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The use of mathematics in art can be dated back to the 5th century BCE when the Greek High Classical sculptor; Polykleitos implemented the 1:√2 ratio of human body proportions in his sculptures. Polykleitos believed that sculpting each successive body part, so that it is √2 times larger than the last, beginning with the fingers, would create the aesthetically ideal body.

While mathematics can assist in the aesthetic appeal of visual art, visual art is able to depict mathematical concepts in an elegant and effective manner.

Since the time of Polykleitos, a large number of well-known artworks were produced with the assistance of mathematics. These artworks all have a strong aesthetic appeal that can be credited to the innovative implementation of mathematical concepts. This article is a tribute to those mathematical artists and artist mathematicians.

Here is all you need to know about the evolution of the perceptions towards and pedagogy of Mathematics.

## Optical Art: The Use of Geometry in Art

Geometry offers the most obvious connection between the disciplines of mathematics and art. Both art and math involve drawing and the use of shapes and forms, as well as an understanding of spatial concepts, two and three dimensions, measurement, estimation, and pattern. Many of these concepts are evident in an artwork’s composition, how the artist uses the elements of art and applies the principles of design.

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Nowadays, artists often use geometrical elements such as lines, angles, and shapes to create a theme throughout their artwork. Also, artists started using these geometrical elements as a way to create the illusion of the third dimension. This art is known as Optical or Op Art.

Students of optical art should start by creating line designs and working with symmetry. Then, they can apply the concept of shading to their designs to create a sense of perspective. This way, students can build their spatial intelligence for understanding advanced mathematics.

### Perspective Drawing

Perspective drawing is an application of geometry that artists use to organize the arrangement of space in a picture. For generations, artists have been inspired by the visual beauty and order that exists in geometry and have used it in many ways to help the composition of their art. There is no greater nor more obvious example of this than The Last Supper by Leonardo da Vinci.

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Perspective creates an illusion of three dimensions (depth and space) on a two-dimensional (flat) surface. Perspective is what makes a painting seem to have form, distance, and look "real." The same rules of perspective apply to all subjects of art, whether it is a landscape, seascape, still life, interior scene, portrait, or figure painting.

In Western art, perspective is often called linear perspective and was developed in the early 15th century. The system uses straight lines to plot things in a piece of art, be it a painting or a sculpture or architecture. The Renaissance artist, Leon Battista Alberti, and architect Filippo Brunelleschi are credited with the "invention" of linear perspective. Alberti set out his theory in his book On Painting, published in 1435.

## The Golden Ratio: Applied Maths in Painting

Also known as the Golden Section or the Divine Proportion, this mathematical principle is an expression of the ratio of two sums whereby their ratio is equal to the larger of the two quantities.

During the Renaissance, painter and draftsman Leonardo Da Vinci used the proportions set forth by the Golden Ratio to construct his masterpieces. Sandro Botticelli, Michaelangelo, Georges Seurat, and others also appear to have employed this technique in their artwork.

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In Modernism, there is a shift away from a strict use of the Golden Ratio. However, geometry figures heavily in many movements at this time. Clean lines and shapes in primary colors populate paintings and graphics, as evidenced by Constructivism, Suprematism, and De Stijl.

The Golden Ratio is an irrational number, approximately 1.618, which is prevalent in nature, art, architecture, and design. Other names for it are golden mean, golden section, Phi (in mathematics), divine section, golden number, Fibonacci sequence.

### The Golden Ratio Rectangle

Visually, the Golden Ratio Rectangle is a rectangle that, when cut into a square, results in the remaining rectangle being the same proportion as the original rectangle. The rectangle possesses many properties and holds many different patterns within it.

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## Applications of Golden Ration in Art

Since the discovery of the Golden Ratio, it has been widely adopted by artists, designers, and architects to determine the most visually pleasing proportions to make their creations.

There are many ways artists have used the golden ratio in art: using the golden rectangle itself to determine the composition of the artwork, using the path of the spiral in the golden rectangle, and even placing important subject matter at measured points inside the rectangle.

### Leonardo da Vinci

Da Vinci illustrated a book written by Luca Pacioli in the late 15th century all about the Divine Proportion. He used the measurement in many of his paintings, including Mona Lisa and The Last Supper.

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### M.C. Escher

Escher created mathematically challenging artwork. He used only simple drawing tools and the naked eye but was able to create stunning mathematical pieces. He focused on the division of the plane and played with impossible spaces. He produced polytypes, sometimes in drawings, which cannot be constructed in the real world but can be described using mathematics.

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What are some examples of maths in art?

### Salvador Dali

Salvador Dali’s painting, The Sacrament of the Last Supper (1955), is widely cited as utilizing the Golden Ratio. The painting can be broken down into these terms:

- The room is a dodecahedron, which is related to a golden rectangle in a mathematical way.
- The entire painting is a golden rectangle.
- The table and 2 disciples next to Christ are positioned perfectly at the sections of the golden rectangle.

### Piet Mondrian

Mondrian is said to have used the Golden Ratio in his abstract paintings. Apparently, some of his paintings line up better with the proportions than others, which means he wasn’t too picky about precise measurements.

Enrich your mathematical horizons by learning about the history and evolution of mathematics.

Problem-solving skills such as visualization and spatial reasoning are important for artists and professionals in math, science, and technology. By taking an interdisciplinary approach to art and mathematics, students can identify and apply authentic connections between the two subjects and understand concepts that transcend the individual disciplines.

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