Geometry in nature
Hi little bloggers! Do you remember my previous post? The other day I discussed the geometry found in Gaudí’s architecture, which in turn was inspired by the forms of nature. That is why this post will focus on observing the presence of geometry in the natural elements of our planet, so that we can introduce students to geometric concepts through the observation of the natural world.
Firstly, I will refer to fractals, self-similar geometric patterns that repeat at different scales, which are fundamental in nature for maximising structural efficiency whilst using minimal material. Common examples include Romanesco broccoli, ferns, lightning bolts, coastlines, trees and the human vascular system, where the small part resembles the whole. Mandelbrot concluded that objects in nature have a fractional, irregular or fragmented dimension, and defined a fractal as “a geometric object whose basic structure, fragmented or apparently irregular, repeats itself at different scales”.
Figure 1.
Fractals.
Furthermore, fractals are not only found in the external world; within our own bodies, fractals are constantly used to optimise vital functions. For example, the human lungs employ a fractal structure to maximise the surface area for gas exchange within a limited space, and the circulatory system does the same to distribute blood efficiently (Meditation and Psychology, 2026). We can also find hexagonal structures in nature, for example in honeycombs. Around the year 100 BCE, Marcus Terentius Varro, a Roman scholar and beekeeper, concluded, based on his observations, that the hexagonal shape of honeycombs was due to the fact that this structure allowed for the construction of cells with the greatest possible space—which was important for storing as much honey as possible—using the least amount of material (Varro, 36 BC, as cited in García Molina, 2017). Just as our bodies use fractal structures to be more efficient, bees construct their honeycombs in a hexagonal pattern to store more honey, making geometry a key element in making life easier.
Figure 2.
Honeycombs.
Finally, I will discuss spirals. Spirals are common patterns found in nature, observed on scales ranging from the microscopic to the galactic, which optimise growth and adaptation. These shapes, often logarithmic growth spirals, appear in mollusc shells, sunflowers, hurricanes and galaxies, reflecting mathematical principles such as the Fibonacci sequence. Jacob Bernoulli (1654–1705) called the logarithmic spiral spira mirabilis (wonderful spiral) and dedicated an entire treatise to it under the same title. Although logarithmic spirals had already been described by Descartes, Bernoulli delved deeper into their study and described their mathematical properties in great detail (Cuaderno de Cultura Científica, 2020).
Figure 3.
Spirals.
In conclusion, geometry can be found in nature and living things, so teaching it through examples from the natural world can be very engaging and motivating for pupils, who will see that geometry is not just a set of abstract mathematical concepts, but real patterns that recur all around them and even within their own bodies.
References
Cuaderno de Cultura Científica. (2020, junio 18). La espiral maravillosa. Universidad del País Vasco. https://culturacientifica.com/2020/06/18/la-espiral-maravillosa/
García Molina, R. (2017, marzo 29). Sobre abejas, matemáticas y pompas de jabón. Naukas. https://naukas.com/2017/03/29/sobre-abejas-matematicas-y-pompas-de-jabon/
Mandelbrot, B. (1977). The Fractal Geometry of Nature. W. H. Freeman and Company. Citado en: Meer.com, "La artística geometría de la naturaleza" (2023). https://www.meer.com/es/72913-la-artistica-geometria-de-la-naturaleza
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