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The midpoint of a segment \(\overline{AB}\) is defined as the point \(M\) belonging to the segment itself and which measures the same distance from its ends \(A\) and \(B\). In general, in the plane, given two points \(A(x_A,y_A)\) and \(B(x_B,y_B)\), the midpoint between them is calculated with the following formulas, which provide the respective coordinates of point


The point is a primitive concept of Geometry. Intuitively equivalent to a dimensionless spatial entity, for which it may be considered simply as a position, that is, as a coordinate. In topology and calculus, any element of a topological space and, in particular, a functional space is often called a point. A point in Euclidean geometry has


The length, quantitatively and objectively, identifies a material body according to a single main or prevalent dimension of the body itself. The measure of length leads to the knowledge of the geometry of bodies, that is to their “dimensions.“ Many length measurements are also based on many (indirect) measurements of other physical quantities. Length measurements can be obtained

Roto-translation (rigid transformation)

The rigid transformation (or roto-translation motion) is the composition between reflection, translation, and rotation, and therefore it is an isometry, that is, a geometric transformation that leaves the distances unchanged. In other words, we can think of roto-translation as a rigid movement in which a geometric figure first rotates and then translates. The rototranslation motion of a rigid body


Rotation is defined as rigid movement having as fixed points a point called center (in two dimensions) or a straight line called axis (in three dimensions) of rotation. This movement shifts all points around the center, or axis, by a fixed angle. In other words a rotation is the movement of a body following a circular


In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or space by the same distance in a given direction. It can also be interpreted as the addition of a constant vector at each point, or as a displacement of the origin of the coordinate system. In Physics, translation is defined


Polygonal chain.


Statistical hypothesis testing.


Euclidean geometry. Non-Euclidean geometry.

Coordinate systems

A coordinate system is a system that uses one or more numbers, called coordinates, to uniquely determine the position of a point or other geometric elements on 1D, 2D, and 3D dimensions. Each of these numbers indicates the distance between the point and some fixed reference point, called the origin. The first number, known as the \(x\) value, indicates how far left


Vectors are indicated in the scientific literature with a letter, generally lowercase, with an arrow above it: \(\vec{v}\). Vectors are essential to physics and engineering. Many fundamental physical quantities are vectors, including displacement, velocity, force, and electric and magnetic vector fields. In this context, the following fundamental entities are assigned: free vectors: characterized by magnitude, direction,


In geometry, the volume is defined as the measure of space occupied by a three-dimensional body. The volume of a three-dimensional body is a numerical characteristic of the body; in the simplest case, when the body can be decomposed into a finite set of unit cubes (i.e., cubes with edges of unit length), it is equal to


Distance formula.


In order to describe the motion of an object, you must first be able to describe its position (where it is at any particular time). More precisely, you need to specify its position relative to a convenient reference frame. So the position of a point \(P\) can be described by a pair or a set of coordinates,


The displacement of an object is defined as the vector distance from some initial point to a final point. This change in position is known as displacement. The word “displacement“ implies that an object has moved, or has been displaced. It is therefore distinctly different from the distance traveled except in the case of straight-line motion in


It is defined monomial as a literal algebraic expression, consisting of a numerical part (coefficient) and a literal part among which only multiplication and exponentiation operations appear; for example: \[\dfrac{1}{2}x;\;7x^2y;\;-9x^n\] The monomial degree is defined as the sum of all the exponents of the literal part. Monomes that have the same literal part (with identical exponent) are

Statistical hypothesis testing

Hypothesis testing is a branch of statistics that tries to evaluate the reliability of a hypothesis through the results of an experiment or a series of observations. The hypotheses considered can be the most varied and in the most disparate fields; that is, one can try to ascertain by experiment the validity of a natural law