Geometry in nature

In the previous entry, we saw how we can bring geometry into a classroom of primary education from a more

realistic perspective, specifically by observing the geometric shapes found in our urban environment.

However, we don't only find geometric shapes in human-made spaces. Nature also provides a landscape

full of shapes, symmetries, and patterns.


According to Stephen Skinner, many shapes and other geometric concepts found in nature have been studied

since Antiquity because of their harmony. The author highlights figures such as circles or spirals, explaining

that they frequently appear in elements from nature and from architecture (Skinner, 2007). 


When we incorporate these elements with the pupils in our classroom, it doesn't just allow us to work geometric

content but it also fosters observation and critical thinking, connecting mathematics to the real world around us.

Thus, learning becomes more experiential, motivating and relevant to students’ everyday lives. 


Once all of this has been said, where can we find all of that ? Well, when we see flowers, its central part is

usually a circumference. Then, what is the difference between the circumference and the circle, which we saw

the other day in the previous entry? The first one is only the outer contour and the second one also includes the

entire inner area (Zárate, 2016).


Figure 1 

A flower with a circumference in its centre. 


Note. Zárate, 2016.


In the case of spirals, we find them, for example, in snail shells. Regarding polygons, the hexagon is an

example of a polygon that as its own name says, it has six sides. For instance, this polygon can be seen in the

hive of bees. 


Figure 2 

Spiral in snail shell. 



Figure 3

Hexagons in a hive of bees.  



Note. Zárate, 2016.

 

Furthermore, in nature there are several elements that show symmetry. One of the main examples when

teaching this concept to children is usually the butterfly, whose symmetry is bilateral which means that when it is

cut in half, there are two equal parts. Moreover, there are other insects with this type of symmetry such as the ones

we can see in the image. 


Figure 4

Insects with bilateral symmetry



Relating geometry to nature, and considering that we increasingly live in a digital world where we often stop

paying attention to our surroundings, promoting a day trip in nature could be such a great idea. Some examples

include a forest, a natural park, or a rural area, or if access to these places is more difficult because of being far

from them, a trip to a botanical garden, for example could be organized. In these types of spaces, students could

observe geometric shapes while connecting with the natural environment. 


References: 

Skinner, S. (2007). Geometría sagrada. Madrid. Gaia. 

Zárate, J. I. P. (2016). Geometría en la naturaleza. Con-Ciencia Boletín Científico de la Escuela Preparatoria No. 3, 3(5). https://repository.uaeh.edu.mx/revistas/index.php/prepa3/article/view/1718/5410


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