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The Module on Geometry starts by looking at the historical development of knowledge that the humankind gather along centuries and became later, about 300 BC, the mathematical subject called “Euclidian Geometry” because of the great work of Euclid. The inductive-deductive reasoning which characterizes this subject will be developed through investigation of your own conjectures on geometric objects and properties. You will explore geometry by using basic mechanical instruments (compass and straightedge) and computer software.
As you progress you will treat the Euclidian geometry using a referential system to locate points. The orthogonal Cartesian system of coordinates that you already know from secondary school is the most common referential system you will use in both two and three dimensions. You will also learn some other systems of coordinates that will empower you to do research in geometry and in other mathematical modules as well.
Going deeper in analyzing the axiomatic construction of Euclidean geometry you will learn new geometrical structures, generally designated as Non-Euclidian geometry. So, summarily speaking, this Module is about Euclidean geometry treated in both syntactical and analytical ways and encloses an introduction to Non-Euclidean Geometry, handled synthetically only.