The Fibonacci sequence refers to a series of numbers wherein each number is the sum of the preceding to numbers appearing in the sequence. While it is explicitly a mathematical concept, it is widely used in architecture as well to establish a sense of proportion and visual harmony. Inspired by the natural pattern of perfection, this sequence is closely related to the golden ratio and has been widely used in the construction of famous monuments such as Taj Mahal and the Pyramids of Egypt due to the eye-pleasing results it brings. In this article, we delve deeper into the relevance of the Fibonacci sequence in architecture.
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See also: Ashlar architecture: The style from the pages of history
How is the Fibonacci sequence used in architecture?
The Fibonacci sequence is used in architecture to obtain specific types of designs that appear harmonious and visually pleasing. Here are the uses of this sequence in architecture:
Proportional harmony
Architects use the mathematical proportions fixed by the Fibonacci sequence to determine the proportion of elements of the structure being constructed. These elements include height and width of doors, windows and facades. The Fibonacci sequence helps in obtaining harmonious proportions for these elements.
Shell and spiral structures
The Fibonacci sequence is intimately linked to the golden ration and the golden spiral. Shell-like structures resembling the spiral are widely used by architects in designer elements of buildings for proportional and eye-pleasing results.
Usage in Indian architecture
The Fibonacci sequence has been widely used in Indian architecture through the ages.One of the seven wonders of the world, it is no surprise that the Taj Mahal makes use of this pattern. The geometric harmony and clean proportions of the Taj Mahal are widely believed to be based on the Fibonacci sequence. The main dome and various other architectural elements of the building are aligned with the golden ratio. The presence of the golden ratio has also been seen in the width of the central arch and the windows inside it located right below the dome.
Various other historical monuments, such as the Ajanta and Ellora Caves in Maharashtra, the Khajuraho Temple in Madhya Pradesh and the Konark Temple in Odisha also show meticulous attention to geometric harmony and intricate detailing. While not explicitly linked with the Fibonacci sequence, the high degree of symmetry and geometric precision has been a cause of fascination.
Relevance in modern day architecture
Alongside its wide use in historical buildings, the Fibonacci sequence holds great relevance for modern day architecture as well. Here is how it is significant to us today:
The spiral pattern derived from the Fibonacci sequence has been an inspiration for a lot of architects. These patterns can be used in designs that imitate the organic and naturally occurring designs in nature even if they do not explicitly follow the sequence in precise mathematical terms.
Biophilic design
The Fibonacci sequence is associated with patterns found in nature, such as the arrangement of leaves, petals and sea shells. Enthusiasts of biophilic design, that aims to incorporate these ecological elements, can draw on this sequence for reference to establish a link with the natural world.
Parametric design
The exploration of parametric design has been made easier with modern technologies that enable architects to access complex geometries and mathematical relationships more conveniently than before. The sequence can be used as a basis for such design algorithms that promote harmony in intricate forms.
Sustainable design
The patterns derived from the sequence design a layout of structures in a way that optimises energy use, ventilation and lighting. Therefore, more and more architects are showing their interest in this pattern for efficient and sustainable infrastructure design.
Facade design and ornamentation
Architects use the proportions of the sequence to create a rhythm and balance in the external appearance of buildings. As a result, the sequence is widely used in the designing of ornamental elements of structures, such as facades, windows and similar architectural details.
FAQs
How is the Fibonacci sequence related to architecture?
In case of architecture, the Fibonacci sequence is used to establish proportional harmony and aesthetics and mostly influences the designer aspect of spaces, facades and structural elements.
How is the sequence related to the golden ratio in architecture?
The ratio of consecutively appearing Fibonacci numbers converge towards the golden ratio, i.e approximately 1.62. Therefore, both these concepts are taken into account for architectural purposes to achieve visually pleasing proportions.
Which monuments use the Fibonacci sequence in their design?
The Parthenon in Greece and the Taj Mahal in Agra have been linked to the golden ratio and Fibonacci numbers due to their geometrical precision and symmetry.
How is the sequence applied to achieve proportional harmony in buildings?
The sequence is often used to determine proportions of windows, doors and structures and create a sense of visual balance and harmony.
Is the Fibonacci sequence used universally in architecture?
The use of Fibonacci sequence depends on the design philosophy and aesthetics adopted by the architect. Different architects might prioritise different principles and mathematical concepts.
Can the sequence be applied to modern architecture?
The sequence can inspire contemporary and harmonious styles in modern architecture. With the use of digital tools, architects can explore more complex geometries inspired by the sequence and apply it to architecture.
Does the sequence have a positive impact on human perception?
While aesthetic preferences are subjective, the wide use of the sequence indicates a positive reception of the sequence by the human mind.
Got any questions or point of view on our article? We would love to hear from you. Write to our Editor-in-Chief Jhumur Ghosh at jhumur.ghosh1@housing.com
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Riddhi Chatterji
Riddhi Chatterji is currently pursuing a master’s degree in English literature from University of Delhi. Her meticulous attention to detail and the desire to make a learning experience out of every opportunity has allowed her to work with different forms of textual content for digital platforms, ranging from social media to news desks. When not working or studying , you can find her with her head buried in a book, discovering new music and movies, or out and about exploring the city on the metro.
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The Golden Ratio is a design concept based on using the Fibonacci sequence to create visually appealing proportions in art, architecture, and graphic design. The proportion, size and placement of one element compared to another creates a sense of harmony that our subconscious mind is attracted to.
Architects use the mathematical proportions fixed by the Fibonacci sequence to determine the proportion of elements of the structure being constructed. These elements include height and width of doors, windows and facades. The Fibonacci sequence helps in obtaining harmonious proportions for these elements.
Allowing architects and designers to systematically achieve precise visual balance by applying a logical system to determine proportions that are naturally pleasing to the eye.
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The golden ratio, also defined by the letter φ (phi), is the most telling example. This mathematical formula is considered by some as a universal rule of beauty. With a proportion equal to x²=x+1, the golden ratio in art creates a balanced relationship that the mind's eye loves.
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The Golden Ratio is a relationship between two numbers that are next to each other in the Fibonacci sequence. When you divide the larger one by the smaller one, the answer is something close to Phi. The further you go along the Fibonacci Sequence, the closer the answers get to Phi.
The Fibonacci sequence is the series of numbers where each number is the sum of the two preceding numbers. For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, … Mathematically we can describe this as: xn= xn-1 + xn-2.
“The golden ratio is all about blank space and its relation to the 'pay attention' space,” says Berndt. “There's only so much that people can take visually. This is a guiding principle to help you understand the limits of human attention so you can create something that is aesthetically pleasing.”
In stock trading, Fibonacci levels help identify entry and exit points. For instance, if a stock has surged and then pulls back to a 38.2% retracement level, a trader might see this as a buying opportunity, anticipating a continuation of the uptrend.
The Fibonacci sequence is widely used in engineering applications including computer data structures and sorting algorithms, financial engineering, audio compression, and architectural engineering. The Fibonacci sequence can be seen in nature in the spirals of a sunflower's seeds and the shape of a snail's shell.
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The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five (pictured at left), the chicory's 21, the daisy's 34, and so on.
The Fibonacci sequence is found in many different disciplines and in nature. For example, it has been used to describe plant life growth, estimate population increases over a specified timeframe, model virus breakouts, and predict the behavior of financial markets.
Fibonacci numbers do appear in nature often enough to prove they reflect some naturally occurring patterns. You can commonly spot these by studying the manner in which various plants grow. Many seed heads, pinecones, fruits and vegetables display spiral patterns that when counted express Fibonacci numbers.
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