Mathematics on Roman's tracks

Mathematics on Romans' tracks

identifying some friezes of the Conímbriga's mosaics

The ruins of Conímbriga are the main Portuguese archaeological station, being considered an important point of reference of our culture and scientific investigation.

In the Conímbriga's ruins it's possible to find traces of an architecture marked by the abundant presence of decorative materials, in which the mosaics stand out.
The geometric richness present in Conímbriga's mosaics gives rise to the demand for symmetries, in particular friezes and patterns. In fact, the friezes have special prominence in the Conímbriga's pavements and it's possible to find the seven frieze groups.

We proceed to the classification of some of the friezes present in the Conímbriga's mosaics, using a frieze classification algorithm. It should be noted that in the classification of the friezes we noticed small imperfections from the geometric point of view.

Use in the Classroom

One way of using photography to learn mathematics is to try to find different symmetries in friezes. There are actually only seven frieze groups. From photographs taken in Conímbriga it is possible to find the seven groups.

Before having the students begin the activity, you might talk about the classification of the seven frieze groups to familiarize the students with the different
characteristics of this classification.

Distribute the sheet of the classification of the seven frieze groups and some photos of Conimbriga's mosaics. The students must analyze each photo according to the classification presented. Working in groups may elicit different approaches that the students can discuss and pursue.

When the students have completed work, each group presents their solutions and invites comments from their classmates.

It is important if the teacher leads the discussion that engages students in comparing and contrasting solution strategies. This discussion might include, but would not be limited to, the strengths and weaknesses of different approaches.

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Classification of the seven frieze groups:
The friezes have a reflection of the vertical axis?

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YES

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NO

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no sliding or horizontal reflections - pm1

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there is only translation symmetry - p11

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