Medidas e forma em geometria - Santos, Edjan Fernandes dos (2015)
The work initially brings a historical approach, Greece (with the Pythagoreans), with the mathematician Eudoxus, referring to perhaps the greatest mathematical work, Euclid’s books. Then bring definitions and constructions of the real numbers as a complete body, the concepts of tiny, supreme, infinite sequences especially the convergent, Cauchy sequences and the three fundamental theorems for the calculus course, the annulment of the theorem, the intermediate value and Weierstrass. Soon after, we define metric and metric space in the plan, we show that the process of comparing an arbitrary segment with another set as unit leads to various types of positive real numbers: integers, rational and irrational, where the notion of measurable and immeasurable segment is explained. The area calculation for plane figures, where the usual formulas for the areas of simple polygons are presented, we present and application, Pick’s formula, without demonstration of the theorem, simple, fun, practical and efficient for area calculation, one this mathematical discipline of content throughout basic education in Brazil always present in external evaluation as OBMEP.