Abstract:

This is an overview of some activities experienced at Politecnico di Torino’s three years Architecture Degree students Mathematics course.
Future architects, during the first year, are requested to attend a Mathematics course that gives them adequate mathematics methodological knowledge and operational aspects, about geometry and calculus particularly. Difficulties in studying these topics are mainly due to: 1) understand the contents and 2) distance from their own interests.
Here are some examples of the proposed activities in this course and enthusiastically received from the students. For this purpose, different tools are used: from the ancient origami art to modern software as GeoGebra. This approach often surprises students and shows them that they can see and use mathematics in many different ways.

Working on these kinds of difficulties, two different groups of activities are proposed.
1) To understand contents via origami models students fold:
(i) fundamental frame, useful also in Drawing courses;
(ii) vectors sum and mixed vectors product;
(iii) a very easy antiprism in order to introduce and study relative positions of line and plane in three dimensional space;
(iv) conics: parabola, ellipse and hyperbola.

Note that we fold very easy models, using simply A5 and squared sheet, in order to work with a large number of students, about 200 people per course.

2) To connect mathematics to students’ interests, they prepare two different designs
(i) a building façade using AutoCAD or GeoGebra or simply ruler and compass. The façade have to appear some fixed geometric elements (for example: a circle, a piece of ellipse a polycentric curve).
(ii) A restyling of a picture (a famous painting, a skyline, a panorama..) imported in a GeoGebra sheet, using elementary transformation (translations, dilations, reflections,...) of basic functions (cosine, sine, exponential, logarithm,..) to trace over some significant lines.

Finally, a funny lesson is described: after giving an overview of some different kind of surfaces (ruled, developable..), as well as pictures of architectural examples, I offer the Merenda Superficiale, a “mathematical snack” consisting in chips or biscuits of the same shapes of the studies surfaces.

Students appreciate this approach and find a very clever remark about mathematical properties of the object and also improved they results in their examination tests.

Keywords:

Mathematics, teaching, origami, geogebra.