Euphorbia

There are lots of cool things about nature geometry, but one of my favorite patterns is the spiral. The Golden Ratio and Fibonacci sequence have been used to try to describe this natural pattern that most people consider very pleasing to the eye. The Golden ratio is represented by the symbol Phi (φ), which is roughly equal to 1.618033988… Phi is considered an irrational number because it cannot be expressed as a simple fraction, and its precise calculation requires an infinite number of decimal places and has no repeating pattern of numbers. Irrational numbers are not unusual in nature math. Phi’s better known cousin Pi (π = 3.14159…) is also irrational, and is used to calculate the various intricacies of arches and perfect circles. The natural logarithm is another irrational number used to explain many natural phenomena —

*e = 2.71828182845904523536028747135266249775724709369995…* I don’t know enough about mathematics to try to explain how these numbers are calculated. I just know that I’ve always found them confusing whenever I tried to wrap my brain around them in math class.

These irrational numbers are responsible for explaining the shapes and patterns taken by the natural world around us. I find it completely appropriate that those things we find most pleasing to the eye seem to defy a neat mathematical explanation. If all the patterns found in nature can only be explained through the use of *irrational* numbers, it leaves me wondering. Is it the world around us that is naturally irrational, or Homo sapiens quest to define every little phenomenon with a neat mathematical equation?

Some things may beyond the realm of the rational brain. Some things are just irrational. Some things we should just take a step back from and appreciate without trying to explain.

Mammillaria

Haworthia

Astrophytum

Euphorbia

did it really look like this

Spirals are twists of nature. Photos of plants twisting.

DP Weekly Photo Challenge: Twist

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All the mathematics: over my head.

But…I do get some of it.

And the photos are awesome!

Stunning captures! I have yet to capture the Fibonacci sequence, but I am always in awe of it in nature photos! Great job!