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Mathematics on Romans' tracksLoading...
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.
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.
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.
Classification of the seven frieze groups:
The friezes have a reflection of the vertical axis?
The friezes have a reflection of the vertical axis?
YES
NO
no sliding or horizontal reflections - pm1
there is only translation symmetry - p11
there is a half turn symmetry - p12
there is a sliding reflection - pmg
there is a sliding reflection - p1g
there is a horizontal axis reflection - pmm
there is a horizontal axis reflection - p1m
Mosaic from the dinner room of the House of Cantaber
Mosaic from the House of squeletons
