Archives des Geometry

December 8, 20220Comments

The natural scalar (or dot) product: a numerical combination of vectors

The scalar or dot product of two vectors in real space is a real number that takes into account the direction, sense and magnitude of both vectors. 1.The natural scalar product

Functions

Geometry

May 9, 20220Comments

The derivative of a function: definition and geometric interpretation

The derivative of a function is its instantaneous variation, i.e. the slope of the tangent to the graphical representation of the function at that point. 1. General idea: an instantaneous variation We

Algebra

Geometry

April 28, 20220Comments

Linear transformations of the plane: determinant, bases and inversion

The linear transformations of the Euclidean plane are the invertible linear applications, i.e. of non-zero determinant. They allow us to move from one basis of the plane to another, and

Algebra

Geometry

April 23, 20220Comments

The bases of the Euclidean plane: vectors and coordinates

The representation of the Euclidean plane as the Cartesian product \(\mathbb R^2\) allows us to decompose any vector of the plane into two coordinates, its abscissa and its ordinate. This

Geometry

April 20, 20220Comments

Vector rotations of the plane: the analytical approach

The vector rotations of the plane (i.e. centred in the origin), are derived analytically (by coordinates) as linear applications of determinant \(1\), which makes it possible to characterise them integrally

Functions

Geometry

January 28, 20220Comments

Drawing a circle on the plane: equation and parameters

The definition of a circle is simple: it is a set of points located at the same distance from a given point. This distance is called the radius and this

Geometry

September 13, 20210Comments

The Euclidean Plane: Ancient Geometry and Modern Approach

From Descartes' analytic approach, which consists in introducing coordinates to represent the points of the plane, and from Cauchy's construction of the real numbers, we can give a modern representation