Plane Euclidean geometry
About the CourseThis course recalls main techniques and results in plane geometry, that can be used in all technical or scientific degree programs, in particular -but not exclusively- in the preparation of first year exams.
To begin with, the basic notions of set theory and equalities/inequalities properties will be reviewed; after that, the founding postulates will be given, along with first results on straight lines, segments, planes, angles and orthogonality.
In another section, polygons will be introduced and described, with a particular attention to triangles; congruence criteria and basic inequalities are then analysed.
After that, a further section on parallelism issues will introduce rhomboids and basic proportionality Thales’ theorem. Circles and regular polygons will be introduced in another section, along with main results related to those figures.
All results obtained will lead to the final two sections: the first one concerning areas, equivalence, and Euclidean and Pythagorean theorems on right-angled triangles; and the second one dealing with similarity and homothety.
Learning outcomesThe expected learning outcomes are:
- Mastering different techniques of mathematical proofs within an axiomatic system.
- Rehearsing/learning main results in plane geometry and their applications (parallelism and orthogonality, congruence of angles, basic proportionality theorem, congruence/similarity of triangles, circles and angles, regular polygons, computing areas of main figures, Pythagorean theorem).
- Drawing a figure given some prescribed conditions (including straightedge and compass constructions).
- Deducing more properties of figures starting on those with which they have been constructed. This means obtaining the properties by reasoning on a qualitative non-accurate figure.
Background and RequirementsThis course is aimed at anyone who wants to learn or recall basic high school plane geometry; in particular, it can be useful for students who intend to enroll (or have already enrolled) in a science-based degree program. No specific prerequisites are required to take advantage of the course content; in fact, basic notions of elementary set theory and of the properties of equalities or inequalities will be given in the first section in any case.
TextbooksGeometria.blu. M. Bergamini, A. Trifone, G. Barozzi. Zanichelli, 2010
Course FormatThe course is made by video lessons, introducing the theory issues, and showing how results in geometry can be progressively obtained through the proofs of some selected propositions. Several lessons will be provided with note in PDF format, written by the instructor, often completed with exercises, that can be used by the students to assess the amount and quality of the knowledge acquired at the end of any section.
Certificates and Exam rules
Per ottenere l'attestato di partecipazione è necessario superare il questionario finale presente nel corso.