Task of the Week: Hercules Fountain
Our new Task of the Week is located in Montesarchio, an Italian town near Naples. Here, the math teacher Angela Fuggi created the task “Hercules Fountain”. In the interview, she presents her task and gives us an insight in the ERASMUS+ programme “Maths Everywhere”.
How did you get to know MathCityMap?
In this last school year I participated in the Erasmus project “ERASMUS + Maths Everywhere”. From 16th to 22nd February my school, the Istituto di Istruzione Superiore “E.Fermi” in Montesarchio (Benevento, Campania, Italy) hosted a group of 10 teachers and 29 students from Greece, Latvia, Spain and Turkey.
The focus of the project meeting in Montesarchio was “Math in the street”. Mathematics was viewed in close connection with the geographical area and its artistic and cultural heritage. One of the main activities was a treasure hunt and it was at this moment that MathCityMap came into play. The path created with the related activities had to be loaded onto MathCityMap and for this reason I started to use the app.
Please describe your task. How could you solve it?
My task related to the fountain located in the main square of Montesarchio. The artistic work, dating back to the second half of the 19th century, consists of a circular base with a basin, surmounted by a sculptural group of four lions and on a podium the figure of the warrior Hercules, the same mythical character who also appears on the emblem of the municipality. The task formulation is as follows:
In Umberto I square (the most famous square in Montesarchio) there is a fountain with 4 lions that surround Hercules, the Olympian god. The 4 lions are arranged at the vertices of a square on the side L. The statue of Hercules is supported by a circular base placed above the lions. Seen from above, this base is inscribed in the square with the 4 lions at the top. After measuring the distance between two consecutive lions, and therefore the side of the square, calculate the area of the circular base that supports the statue of Hercules (m²).
How could you solve it? Which is the didactic aim of this task?
The distance between two consecutive lions is the side of square L=2m. The side of the square coincides with the diameter D of the inscribed circumference, L = D, D=2m. The area of the circumference is A=π⋅(D:2)²=π⋅(2:2)²≈3,14 m²
The didactic aims were to represent, compare and analyze geometric figures and to work with them, identifying variations, invariants and relationships, above all starting from real contexts.