Week 2: Mathematics and Art

Triangles used to depict perspective.
(http://weeklydoodles.blogspot.com/2014/09/how-to-draw-triangle-in-perspective.html)

            Mathematics is perhaps one of the sciences that has had the greatest impact on the arts. The close ties between mathematics and art likely started when artists started to depict 3D images on a 2D canvas. The artist Duccio was one of the pioneers in this field, but many of his depictions. 3D depictions became more and more sophisticated as artists began to integrate more mathematics into their art, specifically math about perspective and optics. One of the many influential mathematicians that influenced Renaissance art was Ibn al-Haytham’s Book of Optics. Much of his research and mathematical formulas allowed for greater accuracy and realism when depicting the 3D on 2D canvases.

 

Ibn al-Haytham and his Book of Optics
(http://www.famousinventors.org/alhazen)

            Ever since this early encounter, the relationship between mathematics and art has been inseparable. I had never realized how much mathematics went into portrayals of perspective and the creation of art pieces. The relationship between math and art is so close that when a revolution happens in one field, the other experiences a similar revolution. At the turn of the 19^th century mathematics began to view the world as having four dimensions (that of time). In turn, new art styles emerged that incorporated depictions of this fourth dimension. Cubism emerged as artists embraced the fourth dimension and depicted one scene on a canvas but fragmented the picture into many fragments taken from different perspectives and portrayed them all at once. Artists like Picasso and Jean Metzinger incorporated the fourth dimension into their works and used it as a tool to capture their subjects in 4D space and project this new perspective onto a 2D canvas.

 

Cubist painting by Jean Metzinger
(https://upload.wikimedia.org/wikipedia/en/5/58/Jean_Metzinger%2C_Le_go%C3%BBter%2C_Tea_Time%
2C_1911%2C_75.9_x_70.2_cm%2C_Philadelphia_Museum_of_Art.jpg)

            Art and mathematics have become so entwined that they very well may be inseparable. With each new advance in either field, the corresponding one also comes up with something new. Insights into this relationship are revealed by artists, scientists, and others who use both art and math in their work. Artists like M.C. Escher use tessellations in their works as mathematics invents new formulas to study this phenomenon and architects like Le Corbusier use the Golden Ratio of mathematics to pioneer modern architecture. Truly these fields are inseparable and each influence the other.

References

Abbott, E. (1953). Flatland (6th ed.). Princeton: Dover Publications.

Al-Khalili, J. (2015). In retrospect: Book of Optics. Nature, 518(7538), 164-165. http://dx.doi.org/10.1038/518164a

Henderson, L. (1984). The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion. Leonardo, 17(3), 205. http://dx.doi.org/10.2307/1575193

Smith, S. (2014). The Mathematical Art of M.C. Escher. Platonicrealms.com. Retrieved 16 April 2018, from http://platonicrealms.com/minitexts/Mathematical-Art-Of-M-C-Escher/

Theodor. (2011). The Fourth Dimension in Painting: Cubism and Futurism. The Peacock's Tail. Retrieved 16 April 2018, from https://pavlopoulos.wordpress.com/2011/03/19/painting-and-fourth-dimension-cubism-and-futurism/