For most of us, Mathematics and Art are two subjects that are totally unrelated.  That one could possibly influence the other and in fact, elevate what it has to offer may sound bizarre. But principles of Geometry which is one of the oldest branches of Mathematics have since ancient times been considered by many artists as fundamental to achieving precision in their paintings. For instance, the great Renaissance artist Leonardo da Vinci is known to have used the golden ratio in some of his most renowned pieces like the 'Mona Lisa', 'Vitruvian Man', and The Last Supper among others.

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golden spiral
The golden ratio is widely used in art since Renaissance to achieve perfection in proportion. | Source: pixabay.com

While the use of the golden ratio helped produce the perfectly proportionate figure of the Mona Lisa, the application of linear perspective gave a strong aesthetic appeal to Gustave Caillebotte’s 'Paris Street, A Rainy Day. The use of such mathematical concepts in art and architecture to achieve symmetry in form and figure continues to be an important practice. Going ahead, we shall explore some of the best examples of maths in art over the ages. For those who want to ace Maths and know about all the wonderful aspects of this subject, it is recommended that you take the help of an experienced teacher. To find one, look up Maths tuitions near me.

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Using Maths to Create Art

To make mathematical discoveries, a creative mind is necessary, one that is capable of visualizing concepts and establishing connections and correlations between numbers. This is akin to the manner in which an artist functions. On the other hand, artists require mathematical tools to achieve perfection in their work. Patterns and forms conceived by their creative faculties which when expressed through art need to have perfect geometry. The proportion of each figure, the accuracy of the lines drawn to create an object have to be executed perfectly and that is where mathematical concepts come into use.

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The linking of mathematics to art dates back to the Renaissance, a time when advanced ideas were conceived that redefined science and arts.  That mathematical ideas such as linear perspective, symmetry, the golden ratio, and geometric shapes have a direct influence on art was established during this time. They came to be seriously considered when their impact was felt in artistic works whose quality improved with the application of these concepts. It was Leonardo Da Vinci, the Renaissance artist, scientist, and inventor who is credited for introducing mathematical concepts in artistic creations and popularizing the practice.

Math in Leonardo da Vinci's Art

In the early 16th century, Luca Pacioli the Italian mathematician published 'De Divina Proportione' whose subject was mathematical proportions and their applications to geometry, architecture and, visual art through perspective. The work discusses perspective in the works of Piero Della Francesca, Melozzo da Forlì, and Marco Palmezzano The title of the book which refers to the golden ratio contains illustrations by Leonardo Da Vinci. These are illustrations in woodcuts of regular solids which he studied under Pacioli in the 1490s. The thoroughly detailed text by the author along with the diagrams by the artist made the book very popular in mathematical circles and helped to popularize contemporary concepts and images in geometry.

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Leonardo
The usage of linear perspective helped da Vinci add depth to his paintings like 'The Last Supper'. | Source: pixabay.com

Having studied with Pacioli, Da Vinci made use of the idea of the golden ratio in some of his paintings and drawings. Its use appears in works such as the 'Mona Lisa'. Leonardo Da Vinci was someone who used his knowledge of mathematics to create a number of drawings that show what were thought to be the ideal human proportions. One of his best-known works on human proportions was the ‘Vitruvian Man’. It is a visual image of the perfect human form through the use of mathematics. To people like Da Vinci mathematics, was a universal constant that allowed proportions to be seen everywhere.

Da Vinci also used the mathematical principles of linear perspective in his works. The three elements needed for linear perspective are parallel lines, the horizon line, and a vanishing point. He was able to make it seem as if objects were further away from the viewer. Da Vinci was able to create the illusion of depth on a flat surface such as a painting or drawing. In 'The Last Supper', Da Vinci's work incorporated linear perspective with a vanishing point to provide apparent depth.

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Graphic Art of M.C. Escher

The Dutch artist M.C. Escher was greatly influenced by Mathematics though he never had any formal education in the subject. For him, mathematical concepts found their best expression in visual art and he spent a lot of time in find ways to express them through art. This led to his popularity among scientists.

In 1951, Escher’s illustration titled 'Relativity' depicted the faultless image of a staircase that seemed impossible to construct physically. The precision in symmetry and form that he had achieved in his art was of particular mathematical interest to mathematician and cosmologist Professor Sir Roger Penrose.

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The artist's creation was the source of inspiration behind Penrose's mathematical research paper, 'Impossible Objects: A Special Type of Visual Illusion', which he co-authored with his father.  The work explored in great detail the concept of physically impossible geometries such as those depicted in 'Relativity'. It also contained sketches and analysis of two of his renowned 'impossible objects; the Penrose triangle and the Penrose stairs.

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Escher
Escher's art portraying geometrically perfect figures could not be physically built. | Source: pixabay.com

Use of Fractals

Fractal is a mathematical term that is used to denote complex geometric shapes that are different from simple figures like the circle, square, etc.  As patterns, fractals are repetitive in design but vary in scale. They are created by repeating a simple process over and over again in varying measurements. Fractals appear in abundance in nature. For example, the pattern of leaves stemming from a branch repeats itself across the entire plant but varies in dimension. While trying to unravel what makes particular works of art or natural scenes visually appealing and stress-relieving, researchers have found that one of the crucial factors is the presence of these repetitive patterns called fractals.

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Since fractals in nature appeal to our senses, it’s therefore not surprising that visual experts and artists often incorporate fractal patterns in their works. This practice has been in vogue through the centuries and across many cultures. There is evidence of the use of fractals in ancient art and architecture of  Egyptian, Roman, Mayan, Incan, and Mayan works. The history of using fractals to create pieces of art, therefore, dates back to many centuries. Fractal art has found expression through da Vinci’s Turbulence, Hokusai’s Great Wave, M.C. Escher’s Circle Series, and, Pollock’s poured paintings.

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fractal
Fractals in digital art help artists produce fabulous works of art. | Source: pixabay.com

In modern times, fractals have made their way to digital art. Playful yet intricate digital art can be created through the use of fractals. Fractal art is achieved through the use of self-similar transforms. They are assigned geometric properties to produce multiple variations of the shape in continually reducing patterns. Though the process may sound extremely technical with little to no use of creativity, it is not so.  The algorithms that are used, end up producing mesmerizing and stimulating pieces of art, that are rich in colour and fascinating in shape.

The role that math plays in art is to bring symmetry and precision to the work of artists. In order to achieve perfection in the proportion of forms and figures, mathematical concepts are used. Since proportions are exceedingly important in order to create art that is lifelike, the use of concepts like the golden ratio, linear perspectives are practiced. Modern artists continue to look up to math for inspiration and try to figure out new ways of applying mathematical concepts to their works.

Mathematics undoubtedly is an interesting subject that has applications in various fields. Though the subject may appear to be difficult, with regular practice, it is possible to score full marks in the examination.  To master the subject, the foremost requirement is that of a teacher who can make learning math fun.

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The application of formulas to solve complex sums might seem like a daunting affair. But with proper guidance from an experienced teacher, the entire process can become easy.  Portals like Superprof help students to find online Maths tutors in India. The first class is offered for free to help students understand whether the teacher is the right fit. So without further delay, start looking for a mentor to help you delve deep into the mysterious world of Mathematics.

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Shreyanjana

Shreyanjana is an archaeologist who ironically finds the written word to be the most powerful means of storytelling. A travel buff and a photography enthusiast, she has been writing and sharing stories of all sorts ever since she can remember.