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It is enough to walk around in any city to notice that many architectural works are based on geometric shapes. This is not something aesthetic or purely stylistic. The main reason is that architecture is a science that joints several disciplines and areas, as it is the case of geometry.


This subject has special importance within architecture. In fact, there is a branch called geometric architecture. Do you want to know what it is? We will define you what geometric architecture is, why it is relevant in architecture and what aspects of the subject greatly influence the architectural works.


What is geometry and why is it relevant in architecture?

Geometry is considered one of the oldest sciences, being a branch of mathematics where lengths, areas and volumes become more important. This branch deals with geometric shapes and their properties, both in planes and in spaces.


Geometry has been present in architecture since its beginnings. Within this context, in classical architecture -from ancient Greece and Rome- we see that it acquires its own language and style when the elements relate to each other and geometric shapes create harmony and proportion in buildings.


If we focus on modern architecture, geometry is a key element of buildings. All of them, in general, create geometric spaces where the economy of means takes on special relevance.  The mission of geometric architecture is to economize buildings, saving in materials and maximazing the use of space . Materials are resonably used and useful space is not wasted.


In Geometric architecture the different elements and designs are made with simple and specific strokes. The correct interpretation of the use of geometry in architecturesimplifies the calculation of structural load and also considers its relation with the logic of construction.


Geometric aspects influencing architecture

As we have already mentioned, there are aspects related to geometry that have a direct impact on architectural practices. These are some of the most important ones.



When we design any architectural work, there are modules that are the similar to others, in order to enhance the construction with harmony, symmetry and plasticity. Modularity also simplifies construction, in general.


Polygonal and circular shapes

Polygonal shapes consist of a surface portion containing several points aligned in the plane, so that none of the connecting lines pass through more than two of them at a time. For instance, door and window frames. They are rectangles or squares, with 180-degree rotations when you open them.


Geometric representation

The representation of geometric shapes is mostly done by specialized software, where the data is introduced and, if necessary, the relevant calculations are made in order to execute the architectural work.


Structural inclination

The geometrical resources available today allow the development of vertical calculation techniques to work with the increasing heights of many buildings or dwellings.



The hyperboloid is obtained by rotating a hyperbola around one of the axes of  symmetry. This geometric shape is often used to make columns, chimneys and light entrances with a large surface area.


Conoidal and cylindrical shapes

If you visualize a spiral staircase, you can see the conoidal geometric shape contained in it, but it is also used in columns, tunnels or chimneys.


Bends and arcs

Bends and arcs are also used in windows and doors. Semicircles, elliptic, parabolic, etc. There are many geometric shapes used for the creation of arches and curves and with which horseshoe shapes, lobed, arches, etc. are achieved.


Polyhedral shapes

The polyhedrons most commonly used in architecture are cubes and octahedrons. The application of these shapes in architecture results in buildings characterized by achieving proportionate and harmonious spaces, obtaining functionally comfortable and resistant spaces that also favor their integration with the rest of the spaces in the building.

Master in Collective Housing UPM/ETH

The Master of Advanced Studies in Collective Housing is a professional and international postgraduate programme that is developed on a full-time basis, dealing with advanced architectural design in the city and housing. It is designed and taught jointly by the Polytechnic University of Madrid (UPM) and the Swiss Federal Institute of Technology Zurich (ETH).


For more information, click here!

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