Geometry, the word brings images of lines, points, circles, squares, and other shapes and forms to one’s mind. Geometry has an impact on our day-to-day life. Everything around us is a measurement, either defined or perceived, with a visual impression. In the same way, architecture is a domain that majorly deals with geometry and visuals. It plays a vital role in design as well as construction. Euclidean geometry was the only one used for over two thousand years. Now, there are many different aspects developed with time—projective geometry, perspective, Cartesian geometry, trigonometry, fractal geometry, differential geometry, typology, etc. are some of them.
Galileo Galilei says,” The book of nature is written in the language of mathematics.” Le Corbusier’s design philosophy has revolved around harmony and proportion. His utter faith prevailsin the mathematical order of the universe and nature, connected to the Fibonacci Series and the golden ratio which he described as “rhythms apparent to the eye and clear in their relations with one another.” These rhythmic patterns are inevitably seen in human activities. Hence, he developed an anthropometric system of Modulor, which goes by the principles of the golden ratio and divine proportion.
Below are the most notable buildings starring the influence of geometry in architecture.
1. Taj Mahal, Agra, India
The world-renowned monument displays a golden ratio in the width of its facade with a grand central arch and the heights of the windows. Mughal architecture has a particular mathematical order and astounding aesthetics with perfect symmetry and harmony.
2. Farnsworth House, Plano, Illinois
The incredibly gorgeous Farnsworth house by Mies van der Rohe is an authentic display of golden proportions in every aspect of design, from the floor plan, deck plan, overhangs of the roof to elevations, the house is in classic sync with nature.
3. Rietveld Schroder House, Netherlands
A notable example in the De Stijl movement, which emphasizes on proportions, is constructed using rectilinear Euclidean geometries. The geometrical lengths and widths of the house in plan suffice the 1:1.618 criteria of the golden ratio with the color palette depicting De Stijl’s style of architecture.
4. Parthenon, Athens, Greece
Dedicated to the Greek goddess Athena, Parthenon characterizes harmony with the building’s ideal proportions. The 9:4 width to height ratio depicts the vertical and horizontal proportions; the elements of its facade can be seen symbolizing golden rectangles.
5. CN Tower, Toronto
One of the tallest and freestanding structures in the world, although modern, is designed with consideration of the golden ratio. With varied geometrical forms and shapes, the ratio of the observation deck to the total height is 0.618. The design is unique with a balanced structure.
6. Notre Dame Cathedral, Paris
The cathedral is the most beautiful example of French Gothic architecture, which reflects golden proportions in the heights of each stage of the structure. A similar ratio is seen in the width of the columns at the top, making it an eye-pleasing design.
7. United Nations Building, New York
With the use of the mathematics ofdimensions, the building facade extensively incorporates the golden ratio bringing in the principles of harmony and proportions derived by Le Corbusier.
8. The Eden Project, UK
The geodesic domes made up of hexagonal and pentagonal cells comprise greenhouses. The structure, derived from phyllotaxis (the mathematical basis for plant growth), also implements the Fibonacci sequence in its design. This project shows thatmath in nature and architecture walks synchronically.
9. La Sagrada Familia, Barcelona, Spain
Sagrada Familiafeatures a magic square in which the numbers in columns, rows, and diagonals sum up to 33. An outstanding structure of Gaudi’s architecture seamlessly connects geometry, nature, and organic elements.
10. Pyramid of Giza, Egypt
The Great Pyramid of Giza is amongst the most significant and oldest structures, featuring a golden triangle with a height to base ratio of 0.636. The King’s chamber is designed based on the Pythagorean triangle and is the most stable structural form. Mathematics makes the design more interesting as the perimeter of the pyramid is 365.24 – the number of days in the year.
11. Sydney Opera House, Australia
Sydney Opera House is appealing through its repetitive geometry and simplicity. The roof designs evolve from parabolic, ellipsoid to finally spherical geometry for the final form of the building shells.
12. Philips Pavilion, Brussels, Belgium
A modern approach in design using technology backed with a mind-boggling geometrical collection of asymmetrical hyperbolic paraboloids is something that won’t go unnoticed.
13. Guggenheim Museum, Bilbao, Spain
A display of varied and unconventional shapes and forms not only raises the curiosity of understanding the structure but makes us recognize the treasures of geometrical implementation. The random configuration of the building mimicking a ship and the titanium panels, which look like fish scales is achieved with Computer Aided Three-dimensional Interactive Application.
14. Chichen Itza, Mexico
A 78-feet tall structure is based on the astrological system with 52 panels on each side of the pyramid representing the number of years in the Mayan Cycle. It also depicts the Mayan Calendar and the Solar year, thus extending the geometric correlation with astrology, extending into architecture.
15. The Gherkin, London, UK
Structured with the help of CAD and parametric modelling, the Gherkin is now a unique piece in London’s city skyline. The unusual and round building with spiral design gives an illusion of being a shorter one.
16. Cathedral of Brasilia
A crown-like hyperboloid that looks like clasped to the ground is a stunning geometrical creation by Oscar Niemeyer.
17. Santa Maria Novella, Florence, Italy
With basic geometrical figures and platonic philosophy, the structure is a beautiful series of harmonious relationships. The facade is reflecting the influence of geometry and mathematics applied to nature and art.
18. Virupaksha Temple Gopuram, Hampi, India
With a fractal-like design where the parts resemble the whole, the temple employs symmetrical design known as mandalas. Complex calculations and integration with nature, using geometric patterns and alignments form the structure.
19. Eiffel Tower, Paris, France
With hundreds of triangles and parallelograms, Eiffel is one of the ideal examples of geometry and technology. A pyramid-like geometric shape on four sides with four large half-circles on each side is a design wonder.
20. Bauhaus School, Dessau, Germany
Theories in Bauhaus architecture see simple forms in geometry as the basis of natural and organic shapes. The new complex for theBauhaus school is a representation of these theories, which became the emblem of the style.
“The geometry reveals five development directions for applications (each with endless possibilities); dividing, dwelling, trestle, fenestration, and art installation. I find these enabled designs so reflective of an ever-changing world where contextual factors and technological resources are shifting definitions of architecture, design, and the traditional boundaries between disciplines.”