Geometry and architecture have a connection that has been around for years and will continue to be for the foreseeable future. Every building you have ever been in, including your house, school, and library, is a product of mathematical principles applied to design. While geometry doesn’t shout so loudly, you can see it in some buildings – like the Great Pyramids.

Geometry is that unsung yet essential tool architects use in whatever they do, from designing a bridge to building a block of flats. This article will clarify if you have ever wondered how architects incorporate mathematical principles into creating structures. Additionally, for students who struggle with geometry or need assistance with their homework, it is not uncommon to seek help from professionals who can provide guidance and support. The option to buy a dissertation online in geometry allows students to overcome challenges and grasp the concepts necessary for success in architectural studies or related fields.

Geometry in architecture: How it started

According to the Roman architect and writer Vitruvius, every good building has three conditions: firmness, delight, and commodity. Where commodity refers to a building’s ability to fit its purpose, firmness refers to its ability to stand up. However, the “delight” condition is the hardest to measure and is very subjective. For Vitruvius, creating structures connected to nature is the path to delight, and geometry is the primary tool for understanding nature’s constructions.

Geometry in architecture did not start today; both have been intertwined since ancient times. However, geometry became more fully integrated into architecture during the Renaissance when it was made a subject officially. Ancient architects were particularly interested in the underlying mathematical principles in architecture, thus using geometry to design more structurally sound and aesthetically pleasing buildings. One of the Renaissance-era architects, Alberti, believed that nature and all of art, in fact, are governed by geometric principles.

Historically, the Greeks, Romans, and Egyptians were arguably the most appreciative of geometry, as evidenced in their buildings and structure. A good example is the great pyramid of Giza, whose construction remains a mystery to historians and scholars. However, the ancient Egyptians were not the only ones who appreciated geometry; geometry appreciation extends to almost every culture and nation.

Johannes Kepler, a German mathematician, and astronomer, used laws of planetary motion to show the importance of geometry in understanding the physical world. The laws are considered one of the most important contributions to geometry in architecture. More than that, they impacted the way architects think about designing buildings.

The role and importance of geometry in Architecture

Geometry, an ancient branch of mathematics, involves using points, angles, lines, and 2D and 3D shape surfaces. Geometry in Architecture is non-negotiable; without it, it is near impossible to be sure that buildings are safe. Also, with geometry, it would be much easier to make our buildings look nice; geometry gives architecture plans and drawings a voice. Unless an architect has a good understanding of some basic geometrical concepts, they cannot do their job.

Without proper geometry calculations used in architecture, buildings would either collapse or look awful. However, this is only one of the reasons geometry is so important in architecture or why contemporary architects are particularly interested in it. Present-day architects tend to think of Euclidean geometry when they think of the subject. Euclidean geometry principles were devised by Euclid, the Greek mathematician, more than 2,000 years ago.

To build a habitable structure, an architect must design before construction workers can do anything. Besides geometry, algebra and trigonometry also play crucial roles in architectural design and are typically applied to blueprints or sketch designs. Furthermore, these mathematical tools calculate the probability of issues that can be experienced as construction workers bring the design to life.

How Architects used geometry in the past

Ancient architects believed the key to ensuring buildings were as aesthetically pleasing as possible was strictly adhering to geometric rules and calculations. Five hundred years after Marcus Vitruvius wrote his book, “Ten Books on Architecture,” Renaissance polymaths rediscovered his writings. In the book, he enumerated the ideal proportions a building should have based on the human body proportions.

Two Renaissance polymaths that rediscovered the principles in Vitruvius’s books included Leon Battista Alberti and Leonardo da Vinci. Alberti developed some of the principles in Vitruvius’s books in his version of the book. These included the need to ensure the maintenance of ratios between elements across the whole of a building. These ideas have stuck for centuries; even today, some are still being used and rarely questioned.

How Architects use geometry today

Many ancient mathematical principles used in architecture are no longer strictly followed like before, although they still hold good. Contemporary architects view geometry more like a servant than a master, using it differently. Present-day architects use geometrical principles to ensure someone from the outside world can understand building plans. Also, they use it to ensure their buildings remain standing and that cities are not populated with imbalanced theoretical architecture.

Adopting biomorphic geometric forms is another way architects use geometry today, which Vitruvius and his followers did to some extent. This involves replicating forms in the natural world; ancient architects used proportions of the human body, while modern architects used plants and animals.

Various geometrical concepts and how Architects use them

Several geometrical concepts and calculations makeup architecture as it is today. These include the golden ratio, symmetry, and tessellation; let’s look at them one after the other.

The golden ratio

The Golden Ratio is a mathematical law of nature that has survived centuries and is still being used today. Defined by Euclid in 300 B.C., the Golden Ratio is a basic geometric principle also called a timeless archetype. Architects use this concept, with its geometric shapes, to create proportion and balance.


Symmetry is another geometrical concept used by architects; they use it to create balance and harmony in architecture. Designs made with this concept feature a balanced composition of shapes and patterns; a good example is the Taj Mahal.


Tessellation involves the repetition of the same shape to fill a plane without leaving overlaps or gaps. Architects use this principle to create intricate and detailed patterns in the design of a building.


The link between geometry and architecture has existed for thousands of years and will remain for thousands of years. Nevertheless, mathematics in architecture is not just about the exterior looks of a building but also its interior spaces. Geometry will maintain its importance in architecture as the art and science of designing buildings using geometric rules.