Concept in Definition ABC

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

Examples of diagonals in geometric figures

In a parallelogram there are four sides (A, B, C, and D) and there are two diagonals: the line from A to D and the line from C to B. Both diagonals intersect at the intersection point of the two lines.

In a polygon of five sides there are five diagonals, in a six-sided polygon there are nine diagonals and one that has seven sides will have 14 diagonals.

The four examples listed above help us to ask ourselves the following question: how many diagonals does a polygon have? First of all, the first item to consider is the number of sides. On the other hand, a regularity is observed in the number of diagonals and this regularity is expressed with the following formulation: start from the number of sides and multiply it by the same number minus three and divide the result by two.

La Diagonal, an urban solution for Barcelona

The language of math it has a theoretical dimension that can be projected onto tangible realities. This is what happened to the planning urban planning of the city of Barcelona. In the second half of the 19th century, a new planning of the city was designed to solve its growth. To do this, a design in the form of a grid or hypodamic plan (rectilinear streets that intersect at right angles). The large grid that was built to house the so-called expansion area was crossed by an avenue in the shape of a diagonal and for this reason it received the name of the Diagonal. Thus, geometry was put at the service of the town planning so that the diagonal line had several functions: to cross the city more quickly, to connect the different areas and to facilitate the transport in general.

The architect of the Eixample of Barcelona was Ildefonso Cerdá, who was commissioned by the city council after the walls that surrounded the urban nucleus were demolished. At present this urban proposal is considered as a achievement important in the history of the city of Barcelona, ​​but initially the solution of Ildefonso Cerdá was rejected by the authorities of the city council and by wide sectors of the Barcelona society. Despite initial misgivings, his plan was finally approved and it is now possible to get to know Barcelona by following the line marked by the Diagonal.

Photo: iStock - JulieanneBirch