Unit COMPLEMENTARY MATHEMATICS AND MUSEOLOGY

Course
Mathematics
Study-unit Code
A002582
Curriculum
Didattico-generale
Teacher
Nicla Palladino
Teachers
  • Nicla Palladino
Hours
  • 42 ore - Nicla Palladino
CFU
6
Course Regulation
Coorte 2022
Offered
2022/23
Learning activities
Affine/integrativa
Area
Attività formative affini o integrative
Academic discipline
MAT/04
Type of study-unit
Opzionale (Optional)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents
Museology and mathematical museology. Interactive science museums. The roles of the museum: conservation, teaching, research.
Non-Euclidean geometries: theoretical and historical aspects and elliptic and hyperbolic models. Their use in mathematics education.
The classical problems and The constructions by ruler and compass.
Reference texts
C.B.Boyer, Storia della matematica, Mondadori, 1990.
• Evandro Agazzi, Dario Palladino: LE GEOMETRIE NON EUCLIDEE e i fondamenti della geometria. Editore: Mondadori.
Additional notes will be provided during the course
Educational objectives
The aim are to provide an adequate knowledge of topics on mathematical foundations, framing them in the historical context of origin, which constitute the conceptual and epistemological bases of modern mathematics. To develop and consolidate the skills related to the resolution of plane geometry problems, acquiring tools for an epistemological and didactic analysis of geometry. These will be topics, chosen for their historical and didactic interest, inherent to different areas of the discipline, fundamental for the development of mathematical thought. To provide the key concepts and basic skills for the formation of the figure of the mathematician curator in scientific museums
Prerequisites
Basic knowledge of differential and integral calculus, algebra and geometry.
Teaching methods
Individual and group-work activities and exercises
on mathematics problems; brain storming, problem solving, software.
Other information
Additional notes will be provided during the course
Learning verification modality
Preparation of a museum panel on mathematical objects agreed with the teacher. Laboratory activities to be delivered. Oral exam. The final test aims to assess whether the student has knowledge and understanding of the topics, has acquired interpretative competence and autonomy of judgment. The following grid will be used for the evaluation:
Insufficient: The student does not have an acceptable knowledge of the topics covered in the teaching.
18-20: The student shows knowledge and understanding of the topics in general lines; you have just adequate expository and communication skills to allow the transmission of acquired knowledge useful for professional training purposes
21-23: Student shows adequate knowledge and understanding of topics; you have satisfactory expository and communication skills, but little
articulated, to allow the transmission of the acquired knowledge for the purposes of professional training
24-26: The student shows a fair knowledge and understanding of the topics; has discrete and barely articulated expository and communication skills, to allow the transmission of acquired knowledge for the purposes of professional training
27-29: Student shows good knowledge and understanding of topics; has good and well-articulated expository and communication skills, a
allow the transmission of the knowledge acquired for the purpose of professional training
30-30 cum laude: The student shows excellent knowledge and understanding of the topics; has excellent and well-articulated expository and communication skills, to allow the transmission of acquired knowledge for the purposes of professional training.
The duration of the interview can vary between about 30 and 45 minutes. See also http://www.unipg.it/disabilita-e-dsa
Extended program
Non-Euclidean geometries: Euclid's Elements: structure of the work, classical axiomatics, the first book. The question on the V postulate, equivalence with other propositions. Demonstrations of the V postulate. Hyperbolic geometry software and its use for the verification of some propositions and exercises. Saccheri's work, refutation of the hypothesis of the obtuse angle and acute angle. Hyperbolic geometry. The works of the nineteenth century. The coherence of hyperbolic geometry. Modern axiomatics. Klein model, Poincarè model, Beltrami model. Gauss's work. Riemann's work. Spherical geometry. Applets and exercises for spherical geometry. Elliptical geometry. Presentation of an approach in mathematics education.
The classical problems: The constructions with ruler and compass. The problem of cube's duplication. The solutions of Menecmo. Mesolabe of Eratosthenes and compass of Descartes. Diocle's cissoid. Plato's solution. The problem of angle's trisection. Pappus of Alexandria and the mathematical collections. The conchoid of Nicomedes. The triadressor or quadratrice of Ippia. The Archimedes method. The spiral of Archimedes. The problem of circumference rectification. The lunulas of Hippocrates. The problem of the division of the circumference.
Museology and mathematical museology. The origins of the scientific museum. Interactive science museums. The roles of the museum: conservation, teaching, research. Some scientific museums in Italy and their educational offer. The museum audience; museum guides. The educational role of the scientific museum. Explanatory panels: structure and functions. Some examples of didactics in museums: the MINERALOGY museum of Federico II. The digital collections of mathematical models in Italy and in the world. Nineteenth-century mathematical models. Mathematical machines and tools in museums: Aritmometro and Anaglifi. Software for digital reconstruction of mathematical objects. Virtual tours of the rooms of mathematical museums: some examples and reflections. Mathematical museums in Italy and in the world. Educational films and their role in museums.
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