# Introduction to the study of the hyperbolic paraboloid [ Animation ] [ Surfaces ]

The surfaces used in the engineering are different natures. Su classification based on different criteria serves to facilitate understanding and su deduce common groups ellas.
One aspect which differentiates these surfaces is the possibility of generating by straight movement along a curve, or subject to a law of generation. These include the so-called “Hyperbolic paraboloid”

# Power Concepts [ Prezi ]

The concept of power is fundamental to solving problems in a structured way and generalization of tangency where angularity.
This concept, initially apply the fundamental problem of tangents, allow us to use a systematic analysis of different cases, because we can reduce the remaining exercises tangent circles to three given to a single basic problem.
In this presentation, made with Prezi, the basic ideas associated with this important concept is.

# Geometría proyectiva: Determination of homologous elements in projective beams

One of the first problems we must learn to work in projective geometry is the determination of homologous elements, both in series and in bundles and in any provision of bases, or separate superimposed.

To continue the study of the methodology to be used will use the dual model the elements based on “points”, ie with straight, further assuming that the bases of the respective beams are separated relate.

# Geometría proyectiva: Projective center of two projective bundles

Using the laws of duality in projective models can get a set of properties and dual theorems from other previously deducted. Obtaining homologous elements in the projective case series was performed by obtaining intermediate pespectividades allowed perspectival do we get what we have called “projective axis”. We will see that in the case of projective bundles, Dual reasoning leads us to determine projective centers.

# Geometría proyectiva: Projective projective axis of two series

The operational prospects relationships is reduced to the concepts of belonging, so we will use these techniques to suit projective models simplify obtaining homologous elements.
How can we define two projective series? On how many homologous elements are necessary to determine a projectivity?How can we obtain homologous elements?

# Geometría proyectiva: Projectivity

The relationship called “cuaterna” or “double ratio of four elements” to define the general homographic transformations perspectivity and projectivity.

# Metric geometry: Curves : Conical

Among the most important curves are studied in geometry is called “Conic curves”. Another common name for these curves is the “Conic Sections” because the first definition given for them, by Apollonius of Perge, was from the sections in a cone of revolution.

# The problem with the pool table

One of the most geometric games there is the “Billiard game”, in which using a drum with a wad (a pool cue) on a ball, we must ensure that this impact on one or more other arranged in a rectangular table. With the “The taco de bill” effects can be given to balls, but if you just hit them in the center, behavior can be compared to the classical transformations that are studied in the axial symmetries.

# Arco able on a segment : Solución [I]

Let the solution to the problem proposed arc capable application, that we proposed with the following statement:

Determine two lines that are based on a point P outside a line r, an angle formed between "alpha" and cut given to the line as a segment of length "L".

# Arco able on a segment : Example [I]

The arc geometry applications capable of an angle on a given segment are many and varied:

From the proof of a theorem, the intermediate solution of a problem or direct application in a case, We can see this construction repeatedly widespread.

# Apollonius and his ten problems

One of the most comprehensive articles they have written my students in geometry classes is describing how to solve the so-called “Apollonius problems”.

Determining come straight circumferences or geometric constraints defined by the tangents are based on a family of geometric problems of great interest.