Meaning and Definition of Diagonal

Definition of Diagonal

The diagonal term is part of the geometry and it is possible to define it as the segment in the form of a line that connects one end or corner of a figure with the vertex which lies on the opposite side.

Examples of diagonals in geometric figures

There are four sides in a parallelogram (A, B, C and D) and there are two diagonals: the straight line that goes from A to D and the line that goes from C until diagonal both B. are cut at the point of intersection of the two lines.
There are five diagonals in a polygon with five sides, there are nine diagonals in a polygon with six sides and one having seven sides will have 14 diagonals.
The four examples mentioned above help us to ask the following question: how many diagonals does a polygon? First of all, the first item to be considered is the number of sides. On the other hand, there is a regularity in the number of diagonals and such regularity is expressed with the following formulation: starting from the number of sides and multiply it by the same least number three and divide the result by two.

The Diagonal, an urban solution for Barcelona

The language of mathematics has a theoretical dimension which can be projected to tangible realities. This is what happened with the urban planning of the city of Barcelona. In the second half of the century XlX designed a new ordering of the city to solve its growth. To do this, a design was made in the form of grid or plan grid (rectilinear streets which intersect at a right angle). The large grid that was built to host the so-called zone of the ensanche was bisected by an avenue diagonal-shaped and for this reason received the name of the Diagonal. Thus, geometry is placed at the service of urbanism so the straight diagonal had several functions: traversing the city faster, connect different areas and facilitate transportation in general.
The architect of the Ensanche of Barcelona was Ildefonso Cerdá, who was commissioned by the City Council of the city once were knocked down the walls surrounding the town. Today this urban proposal is regarded as an important achievement in the history of the city of Barcelona, but initially the Ildefonso Cerdá solution was rejected by the authorities of the City Council and by broad sectors of Barcelona society. Despite initial suspicion his plan is finally approved and currently it is possible to see Barcelona following the line that marks the Diagonal.