Conic Sections : mathematics in architecture

Guggenheim Bilbao conic section

Conic sections in architecture, such as circles, ellipses, parabolas, and hyperbolas, have been used in building design for a long time. Architects have utilised these geometric forms into a variety of structures because they have special aesthetic qualities and characteristics. Let’s examine some prominent instances of conic-section buildings and their relevance.

1. The Pantheon in Rome, Italy.

The Pantheon in Rome, Italy, is among the most well-known instances of conic sections in construction. This historic Roman temple was constructed in 125 AD and has a huge hemispherical dome. The dome exudes majesty and harmony as a beautiful illustration of a circular conic section.

In addition to letting in natural light, the oculus, a circular opening at the top of the construction, also represents the link between the heavens and the interior.

pantheon conic section

2. Spain’s Guggenheim Museum in Bilbao, Spain.

The Guggenheim Museum in Bilbao, which is created by renowned architect Frank Gehry, is a prime example of conic sections being used in a contemporary setting. The atrium and the central glass atrium are two of the conic features that make up the building’s curved shape. The fluid interaction between curves and material makes it a masterpiece.

It is a museum of modern art in Spain. Frank Gehry created the architecture, and it welcomed visitors in 1997. The building’s magnificent architecture is renowned for its curvilinear curves and usage of titanium, which gives it a distinctive metallic sheen.

The Guggenheim Bilbao also presents a number of temporary exhibitions throughout the year that feature pieces by both well-known and up-coming artists in addition to its permanent collection. Visitors can explore the building’s many terraces, bridges and outdoor artwork installations, which are all works of art in and out themselves. Millions of people visits the Guggenheim Bilbao every year, making it a cultural landmark of the Basque Country and all of Spain.

  “Frank Gehry’s work is characterized by unconventional shapes and forms. His buildings have distorted forms that either collide to form a single sculptural object, or are arranged individually in a seemingly random manner within a landscape.”

Guggenheim Bilbao conic section
saddle conic section

3. Eiffel Tower in Paris, France. 

Eiffel Tower is one of the example of parabola in architecture it is known to be in the form of a parabola. The parabola is really an important structure in the tower. It is build and designed that way to support the wind and so it would be more stable.

eiffel tower conic section

4. Chittorgarh Fort in Rajasthan, India. 

The Chittor Fort, also known as Chittorgarh Fort, is a historical structure that can be found in the Indian state of Rajasthan, in the city of Chittorgarh. The fort was constructed in the seventh century, and the main buildings were added in the fourteenth. It has been recognised as a UNESCO World Heritage Site and is the biggest fort in all of India.

The Chittor Fort has a sizeble area and is home to a number of impressive buildings, including palaces, temples, towers, and gates. The Vijay Stambh (Tower of Victory), Kirti Stambh (Tower of Fame), and Rana Kumbha Palace are the most well-known of these buildings.

chittorgarh conic section

5. The Gateway Arch in St. Louis.

On the west bank of the Mississippi River in St. Louis, The Gateway Arch is a 630-foot stainless steel monument. Built in the 1960s, it was designed by Finnish-American architect Eero Saarinen as a representation of the city’s function as the “Gateway to the West”. The top of the arch, where visitors may observe the city and its surroundings, is accessible via tram. Additionally, the Gateway Arch is home to a museum that chronicles the history of westward migration and St. Louis’s contribution to it. With over two million tourists passing through each year, the Gateway Arch is the tallest man-made structure in the country. As well as standing for the American West, it has emerged as a recognisable landmark in St. Louis.

gateway arch conic section

6. Lotus Temple in Delhi , India.

India’s Lotus Temple is a beautiful illustration of how conic sections are used in religious construction. The building, which was finished in 1986, is made up of several shells that resemble petal-like shells and are arranged in a circular pattern to resemble a lotus flower. The building’s distinctive and organic appearance is a result of the use of circular conic sections in the design, which also let light into the interior.

