# Symmetries in Floral Ornaments of Art Nouveau (LS-PT-77)

The analysis of art objects through their symmetries is an interesting mathematics activity for the study of isometries in the plane. It could establish a connection between mathematics and art or other subject studies.

The isometries are part of the subject curriculum of mathematics, specifically in the 8th and 9th-grade classes (13 – 14 years).

The symmetry of a figure is a particularity of it, this means that there is a geometric transformation that preserves distances (it is called an isometry).  Through this transformation, the final figure matches with the initial figure.

When we search for symmetries we can focus on three types of objects in the plane: rosettes, friezes and patterns. And then check if they have symmetries of translation, rotation, reflection and glide reflection.

## Classroom implementation

In this project, students of a 9th-grade class started to study by reviewing the subject of isometrics (100 minutes). They were also solving several practical exercises addressing the curriculum contents (vectors, the addition of vectors, translations, rotations, etc.). In the next class, they studied “symmetries” analysing various figures, trying to identify symmetries. They also observed videos and other materials that facilitated the understanding of the theoretical concepts. Some of the figures they analysed were taken from Europeana, seeking to establish a connection between the study and real examples, in this case, about the Art Noveau decorative art.

Afterwards, students were able to observe Europeana’s research portal and how they could find more images to classify the symmetries. They also paid attention to the creative commons licenses of the images.

During project development, pupils were using a Padlet to support and published their work. It was containing links leading to the necessary resources.

Firstly, in the research of the Europeana portal (Floral Ornaments of Art Nouveau), students have searched for images. Secondly, they classified images according to their symmetries. Thus, during that lesson (100 minutes), the students organized the information in a word page. To illustrate their study, they added vectors, axes, or angles using word tools. They also referred to the research, checked whether the images were protected by copyright, added short explanations about symmetries and information about the Art Nouveau movement.

## Activity assessment

For the assessment of learning, students have done exercises of isometries to check their understanding of the activity topics.

Students though it was easy to use Europeana resources. Although it was important to prepare previous activities to guide them in that research. This activity can be done by students of different ages.