About Rhombus

Abstract

This work shows the conceptual and analytical interrelationship between the contents of plane trigonometry and Euclidean geometry, which are developed in the regular courses of secondary education in our country, besides being subject to the programmatic content of the analytical programs of the Ministry of Education (MINED). The work presents several variants of the mathematical demonstration of the area calculation formulas, operations with diagonals and sides of the rhombus, all of them obtained through the combination of trigonometric demonstrative techniques and Euclidean geometry. The cardinal objective is to provide a theoretical and analytical basis for the development of these theorems and, on the other hand, to simulate them by means of high-level programming using the Python programming language. It should be emphasized that the demonstrative processes include logical methods and procedures that allow new forms of mathematical development in the demonstrative constructions. Other demonstration strategies are presented, so that their construction is appropriate for the secondary school teacher to apply and for university teachers to go deeper into these demonstrations and their different variants. The combination of demonstrative techniques based on the analytical and theoretical characteristics of trigonometry with Euclidean geometry, will allow a higher level in the development of the demonstrative character of mathematics at this level. The constructive method is used to develop all the demonstrations about the rhombus and the deductive and inductive approaches to be able to generalize such results.