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.
Categorías Geometría
Loci: Difference of squares of distances from two fixed points
The study of different loci that appear in the most common graphical models to understand and structure the graphic constructs used to solve many classical problems.
Given two fixed points, B y C en la figura, se trata de determinar las posiciones que puede ocupar el punto A para que la diferencia entre los cuadrados de la distancia desde A a dichos puntos sea constante.
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)
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.
The problem of the two peoples and the bridge
One of the first problems of geometry metric I propose to my students is to start the geometric model analysis while we review the basic transformations studied in earlier.
The problem is posed as a real case study, spiced up with a story that varies as a deeper analysis, and I jokingly call “The Cool River Bridge”, or “problem of the two peoples and the bridge”.
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.
The Secret Code [ Book ]
There are books and books. Some serve mainly to balance a wobbly table, while, others, never cease to fascinate.
The geometry as ancient science is reflected in all aspects surrounding the history of the human. Her knowledge has allowed the development of painting, architecture, interpreting nature …
In particular the segment aureus, the so-called divine proportion or golden rule of geometry, systematically appears in all geometric models to be a basic theme of the training of our current engineers.
The true size of Africa
The term “Immappancy” puede traducirse como “insuficiente conocimiento de geografía”. Incluso aquellos que piensan tener un conocimiento extenso de esta disciplina a veces son poco conscientes de la distorsión espacial que tenemos de la misma, debido a la forma en que contemplamos los documentos gráficos que nos han servido para formarnos.
Uno de los ejemplos más llamativos se da en el tamaño del continente africano que, dado que normalmente usamos proyecciones de “Mercator”, la distorsión que introduce en las regiones situadas en el ecuador es muy inferior a las situadas en los trópicos, magnificando las áreas en estas últimas regiones.
Parallel lines intersect at infinity, Myth or Reality?
One of the hardest concepts to assimilate in the first classes of projective geometry is the improper point. An improper point is a point at infinity and can be translated or interpreted as an address.
While metric geometry two lines intersect or are parallel, in projective geometry always intersect at a point proper or improper, what does not change in any way the operation with this geometric-mathematical model.
Geometry and origami [ Book ]
Geometry and origami Stella is a book published by Homo Sapiens Ricotti transmitting “happiness” from the world of mathematics. The author takes us to the world of geometry “playing” from bases underlying topological a paper sheet.
A teaching resource certainly of great value that can be entered at different educational levels; allows “touch” mathematics from the realization of the geometric models that express perfection.
Metric geometry: Circunferencias con condiciones angulares. Solución al Problema I
From the different solutions to the problem are proposed to obtain circumferences with angular conditions ( passing through a point, are tangent to a circle, forming an angle with a straight), we will analyze this solution using the application of the concepts of power used in the “Fundamental Problem Tangencies” ( PFT ).
The general model search can be the first step of a surveyor training. Later we discuss specific ways this particular problem that could simplify the tracking.