# Geometría y naturaleza

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.

# Determinación de un segmento conocido su punto medio [Solución]

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.

# Determinación de un segmento conocido su punto medio [Statement]

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.

# Metric geometry : Generalization of the fundamental problem of tangents :

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.

# Metric geometry : Make hyperbolic circles

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.

# Metric geometry : Haz elíptico de circunferencias

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.

# Metric geometry : Make circles parabolic

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.

# Metric geometry : Problem of Apollonius : rcc

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).

# Metric geometry : Obtaining the radical axis of two circles

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.

# The problem with football

A curious problem, I usually suggest to my students in class, where we can use geometric knowledge learned by studying the concept of power, is to determine the optimal position of shooting a soccer goal from a given path.

# Applying the Pythagorean Theorem: Equation of the circle

One of the first applications that can be found in the Pythagorean theorem, is its use in determining the equation of a circle.

Metric relationship between the two legs of a right triangle are essentially the expression of the concept of Euclidean measure.

The points of a circle are equidistant from the center of the (O).

A circle is the locus of points in a plane equidistant from a fixed point and coplanar another call center in a constant amount called radio.(W)