What you always wanted to know about plane Euclidean geometry (but were afraid to ask)
About the Course
This 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.
Sciences
Training hours0
LevelBeginner
Course ModeSelf Paced
Italian
DurationType
Online
Course StatusSelf Pacement
Course Agenda
Enrollments Start
Course Opens
Course Closes
Learning outcomes
- 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 Requirements
This 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.
Textbooks
Geometria.blu. M. Bergamini, A. Trifone, G. Barozzi. Zanichelli, 2010
