By: Valentina Varela

Since the beginning of times, man has been exposed to extreme and changing climatic conditions and threatened by other species. Nowadays, we have new needs… Production of functional and beautiful structures applying mathematical principles.

To learn how to appreciate and enjoy the beauty that exists in the Architecture that surrounds us. To identify simple geometric figures in constructions. To understand the properties of some basic geometric shapes.

A shape refers to the configuration of surfaces and edges of a two- or three- dimensional object. We perceive shape by contour or silhouette, rather than by detail. Primary shapes like the circle, triangle, and square generate different volumes. For example: A circle generates the sphere and cylinder. A triangle produces the cone and pyramid. A square forms the cube.

“Music is Mathematics, and Architecture is music in stone” -Howard Roark (Architect from NY)- Mathematics and Architecture have always been connected not only because Architecture depends on mathematical advances, but also they shared a same goal: the search for order and beauty. Geometry is the guiding principle of all this. We will now define some of the most important geometric shapes used in Architecture…

A cube is a three-dimensional solid object bounded by six square faces, all of these with the same dimensions. The sides of every face have the same measures, so any face of a cube could perfectly be its base. The volume of a cube is equal to the product of its three dimensions, and since they are all equal, the volume is the third power, or cube, of any one of its dimensions.

Square balaconies made with red bricks Cubo Negro – Caracas, Venezuela

A pyramid is a three-dimensional structure where the upper surfaces are triangular and converge on one point. The lateral faces of the pyramid are triangles and have a common vertex. The measurements of these triangles uniformly classify the shape as isosceles or equilateral. The volume of a pyramid is equal to one third the product of the altitude and the area of the base.

Pyramids of Giza – Ancient Egyptian Architecture

The word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. cylindrical surface) and two parallel planes. Saint Martin of Tours Church – Frómista, Spain

It’s a solid figure bounded by six rectangular faces: it is a rectangular box. It has right angles, and the opposite faces are equal in dimensions. The cube is a special case of the square prism in which all faces are squares. Lightness House (Zerafa Architecture Studio) - Canada

In general, a cone is a pyramid with a circular cross section. This means that its base is a circle. Reichtag (Foster and Partners) – Berlin, Germany

A sphere is a perfectly round geometrical object in three- dimensional space, such as the shape of a round ball. Like a circle, which is in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point.

Galileo Galilei Planetarium – Buenos Aires, Argentina

Winston Churchill, a British politician, writer and artist once wrote: “we shape our buildings: thereafter they shape us” After taking a look to these geometric shapes, we should be able to recognize them when we observe not only buildings, but also sculptures and even furniture. We should notice the importance of mathematical calculations for the construction of structures since they are part of every creative design process and represent harmonic solutions to our architectural needs. Shapes and forms are everywhere… We just have to open our eyes and find them!

(Kandinsky)