According to digopaul, the word “convex” derives from the Latin convexus. It is usually related to the description of surfaces or curves since it is used to describe something whose appearance is similar to the external face of a sphere or circumference. Concave, on the other hand, is the curvature or surface that is similar to the internal part of the spheres or circumferences.
A convex set, in this sense, is one where it is possible to unite the distance between one point and another in a straight line, without leaving it. The convex hull of a given set C, on the other hand, is the smallest convex inclusion group that includes C.
Another expression linked to the idea of convex is the convex function, which is one that is defined in relation to an interval when the domain of the plane located above its curve is also convex.
Convex polygons are polygons in which the internal angles are less than 180 degrees and the diagonals that can be drawn are all internal. Any straight line that crosses any of its sides, therefore, causes the polygon to be completely covered in one of the semi-planes that were marked from the straight line. It should be noted that all regular polygons and all kinds of triangles are considered as polygons with convex characteristics.
In economics, the term convexity represents a considerable resource for measuring interest rate risk and is used to calculate at what rate the duration of a given fixed-income instrument will change while its yield changes. Translated into mathematical terms, it is obtained by dividing the price by the derivative of the latter, in relation to its performance.
A convex mirror is a fragment of a sphere whose reflective portion is located on the outside. The centric area of the sphere is called the center of curvature, while the principal axis is the line through the center of curvature to the mirror. The convex mirror offers a virtual image (the reflected rays are not concentrated at any point) and smaller than the object.
History of convex mirrors
Convex mirrors, generally associated with parking lots, are also considered luxury and decorative objects, and are used indoors, just like those considered traditional. In fact, in the last three centuries, since France understood how to make flat mirrors (a procedure that until then only the Venetians knew and mastered), the success of convex mirrors has been highly variable.
Needless to say, its function was not to offer precise reflections to its users, but to decorate and illuminate interior spaces. On the other hand, painters used it as a tool to calculate the perspective of their paintings. Within this context, the first appearance of him in a pictorial work dates from the year 1434, in a portrait of the artist Jan van Eyck»s, which also represents the oldest known image of a convex mirror.
They saw their best moment during the neoclassicism and the Gregorian period (early 19th century) in England and North America, and were often molded in the shape of eagles and small spheres. On the other hand, for decades they have been present together with their concave close relatives in fairground attractions that consist of mazes whose walls offer crazy reflections to customers as they walk through them. To this day, they continue to enjoy moderate popularity, especially among people of a certain purchasing power or with a special interest in decorating their homes.
Lastly, and outside the world of decoration, they are used in psychology to treat patients with disorders related to the perception of their own image.