Nautilus aren’t consciously aware of the way their shells grow they are simply benefiting from an advanced evolutionary design. Not every nautilus shell makes a Fibonacci spiral, though they all adhere to some type of logarithmic spiral.You could still be rocking those overalls your mum put you in when you were four years old. Imagine never outgrowing your clothes or shoes. Unlike humans and other animals, whose bodies change proportion as they age, the nautilus’s growth pattern allows it to maintain its shape throughout its entire life.The spiral occurs as the shell grows outwards and tries to maintain its proportional shape. A nautilus shell is grown in a Fibonacci spiral. Although more common in plants, some animals, like the nautilus, showcase Fibonacci numbers.A nautilus is a cephalopod mollusk with a spiral shell and numerous short tentacles around its mouth.This is a very good approximation of the golden ratio. Dr Verguts discovered that, between the ages of sixteen and twenty, when women are at their most fertile, the ratio uterus length to width is 1.6.This steadily decreases through a woman’s life until reaching 1.46 during old age. The data revealed a ratio that is about two at birth. Over a few months, Dr Verguts took ultrasounds of 5,000 women’s uteruses and compared the average ratio of a uterus’s length to its width among different age brackets.According to a gynaecologist at the University Hospital Leuven in Belgium, doctors can tell whether a uterus looks normal and healthy based on its relative dimensions – dimensions that approximate the golden ratio.

So, with any plant following the Fibonacci sequence, there will be an angle corresponding to Phi (or ‘the golden angle’) between each seed, leaf, petal, or branch. Coincidentally, dividing any Fibonacci number by the preceding number in the sequence will garner a number very close to Phi. The most irrational number is known as the golden ratio, or Phi.In simple terms, sunflowers can pack in the maximum number of seeds if each seed is separated by an irrational-numbered angle. So, why do sunflowers and other plants abide by mathematical rules? Scientists theorise that it’s a matter of efficiency.It’s actually the reason it’s so hard to find four-leaf clovers. This is not uncommon many plants produce leaves, petals and seeds in the Fibonacci sequence. Scientists and flower enthusiasts who have taken the time to count the seed spirals in a sunflower have determined that the amount of spirals adds up to a Fibonacci number.

Bright, bold and beloved by bees, sunflowers boast radial symmetry and a type of numerical symmetry known as the Fibonacci sequence, which is a sequence where each number is determined by adding together the two numbers that preceded it.

Each arm of the flake goes through the same conditions, so consequently crystallises in the same way.

Well, when each snowflake falls from the sky, it experiences unique atmospheric conditions, like wind and humidity, and these affect how the crystals on the flake form.As you know, though, no two snowflakes are alike, so how can a snowflake be completely symmetrical within itself, but not match the shape of any other snowflake?.This is what causes the snowflake’s distinct hexagonal shape. These bonds align in an order which maximises attractive forces and reduces repulsive ones. It’s complicated but, basically, when they crystallise, water molecules form weak hydrogen bonds with each other. Snowflakes form because water molecules naturally arrange when they solidify.Researchers already struggle to rationalise why symmetry exists in plant life, and in the animal kingdom, so the fact that the phenomenon appears in inanimate objects totally infuriates them. Snowflakes exhibit six-fold radial symmetry, with elaborate, identical patterns on each arm. You can’t go past the tiny but miraculous snowflake as an example of symmetry in nature.From falling snowflakes to our entire galaxy, we count fifteen incredible examples of mathematics in nature!

Real life fibonacci sequence in nature