Abstract:

When we study the history of mathematical concepts and problems, we deal directly with ancient sources from various periods and it is often necessary to translate directly from ancient languages, such as Greek or Latin.

In the course of History of mathematics, we had the students reconstruct the history of mathematical concepts directly, in a laboratory activity. The document from the Italian Ministry of Education lists the specific learning objectives:
- Place scientific thought, the history of its discoveries and the development of technological inventions in the broader context of the history of ideas.
- The student will have acquired a historical-critical vision of the relationships between the main themes of mathematical thought and the philosophical, scientific and technological context.
- Illustrate and interpret a historical, cultural and scientific phenomenon in essential terms.

For teaching the Latin language, however, we read that the student must acquire the fundamental notions of Latin grammar, with particular attention to morphosyntax and basic vocabulary which acts as a fundamental tool for understanding the text in the original language.

In particular, we must try to avoid grammatical abstractness characterized by the knowledge of rules learned by heart, favoring those basic linguistic elements that lead the student to understand and interpret the texts as soon as possible.

The link between the training purposes of the two disciplines is close; they are characterized by the development of critical and rigorous thinking. When dealing with a translation or a geometric problem, rules are rationally applied which lead us not to learn mechanically but with awareness, in a manner connected to the context.

So we thought of building a didactic activity that could combine all the aspects listed above. The focus of the activity was to translate some passages from Latin to understand the evolution and constructions of "new" geometric figures (star polygons and star polyhedra). The historical period involved was the Middle Ages.

The aim was to try to make more significant reflections on some geometry concepts.

The Activity is divided into 3 parts: we gave the students some passages from Bradwardine's 15th century text on polygons to translate. They therefore started from hypotheses, recognition and translation of already known words, and their syntactic relationships. Grammatical rules and knowledge of the culture and context are used to have the translation of the passage as the final thesis.

The students then geometrically interpreted the readings. Finally, they answered some key-questions. We want to show steps, results and future developments of our project.

References:
[1] Bradwardine T. 1496. Geometria speculativa.
[2] Brigaglia A., Palladino N., Vaccaro M.A. 2018. Historical notes on star geometries in mathematics, art and nature. Imagine Math 6 Between Culture and Mathematics, Springer International Publishing 2018. 197–211.
[3] Indicazioni nazionali riguardanti gli obiettivi specifici di apprendimento” per i percorsi liceali (Mini- stero dell’istruzione, università e ricerca 2010)

Keywords:

Star polygon, Bradwardine, Latin.