Scientific Articles

THE SQUARE OF A SECOND-DEGREE TRINOMIAL

(Teacher Valentina Fabbro):

The article presents a standard to establish if a fourth-degree polynomial which coefficients are Real numbers is the development of a second-degree polynomial which coefficients are Real numbers; if it is so, there is a general formula to determine the second-degree polynomial starting from the coefficients of the original fourth-degree polynomial.

THE CIRCLE OF GAUSS

(Anna Barisan and Teacher Fabio Breda):

The aim of this article is the research of the number of entire solutions for the inequalities of type x² + y² ≤ n, known as the problem of the circle of Gauss, and others like x² + y² + z² ≤ n. The problem will be analyzed both from the algebraic and geometrical point of view, to solve a generic a₁x₁² +a₂x₂² +...+a_mx_m² ≤ n, with m ∈ ℕ₀ and n ∈ ℕ to enlarge then the studying to similar inequalities.

FUNCTIONS

(Teacher Francesco Zampieri):

Under our eyes show up different phenomena, events, situations. For his curiosity and to have control of the surrounding world, man has always tried to give them a description using appropriate encryptions.

CONGRUENT TRIANGLES

(Teacher Valentina Fabbro):

The article presents a demonstration of the following statement: two triangles are congruent if they have congruent two sides and the bisector of the angle included. The need of this demonstration was born from a quiz, found in a Geometry book that contained a mistake.

NOTABLE POINTS

(Teacher Fabio Breda):

The aim of this article is to prove once again the elegance of Math. Here we demonstrate the extremely classy Cartesian formulas of the four notable points of the triangle.

ELEMENTS OF SPECIAL RELATIVITY

(Teacher Francesco Zampieri):

Here we will discuss some theme about the special relativity theory, Einstein's general relativity theory's particular case, in order to comprehend the reasons of the introduction of this new paradigm for physics and to analyze some of the most relevant consequences, both for what concerns the prevision of new phenomena, and for the important historical-philosophical implications.

THE TANGRAM OF THE POLYGONS

(Gioella Lorenzon and Teacher Fabio Breda):

The aim of this article is to produce a general method that allows, given to whatsoever equivalent polygons, to equitable break them. In order to do this we will demonstrate Bolyai's theorem that is that equivalent polygons are equitable breakable, and we will then conclude that for what pertains the polygons' equivalence and equidecomposability are the same relations.

LIMITS

(Teacher Francesco Zampieri):

In this chapter we will face the study of that part of Analysis that goes under the name of Calculus, initially defining the concept of limit of an analytic function in one point (that could also be the infinite) and learning most of all how to calculate limits, with appropriate techniques.

TRANSLATIONS AND DILATATIONS

(Teacher Fabio Breda):

The aim of this article is to clarify the way of creating the graph of functions through translations and dilatations of other functions' graph.

Archimede Project