Desde la formación de las estructuras minerales hasta los diseños biológicos más complejos, la geometría de las formas marca los patrones elementales de estos diseños.
Buscar modelos naturales para su reproducción en sociedades civilizadas ha sido una constante que ha impulsado nuestro desarrollo como sociedad tecnificada.
Al plantear un problema de geometría métrica podemos abordar su resolución con diferentes estrategias. para ilustrar uno de estos métodos vamos a resolver el de determinar un segmento del que se conoce su punto medio junto con otras restricciones adicionales.
En particular analizaremos el caso en el que los extremos del segmento se encuentran situados sobre dos circunferencias coplanarias de radio arbitrario.
An interesting metric geometry problem that can enlighten the way to find solutions is to determine a segment of known its midpoint with additional restrictions.
And that a segment is determined by its ends (colon), in the plane need four values (simple data) to set their Cartesian coordinates.
Working circumferences beams in the plane I got the idea for this wallpaper that recreates the three-dimensional geometric pattern.
A beam fields Parabolic, at a point tangent to the same plane textured glass served to perform this interesting render. We used a checkered texture to define the ground plane and set a reference horizon in the image.
We have solved the fundamental problem we have called for tangents when presented with tangency conditions on a circle or a straight. Conceptually we can assume that both problems are the same, if we consider the straight as a circle of infinite radius. The statement therefore posed circumferences obtaining through two points were tangent to a straight or tangent to a circle.
When defining a beam circumferences as an infinite set simply fulfilling a restriction on the power, sorted the beams depending on the relative position of its elements.
Hyperbolic circumferences beams are among these families circumferences. Of the three existing (Elliptical, parabolic and hyperbolic) are those that offer greater difficulty in its conceptualization to come not defined waypoints. We will see how to determine elements that belong to them as it did in the previous cases.
When defining a beam circumferences as an infinite set simply fulfilling a restriction on the power, sorted the beams depending on the relative position of its elements.
Circumferences elliptical beams are among these families circumferences. We will see how to determine elements that belong.
When defining a beam circumferences as an infinite set simply fulfilling a restriction on the power, sorted the beams depending on the relative position of its elements.
Parabolic circumferences beams are among these families circumferences. We will see how to determine elements that belong.
To study the equation of a circle in the plane. saw a concrete determination is performed by determining three parameters in turn define the coordinates of its center and radius.
We can say therefore that there is a triply-infinite set of circles in the plane, so if we set two restrictions, the parameters, we will be a purely infinite set which we call “beam circumferences”
Any of the problems of tangents that are included under the denomination of “Apollonius problems” can be reduced to one of the studied variants of the most basic of all: the fundamental problem of tangents (PFT).
In all these problems we will consider fundamental objective to reduce the problem to propose to one of these critical cases, by changing the constraints that define other concepts based on the orthogonality.
In this case we will study what we call “Case Apollonius RCC”, namely, For the problem of tangency at which the data are given by condition of tangency to a line (r) and two circles (cc).
The two circumferences radical axis is ellugar locus of points of a plane with equal power on two circles.
Is a straight line having a direction perpendicular to the centerline of the circumferences. To determine this axis is therefore necessary to know a single crossing point.
