Mathematics in Science and Art
| Code: | M4070 | Acronym: | M4070 |
| Keywords | |
|---|---|
| Classification | Keyword |
| OFICIAL | Mathematics |
Instance: 2015/2016 - 2S 
| Active? | Yes |
| Web Page: | https://moodle.up.pt/course/view.php?id=1902 |
| Responsible unit: | Department of Mathematics |
| Course/CS Responsible: | Master in Mathematics Teacher Education for Middle and Secondary Schools |
Cycles of Study/Courses
| Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
|---|---|---|---|---|---|---|---|
| M:ENSM | 12 | Plano de Estudos M:ENSMAT_2015_2016 | 1 | - | 6 | 42 | 162 |
Teaching language
PortugueseObjectives
It is important that the school can provide opportunities for students to experience activities that achieve the multiple aspects of their lives. Interdisciplinary practices addressing various languages and areas of knowledge are particularly interesting. Besides contributing to the motivation of students, they allow them to integrate the various contents in a more global context. This course aims to provide students with contact with various connections between mathematics, science and art, so that they can then explore and apply them both in the school environment and in outreach activities.
This course is structured in various mathematical topics (see syllabus) that cover contents of the new math programs for the 3rd cycle of basic education and secondary education with an emphasis in the field Geometry and Measure. The aim is to work contents of that domain in an integrated way by addressing several applications to science and art.
Learning outcomes and competences
It is intended that students acquire and deepen the mathematical content in the syllabus, become familiar with interdisciplinary practices involving these contents and develop autonomy, critical thinking and creativity in the implementation of learning activities and dissemination.
Working method
PresencialProgram
- Review of fundamental results of synthetic Euclidean geometry (relating to triangles, circles, polygons, constructions with ruler and compass)
- The Golden Ratio: geometrical constructions, Fibonacci sequence, myths and facts about artistic manifestations of the golden ratio in Classical Antiquity, Hambidge’s dynamic symmetry, Le Modulor.
- Plane isometries.
- Symmetry: symmetry groups of plane figures, cyclic and dihedral groups, rosette frieze and wallpaper groups.
- Plane Tillings: regular, arquimedian, demiregular, peridic and non periodic tillings, Wang conjecture, aperiodic tilling, Penrose tillings, and "einstein" problem.
- Polyhedra: Euler’s formula, platonic solids, convex deltahedra, Kepler-Poinsot plyhedra, prisms, antiprisms, arquimedian solids
- Linear Perspective: development and relationship with art throughout the Renaissance, constructions of Alberti and Pélerin, basic rules of linear perspective.
Mandatory literature
Veloso Eduardo; Geometria. ISBN: 972-8353-26-XComplementary Bibliography
Grunbaum Branko; Tilings and patterns. ISBN: 0-7167-1193-1Herz-Fischler Roger; A mathematical history of the golden number. ISBN: 0-486-400007-7
Araújo Paulo Ventura; Curso de geometria. ISBN: 972-662-591-2
Sasho Kalajdzievski; Math and Art- An Introduction to Visual Mathematics. ISBN: 1-58488-913-7
Teaching methods and learning activities
Lectures accompanied by audiovisual material and conducting worksheets.
Evaluation Type
Distributed evaluation without final examAssessment Components
| designation | Weight (%) |
|---|---|
| Participação presencial | 20,00 |
| Trabalho escrito | 80,00 |
| Total: | 100,00 |
Calculation formula of final grade
project: 30%
portfolio: 25%
worksheets: 25%
participation: 20%
Examinations or Special Assignments
No special works.
Classification improvement
May be made in individual portfolio.
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