This photo is by Martin Krzywinski and Cristian Vasile. The digits of pi are connected across the circle with a chord. When a number is Krzywinski and Vasile place a dot at the outer edge of the circle. The more digits that are repeated, the larger the dot.
In a beehive, close packing is important to maximise the use of space. Hexagons fit most closely together without any gaps so hexagonal wax cells are what bees create to store their eggs and larvae.
A Golden Spiral formed from the Golden Ratio in a manner similar to the Fibonacci spiral can be found by tracing the seeds of a sunflower from the centre outwards.
The Blue Sun is a collage of two different Persian works of art, both with deep mathematical roots: Tiling and Tazhib. This structure possesses a 10-fold rotational symmetry.
If you construct a series of squares with lengths equal to the Fibonacci numbers and trace a line through the diagonals of each square, it forms a Fibonacci spiral. Examples of the Fibonacci spiral can be seen in nature, including in the chambers of a nautilus shell.