How Mathematical Models are Used in Art

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, we'll discuss how mathematical models are used in art, including famous paintings like the Mona Lisa. In particular, we'll explore the golden ratio, tessellations, and anamorphic art. Updated: 09/21/2020

The Golden Ratio

Leonardo da Vinci painted the Mona Lisa, while M.C. Escher made some visually intriguing drawings. Both of these artists used mathematical principles in their work.

Leonardo da Vinci used what is known as the golden ratio, which is approximately 1.618 and is represented by the Greek letter phi. This ratio is achieved when you divide a line in such a way that the longer part divided by the smaller part is equal to the whole line divided by the longer part. Mathematically, the golden ratio can be expressed as:

a / b = (a + b) / a

For example, the ratio of the length of Mona Lisa's head (top to chin) and the width of her forehead form a perfect rectangle, thereby fulfilling the golden ratio. The placement of her arms also fit the golden ratio.

Contemporary photographers also use the golden ratio when composing their images. Instead of positioning a skyline in the middle of an image, they'll position it so that it follows the ratio.

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  • 0:04 The Golden Ratio
  • 1:02 Tessellations
  • 1:33 Anamorphic Art
  • 2:25 Lesson Summary
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At first glance, M.C. Escher's paintings appear normal. However, upon a closer look, the elements of the composition are not as they seem and may in fact be mathematically and physically impossible. To achieve this effect, Escher drew tessellations. A tessellation is a group of shapes tiled to form a continuous pattern on an infinite plane. Tessellations aren't always simple grids, they can also be very complex, like this one:

A more complex tessellation
math in art

Notice how there are no overlaps and no gap between each individual component of the drawing.

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