A Geometrician’s view: teaching mathematics through art

Natalija Budinski explores how mathematics can be taught through art

It might be unusual to mention mathematics and art in one sentence in the context of a teaching approach since math and art are considered two different ways of thinking and creativity. Art is usually connected to emotions and personal expressions, while mathematics is viewed as logical and factual. de Morgan, the famous English mathematician, stated that the power of inventions in mathematics is its imagination.  It can be said that mathematics in the physical world is what art is to the world of emotions.

One of the most known examples that illustrate the tie between mathematics and art is The Golden Ratio. Mathematically speaking, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. This concept has been used in architecture and art since ancient Greek times till nowadays. Beyond the use of The Golden Ratio in architecture and the arts, the mathematics of The Golden Ratio can be found in nature such in plants, shells, flowers, or in the proportion of the human body. The Golden Ratio is believed to be a mathematical formula for harmony and beauty. In Figure 1 we can see elements of The Golden Ratio in the famous Leonardo da Vinci picture-Mona Lisa.

Figure 1. Elements of The Golden Ration in Mona Lisa painting

Beside The Golden Ratio, there are many other examples. Many of them are useful for teaching mathematical content in the classroom. Many mathematicians and teachers of mathematics are breaking stereotypes and organizing activities in the classroom that connect mathematics and art to illustrate different mathematical concepts and show the beauty of both disciplines and find the inner logic of things.

One example is a group of teachers and educators collaborating on a project called Geometrician’s view (www.geometricians-views.lesmathsenscene.fr). An Erasmus+ project,it was established in 2021 with the aim of working until 2023 on mathematical culture through art and science. Six partners: Instituto Compresivo Perugia 12 from Italy, Virtual Dor from Spain, Petro Kuzmjak school from Serbia, Middle School Ioan Ciordas from Romania, High school Novska from Croatia, Geniko Lykeio Proastiou Karditsa from Greece and L’association Les Maths en Scène from Francethe coordinator of the project, are working on establishing teaching mathematics through artistic concepts. These various groups of math teachers and professionals are developing lesson plans and strategies for implementing art activities in the mathematical lessons and working with students from both the primary and secondary levels of education. During that work, they are supported by artists and researchers, and the final results will be published in a brochure that will be helpful to other teachers to follow the same example. In Figure 2 we can see the logo of the project.

Figure 2 Logo of the project Geometrician's view

Lesson plans are covering topics such as Anamorphosis, Measurements and Plots, Fractals, Tilling, Knots, Crystals, Constellations or 3D printing, and many more. In Figures 3 and 4 we can see the artwork connected to mathematical content resulting from the various classroom activities. Figure 3 shows the results of teaching Cartesian coordinates together with the concept of Constellations which were an inspiration for the student’s artwork. Figure 4 shows 3D-printed jewelry inspired by mathematics.

Figure 3 Cartesian coordinates and art-work
Figure 4 3D printed jewellery inspired by mathematics

The project has one interesting and future-forward addition and that is the development of strategies for implementing Neotrie (www2.ual.es/neotrie). Neotrie is a virtual reality software for creating, manipulating, and interacting with geometric objects and 3D models in general or different types. It is a great tool for exploring geometry in virtual reality. In Figure 5 we can see the virtual environment of Neotrie.

Figure 5 Netrie virtual environment Mathematics and Art

Contemporary education highlights critical thinking and creativity as skills necessary for the future. During the Geometrician’s view project implementation, we have noticed that involving art in mathematical lessons is a supportive activity to encourage and develop such skills. Art is an excellent way to introduce students to mathematical ideas and develop mathematical vocabulary. Our activities are motivating for students and students respond positively. They engage students and raise their attention in the classroom, which is very helpful in the teaching process. Many students respond more positively to artistic activities that are connected to mathematics rather than to abstract definitions, since it provides them an intuitive understanding of various mathematical content, such as mathematical symbols and proofs, stimulating a sense of curiosity.

You can follow our activities by following #GeomView on social media.


1 Comment

  1. HOUSSAM m kasti

    Very interesting 👍


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