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

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

by M4t_6_onL | Dec 8, 2022 | Algebra, Geometry

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 in the Euclidean plane 1.1.From the distance between two points to the scalar product In...
The derivative of a function: definition and geometric interpretation

The derivative of a function: definition and geometric interpretation

by M4t_6_onL | May 9, 2022 | Functions, Geometry

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 place ourselves here in the framework of functions of a real...
Linear transformations of the plane: determinant, bases and inversion

Linear transformations of the plane: determinant, bases and inversion

by M4t_6_onL | Apr 28, 2022 | Algebra, Geometry

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 the orthogonal transformations, i.e. the vectorial isometries, exchange the...
The bases of the Euclidean plane: vectors and coordinates

The bases of the Euclidean plane: vectors and coordinates

by M4t_6_onL | Apr 23, 2022 | Algebra, Geometry

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 decomposition is linked to a particular and natural “representation...
Vector rotations of the plane: the analytical approach

Vector rotations of the plane: the analytical approach

by M4t_6_onL | Apr 20, 2022 | Geometry

Drawing a circle on the plane: equation and parameters

Drawing a circle on the plane: equation and parameters

by M4t_6_onL | Jan 28, 2022 | Functions, Geometry

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 point is called the centre of the circle. The circle with centre \((-1,-3/2)\) and radius \(\sqrt 6\) 1. Circles as...
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