Fibonacci Quarterly.

The Fibonacci sequence is even displayed in the human hand. We have three parts to each of our five fingers and the length of the digits in our hands, as seen in the image, corresponding approximately to the Golden Ratio which will be explained, is 1.618 times longer than the one above it.

Fibonacci Squares and Spirals

The Fibonacci sequence can be represented as squares and when they are drawn together in a certain way, they have further application.

Fibonacci squares are a visual representation of the Fibonacci sequence where squares are drawn with side lengths corresponding to consecutive numbers in the sequence. When these squares are arranged to form a tiling,[1] and as they are added, they form increasingly large rectangles. A spiral, called a Fibonacci or golden spiral, can be drawn by connecting opposite corners of the squares with quarter-circle arcs as shown.

 

 

 

 

 

Natural examples of the Fibonacci spiral

The nautilus shell, a cyclone and a spiral galaxy

The Golden Ratio

The Golden Ratio, also called by the Greek letter Phi (ɸ) is 1.618 and is obtained from the Fibonacci sequence by dividing any number in the sequence into the number following it. For example, 13/8 = 1.625; 34/21 = 1.619; 144/89 = 1.618. Notice the further down the series the division is applied, the closer the division gets to the golden ratio of 1.618.

Another way of obtaining it is from the mathematical calculation shown below.

For those who are interested in the mathematics, it is fully explained here: https://www.youtube.com/watch?v=JfZMk9qlI7s.

Origin of the Golden Ratio

The first known mention of the golden ratio is from around 300 BC in Euclid’s Elements, the Classical Greek work on mathematics and geometry. Euclid and other early mathematicians like Pythagoras recognised the proportion, but they didn’t call it the golden ratio. It wasn’t until much later that the proportion would take on its mystique. In 1509, Italian mathematician Luca Pacioli published the book De divina proportione, which, with illustrations by Leonardo da Vinci, praised the ratio as representing divinely inspired simplicity and orderliness.

Because of Pacioli’s book and Leonardo’s illustrations, the golden ratio gained fame among mathematicians and artists. In the centuries since Pacioli’s book, many enthusiasts have claimed that the number is naturally pleasing to the eye, that it is a mathematical distillation of beauty and that golden ratio when applied to rectangles with side lengths of the longest being 1.618 times the shorter are represented throughout art history.

A rectangle framing the front of the famous ancient Greek building, the Parthenon (shown, credit; Wikimedia commons), has sides which follow this ‘Golden Ratio’.

Most people, if asked to choose from a series of rectangles the one most pleasing to the eye, will choose one in which the ratio of the two sides (that is, the larger side divided by the smaller) is approximately 1.62. In other words, the long side is 1.62 times the length of the shorter This proportion is widely found in art and architecture.

Authoritative works on art and architecture make bold claims in alleging, for example, that ‘the Golden Section is aesthetically superior to all other proportions’, which claim is said to be ‘supported by an immense quantity of data, collected from both nature and the arts.[2]

Conclusion

The consistent appearance of these patterns in nature could not have come about by a series of random events with no purpose or direction as proposed by evolutionists, because they are too precise and cover all of nature from galaxies right down to dimensions of the DNA molecule.

The inherent beauty and order in these mathematical realities are a revelation of the Designer’s wisdom and love of beauty. Romans 1:19-20:

… since what may be known about God is plain to them, because God has made it plain to them. For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.

[1] A Fibonacci tiling is a geometric construction that uses squares with side lengths corresponding to the Fibonacci sequence.

[2] Dr Carl Wieland, Russell Grigg, Creation, Published 20 October, 2010 and Updated 07 Jun, 2023. The article cited, The Oxford Companion to Art, Ed. Harold Osbome, First Edition, Oxford University Press, Oxford, p.489, 1978.