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.

Diédrico System: True magnitude of the line

By projecting a straight line on a plane orthogonal projection, its projection, generally, is smaller than the original measure.

Given a straight (segment bounded by two points) we want to determine its true magnitude and the angle it makes with the planes of projection.

Diédrico System: Third straight projection

The main projections on two planes straight dihedral (horizontal and vertical planes) possible to determine other new planes orthogonal projections on.

We'll see how generically determine a new projection from two. Later we will consider your application to study the so-called “auxiliary projections”, influencing their usefulness in solving various problems.

Fundamentals del System dihedral

We have seen in presenting Representation Systems descriptive geometry that is the set of techniques that allows to represent geometric character three dimensional space on a two dimensional surface.

In particular we explore in detail the so-called “System dihedral” based on the prospects ratios appearing in the cylindrical projection on two planes orthogonal projection.

Geometría proyectiva: Elements arranged quaterns

Analogously to the definition of saw “ordered triples of elements”, we can state a definition that involves four elements.

The non-conservation of the simple reason conical projections necessary to study a new model that is applicable in these representations, a new invariant present in double reasons.

Perception and contours

Gestalt laws to identify numerous visual recognition processes are unsuccessful leading to optical illusions.

The most common are “Fund-Figure” in which the outline of objects defines what can be found in the first or last plane.

The “Familiarity of objects” also heavily involved in the recognition and constantly compared with the known elements looking for repeating patterns.

Pawel Kuczynski an artist committed

El artista inglés Pawel Kuczynski (“Paul Kuczynski”) is one of those people who turns his social criticism art.

Graduated in Fine Arts from the Academy of Poznan, addresses from 2004 of performing satirical illustrations, rewarded to date 92 awards and honors.

Classification Representation Systems

The representation of technical objects is performed by one or more images that are determined by projecting the objects on an imaginary plane.

The display system is therefore defined by the position of said plane and the center of projection.

The position of the object relative to the center plane and can vary its representation, determining convergence in the projection, varying mediated, lines which are parallel in space.

Metric geometry : Generalization of the concept of “Power”

El concepto de potencia de un punto respecto de una circunferencia se basa en el producto de la mayor por la menor de las distancias de un punto a una circunferencia.
These distance values ​​are given in the string that contains the center of the circle and the point, namely, in diameter containing said point.
Is it possible to generalize this concept to consider other strings passing through the point P?

Pieces animated spatial vision training

Classically, to train our students in spatial vision, static images were used to represent volumes Mechanical.

The technology to create learning environments in which you can add motion to the representations, viewing closer to that obtained with a real object.

Metric geometry : Arco able on a segment

The ratio between the inscribed angle and the central angle in the circumference allows to obtain a locus of great importance for numerous applications in geometry metric; this is called arc locus capable.