Mario Durán-Camejo

It is known that the method of Lagrange multipliers provides the local maxima and minima of a conditioned function, namely, a function whose variables are subjected to some constraints. In fact, it is the same as to say that the variables of the conditioned function must, additionally, satisfy other functional relation(s) which is(are) called the c...

The reflections on a quadric mirror is a very old problem that, nevertheless, has been alive for a considerable time. The first known reference to this problem goes back to 150 A.D. when it was formulated by Ptolemy. In the eleventh century, the Arab mathematician Hasan Ibn al-Haytham (Latinized as Alhazen) gave a geometrical solution in his Book o...

This paper focuses in the curious behaviors of integers when their reciprocal is expanded, say in the decimal numeral system. These expansions behave differently for certain primes respect to the others, and also respect to the non-primes. When expanded in the factorial numeral system those numbers give rise to another kind of interesting behaviors...

This paper presents a very simple proof of a relatively famous geometrical problem, only based in the properties of the triangles. As part of the proof a curious intermediate result is shown. The problem itself is a wonderful introductory problem to plane geometry.

This paper discusses the analytic method of solution of the quartic and cubic equations in historical perspective. Additionally, an alterative method to the graphic Khayyám's solution for the cubic is also provided.

This paper proposes an approach to the elliptic integrals of the first and second kinds from an alternative geometric point of view. This approach also suggests some transformations to be used in solving other different integrals.

In this paper a non-conventional set of geometrical figures derived from the regular polygons sujected to some operations is displayed, and different tessellations obtained by using them are also explored. Additionally, interesting connections between these figures and the non-regular convex polygons are introduced.

Agglomeration processes occur in many different realms of science such as colloid and aerosol formation or formation of bacterial colonies. We study the influence of primary particle density in agglomerate structure using diffusion-controlled Monte Carlo simulations with realistic space scales through different regimes (DLA and DLCA). The equivalen...

Homogeneous condensation of vapours mixed with a carrier gas in the stagnation point boundary layer flow near a cold wall is considered. There is a condensation region near the wall with supersaturated vapour. Assuming that the surface tension times the molecular area is much larger than the thermal energy far from the wall, droplets are nucleated...