The magnificent Lotus Temple, commonly referred to as the Baha’i House of Worship, is situated in New Delhi, India. Fariborz Sahba. An Iranian architect, created the temple, which is formed like a lotus flower, and it was completed in 1986. The temple is accessible to individuals of all religions, but no religious symbols or rituals may be carried out there. In the middle hall, which has seating for up to 2,500 people, visitors are welcome to sit quietly and pray or reflect. Nine pools of water surround the temple, creating a reflected surface that enhances the structure’s splendour. In addition to being aesthetically beautiful, the temple’s flower-like architecture also serves a functional purpose by keeping the interior at a consistent temperature. Millions of tourists from all over the world visit Lotus Temple, which has grown to be one of the most well-known tourist attractions in the city. It is an homage to religious peace and togetherness and a spectacular example of contemporary architecture.

lotus temple conic section

7. Sydney Opera House in Sydney, Australia.

The Sydney Opera House is a world-renowned architectural masterpiece created by Danish architect Jrn Utzon. Hyperbolic paraboloids, a kind of conic section, are reminiscent of the building’s characteristic sail-like shells that make up the roof structure. Sweeping curves and interconnecting shapes add to the building’s aesthetic appeal and distinctive appearance in addition to ensuring structural integrity.

sydney opera house conic section

8. Spanish city of Barcelona’s Sagrada Famlia

The Sagrada Famlia is a magnificent basilica that has been under construction since 1882 and was created by renowned architect Antoni Gaudi. Conic sections appear in a variety of shapes, including as hyperbolic paraboloids and elliptical arches, on the building’s soaring towers and elaborate facades. This masterwork of architecture gains a sense of organic beauty and individuality through Gaud’s creative use of conic geometry.

sagrada familia conic section

These are only a few instances showing how conic sections are used in architecture in a variety of ways. Circles, ellipses, parabolas, and hyperbolas have been ingeniously used by architects to form structures, establish structural stability, enhance aesthetics, and elicit emotional responses. Conic sections enable aesthetically pleasing proportions, dynamic forms, and enduring sensations to architecture.

9. Taj Mahal in Agra, India.

A notable example of Mughal architecture in India is the Taj Mahal. Construction of the Mumtaz Mahal monument, which was built in Agra, Uttar Pradesh, in commemoration of the Mughal emperor Shah Jahan, began in 1632 and was finished in 1653. The Taj Mahal’s design combines elements of Islamic, Persian, and Indian architecture.

The Taj Mahal’s white marble dome, which rises over a central chamber and is encircled by four red sandstone minarets, is its most striking feature. The four minarets of the Taj Mahal are symmetrical and lean slightly outward to protect the palace from their collapse in the event of an earthquake.

taj mahal conic section

10. Burj al Arab in Dubai.

In Dubai, the Burj al Arab hotel is known for its striking sail-like shape, which is created by a series of conic sections. The hotel’s unique design has become a symbol of the city and is one of its most popular landmarks.

burj al arab conic section

11. Industrial Architecture.

Conic sections also feature prominently in industrial architecture, particularly in the design of grain silos. These structures are often cylindrical or conical in shape and are used to store large amounts of grain or other bulk materials. In many cases, they are designed with a series of conical sections that allow for greater storage capacity without sacrificing structural integrity.

industrial conic section

12. Louvre Pyramid in Paris, France.

I.M. Pei, an architect, created the Louvre Pyramid, a notable conical building that stands at the entrance to the Louvre Museum in Paris. The glass and metal pyramid has a distinctive structure made up of a sequence of triangular and trapezoidal faces. This contemporary architectural component gives the old-world setting a modern twist by using conic sections.

The cone is a three-dimensional object, somewhat similar in shape to a pyramid. In fact, you could visualize the cone as a pyramid that has an infinite number of sides (or to put it another way, a pyramid with a circular base). However, the cone is not a polyhedron, simply because it does have a circular base. It has single vertex (the apex of the cone) that lies at some distance from the base, and in a different plane. Whereas a pyramid has a finite number of triangular sides, each one connecting one side of the base polygon to the apex of the pyramid, a cone has a single, smoothly curved and tapered lateral surface that connects the circular base of the cone to its apex. The illustration below shows a square pyramid and a typical cone with similar proportions.

louvre museum conic section

13. Walt Disney Concert Hall in Los Angeles, United States .

The Walt Disney Concert Hall is a well-known cultural landmark in Los Angeles and was created by architect Frank Gehry. The building’s stainless steel facade features flowing curving surfaces that resemble conic sections like parabolas and hyperbolas. The intricate geometry gives the illusion of movement and flow, enhancing the structure’s aesthetic attractiveness.

walt disney conic section

Overall, conic sections offer a unique and visually striking way to enhance the design of buildings and

other structures. Whether used in sweeping domes or towering pyramids, these curves can create a

sense of flow, movement, and interest in any architectural design.

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