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Human makers have not overlooked the frequency of Fibonacci numbers and the Golden Ratio in the natural world. Artists, builders, and designers have included these ratios into their work over history, frequently with amazing outcomes. Human inventions across generations and civilisations show the global attraction of Fibonacci-based ideas by their application.
Many well-known pieces of art use the Golden Ratio for composition. For the face and feature placement of Leonardo da Vinci's "Mona Lisa," for example, the Golden Ratio is allegedly applied. The painting's whole width as well as the way the subject's lips, nose, and eyes are positioned seem to follow Golden Ratio proportions. Salvador Dali's "The Sacrament of the Last Supper" likewise purposefully frames the picture with a Golden Rectangle, with canvas dimensions exactly matching the Golden Ratio.
These are not one-sided occurrences. Golden Ratio proportions have been used by many other well-known artists including Botticelli, Seurat, and Mondrian. Popular composition advice in photography is the "Rule of Thirds," which approximates the Golden Ratio. This idea is applied by many photographers and directors to produce aesthetically pleasing and well balanced photos.
Long ago, these ratios shaped architecture. The Golden Ratio was applied in the Parthenon's construction by the ancient Greeks to produce a harmony and balance valued for millennia. Many of the Parthenon's features also follow these dimensions; its front fits exactly a Golden Rectangle. This application of the Golden Ratio helps to explain the building's ongoing attractiveness as a masterwork of classical design.
Architects such as Le Corbusier created design principles grounded on the Golden Ratio in more recent times. For example, Le Corbusier's "Modulor" method generated a set of harmonic proportions fit for use in architecture and design by means of the Golden Ratio. Many of his buildings and contemporary architecture have been inspired by this concept.
From graphic design to product design, the realm of design also often features Fibonacci numbers and the Golden Ratio. For visually appealing and unforgettable designs, many logos of big corporations—for example, adopt Golden Ratio proportions. Said to include Golden Ratio principles in its design are the Apple logo, Twitter logo, and Pepsi logo.
The Golden Ratio is a common tool in product design for producing ergonomic and aesthetically beautiful things. Many cellphones, tablets, and computer screens have Golden Rectangle based dimensions. Using these ratios in their designs, car makers have also produced aesthetically pleasing and aerodynamic vehicles.
Web designers frequently employ Golden Ratio proportions to produce visually balanced and easily navigable layouts even in the digital sphere. Using the proportions can help one ascertain the dimensions of sidebars, content areas, and other components of a webpage so producing a harmonic and user-friendly design.
Fibonacci numbers have been employed by some musicians to arrange their works. For instance, some of Béla Bartók's compositions—including his "Music for Strings, Percussion, and Celesta—use Fibonacci numbers to guide the placement of significant melodic events and the bar count in particular passages.
Using Fibonacci numbers and the Golden Ratio in design, architecture, and art goes beyond mere aesthetically pleasant results. It also relates to using a basic proportion concept that seems to speak to human experience. People seem to find Golden Ratio proportions naturally beautiful and harmonic, whether from our evolutionary background or the frequency of these ratios in nature.
While many artists deliberately employ these ratios, others could incorporate them unintentionally or find comparable ratios by intuition and experience. The argument concerning whether Golden Ratio proportions' inherent or taught appeal is still ongoing, although their general popularity over many civilisations and eras points to a universal appeal.
Fibonacci numbers and the Golden Ratio applied in human works provide a remarkable link between the domains of mathematics, nature, and human expression. It shows how ideas found in nature could inspire and guide human creative and design projects thereby producing works that appeal to our natural sense of beauty and proportion.