Scientists have found inspiration for their ideas by observing the nature. The symmetries and regularity in the forms and patterns in Nature have been very likely the stimulus towards the foundation of the Euclidian geometry. In the 14th century, several mathematicians start to find a relation between the geometry, mathematics and natural patterns. More recently, in the 20th century, the French-American mathematician Benoit Mandelbrot (1924–2010) has introduced the concept of fractal geometry to describe forms and phenomena in science and nature that cannot otherwise be classified. It was soon clear that fractal pattern occurs everywhere in Nature. From majestic galaxies to infinitesimal molecular worlds, fractal geometry characterizes the structural assembly of stars and molecules as a consequence of invariance of scale present in these structures
All these studies evidenced that simple but powerful mathematical properties and geometric forms are recurrently used by Nature in the shape of organisms, and other natural objects and environments. You can find the golden ratio, the Fibonacci number, spirals shaped forms, and fractals everywhere even in your home garden.
In this presentation, I made an overview of the different pattern observed in Nature from a mathematical and geometric perspective. In the first, I focused the attention on the mathematical properties of the golden ratio and Fibonacci sequence exploring its relation with the plane and spatial geometry and with the number theory. In the second part, an overview of the concept of fractals with some examples of applications are provided.
The PDF version can be downloaded here: Pattern_in_Nature_8_7_2017