What? Mandalas are related to geometry?

 Welcome to my first entry!

I am sure that each of us have seen this kid of patterns at least once in our lives:

At least in my experience in Primary school, we had tons of them to color whenever we wanted to or we had some time to wait until the rest of the class finished with what they had to do. Well, guess what? They are not just pretty patterns—they are masterpieces of geometry hiding in plain sight!

Let’s go step by step. What is a mandala anyway?

Despite of what you may think, they have been around for centuries, appearing in cultures from Hindu and Buddhist traditions to Native American and even modern wellness practices. The word “mandala” literally means “circle” in Sanskrit. It was that important that people gave it even a symbolic meaning: That which encompasses, encloses, and safeguards the essence—whether it be divinity or the true nature of the mind (López, 2006).

But if you look closely…can you really say that it is just a circle? I am sure that that is not the case, since you will see they are much more than just circles—they’re intricate compositions of geometric shapes arranged in perfect harmony.

Within each mandala, you will find:

• Circles (because, duh, it is a mandala!) representing unity and infinity.

• Triangles symbolizing strength and direction.

• Squares adding stability and balance.

• Hexagons (hello, beehive patterns!) showing up in nature’s most efficient designs.

• Radial symmetry, meaning you could spin a mandala around and it would still look the same!

Knowing this, do you not think that they are a good option to start introducing children to the world of geometric figures?

A recent study done by Troncoso (2018) dove into the world of mandalas and found they are not just pretty designs—they are a perfect launchpad for teaching kids the big three of geometric thinking: topological, projective, and metric concepts.

- Topological Magic: No matter how you stretch or twist a mandala, its core layout stays the same. That makes it a great tool to help kids grasp basic shape properties and spatial relationships that do not change—think “shape superpowers.”

- Projective Geometry Fun: The way mandalas are laid out—with shapes radiating from a center like a fancy pizza—helps kids explore ideas like direction, position, and orientation. Where is the center? What is to the left? Geometry in action!

- Metric Mayhem: Mandalas also bring out the rulers and compasses! Kids can measure diameters, talk angles, and even use protractors to dive into the precise, number-loving side of geometry. Who knew art class could serve also as math class?

Moreover, the mandalas are not only a thing of primary students, but for make their implementation worth it, we need to be aware first of how to do it. One way of having a different and modern approach to them is to use the technology. Breda, Serrazina, Menezes, Sousa, and Oliveira (2011), stated that through technology, the results of learning geometry maximises. When kids (and adults) get tools to see geometric ideas from all angles, the learning gets a serious upgrade. Suddenly math class is not just about drawing triangles with a ruler: it’s an interactive, hands-on adventure. Students get to build, tweak, and play with shapes in real time, which turns learning into something way more fun and meaningful.

As Ponte et al. (2007) put it, this approach changes the whole game. We are not just solving the same old problems, we are discovering new ways to think and reason by using geometry in a dynamic, flexible space. It's like giving your brain a new set of glasses to see the math world more clearly.

This could be done thanks to websites like the following: 

https://www.geogebra.org/classic?lang=es

Geogebra is such a well-known website that you might have heard about already but if not, take a try and see by yourself how this website works!

Last but not least, I want to show an example of the creation of a mandala so you can see the relation between it and the geometry from zero:

Well this is all for today! I hope you gained thanks to this entry a new view to look at the traditional mandalas! The next time you talk about mandalas or geometry with your friends, now you know a new thing to say. Not only that but I hope that once you get to be a teacher, you reconsider twice how to introduce and implement mandalas in your classes in order to archieve the most amount of knowledge for your students. 

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REFERENCES

Breda, A., Serrazina, L., Menezes, L., Sousa, L., Oliveira P. (2011). Geometria e Medida no Ensino Básico. Lisboa. Ministério da Educação, Direção Geral de Inovação e Desenvolvimento Curricular.

GeoGebra. (s.f.). GeoGebra Classic [Software]. GeoGebra. https://www.geogebra.org/classic?lang=es

Lopez, P. (2006). Descubre el mundo mágico de los mandalas y conoce tu mundo interno. Santiago de Cali, Colombia: Impresora Feiva.

Ponte, J. P., Serrazina, L., Guimarães, H., Breda, A., Guimarães, F., Sousa, H., Menezes, L., Martins, G., Oliveira, P. (2007). Programa de Matemática do Ensino Básico. Lisboa: Ministério da Educação, Direção Geral de Inovação e Desenvolvimento Curricular.

Troncoso, M. I. (2018). Los mandalas y el pensamiento espacial y geométrico en el pre-escolar. Revista Boletín Redipe, 7(4), 99-106.ç

Zak Korvin. (2020, 6 noviembre). The Intriguing Sacred Geometry of a Mandala [Vídeo]. YouTube. https://www.youtube.com/watch?v=dlqgWJzQMXk