From pyramids to skyscrapers: the evolution of mathematics in architecture 

Since the dawn of mankind, humans have sought to build structures that would protect them from the elements and other dangers. Over the centuries, the architecture has evolved from the pyramids and temples of ancient Egypt to modern skyscrapers and bridges. 

Dry stone hut in Saumane-de-Vaucluse, in Vaucluse (France)

During this evolution, mathematics played a vital role in the design and construction of buildings. Architects used mathematics to determine the dimensions, proportions and forces involved in construction. 

In ancient Egypt, architects used simple mathematical rules to calculate the angles and dimensions of blocks of stone and build massive pyramids. 

The Egyptians developed techniques to create perfect geometric shapes, such as squares and triangles, using ropes and stakes to mark angles. The pyramids were thus built with incredible precision, despite their massive size. 

Egyptian Pyramid (photo credit PXHERE) 
The Parthenon in Athens – The temple goddess Pallas Athena, vintage engraving (photo credit PUBLICDOMAINEPICTURE) 

Greek architecture is an example of how mathematics helped create incredibly beautiful and enduring buildings. The Greeks used geometry and mathematics to build monuments with perfect and clean lines to create harmonious proportions between the different parts of the building. Geometric patterns were also used to decorate buildings and sculptures, creating visual harmony throughout the monument. One of the most famous examples of Greek architecture is the Parthenon in Athens. 

Roman times is another example of how to use mathematics to create sustainable and aesthetic buildings. The Romans used them to build complex structures, such as aqueducts, arches, and domes, which have stood the test of time.

The Colosseum in Rome (Italy) (Photo credit PXHERE) 
The Pont du Gard (France) (Photo credit PXFUEL) 

Arches and vaults were key elements of Roman architecture, their design and construction were based on sound mathematical principles. Again, geometry gave them the means to calculate the size and shape of arches and vaults, using principles of trigonometry and curve calculation to create strong and durable structures. Roman aqueducts, which transported water over long distances, were also impressive examples of the use of mathematics in architecture. They made it possible to create precise slopes that allowed water to flow over long distances without losing pressure or flow.

During the Renaissance, architects began to use more advanced mathematics to create more complex and ambitious buildings to achieve balance and aesthetic harmony in building design.

The Renaissance was a period of renewal in the arts, sciences, and mathematics with the creation of more elaborate forms inspired by ancient works of Greek and Roman architecture. They sought to improve and perfect them by applying principles of geometry, algebra, and trigonometry, creating elegant and innovative structures. 

The architect Andrea Palladio developed a theory of proportions based on geometry, called the “Palladio system”. This theory was widely used in Renaissance building design and influenced Western architecture for centuries. 

San Pietro in Montorio in Rome (Italy) 
Château de Chambord (France) (photo credit WALLPAPER FLARE) 

Over the past centuries, the design of buildings has evolved towards more functional and efficient buildings to design buildings capable of withstanding the various climatic hazards, earthquakes, violent winds… Modern architects have used mathematics to design buildings of larger size and more great height such as skyscrapers and suspension bridges, which can support significant loads. 

The tower built by Edouard Albert in 1960 in Paris (France) (photo credit FLICKR) 
The Châtillon-sur-Loire suspension bridge built in 1841 (France) (photo credit FLICKR) 

Today, it is possible to observe even more ambitious and innovative buildings. Architects use mathematical models to simulate how buildings will behave under different conditions, as well as to design lighter and stronger structures. 

Thanks to the evolution of technology, engineers and architects can use mathematical equations to calculate the resistance of materials, the tension and compression of structures and to model the circulation of air and light in buildings. 

At the same time, mathematics is also experiencing significant advances in the 21st century. Research in applied mathematics, particularly in algebra, geometry, and topology, has led to major advances in mathematical modeling and numerical simulation. These techniques make it possible to virtually test architectural designs, verify their energy efficiency, predict their impact on the environment and optimize their construction cost.  

The Intempo Benidorm skyscraper (Spain) (photo credit Diego Delso)
Le122 Leadenhall in London (photo credit Diego Delso)
The Geode in Paris 
(photo credit FLICKR) 

Finally, the history of architecture is the history of innovation, creativity, and collaboration. Sometimes excessive or extravagant, the architecture reflects the diversity of the civilizations that preceded us. Mathematics has been an essential part of the history of architecture, providing builders with the tools to design and construct some of the most remarkable and enduring buildings in human history. From pyramids to skyscrapers, the evolution of mathematics in architecture is a testament to humanity’s ability to design and create incredible structures through collaboration between the arts and sciences. 

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