Art and Greek Geometry

February 2019’s topic of The GalleseumAcrylic Math’s FREE monthly art newsletter– is about Art and Greek Geometry. And, this is the corresponding Blog Post.

Kandinsky

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Blog Post

This Blog Post describes the relationship between art and Greek (i.e., classical) geometry. A future article will address fractal geometry. Geometry, from the Greek geo (land) and the Greek metria (measurement), is the branch of mathematics that focuses on objects on a plane. There are myriad objects, such as points, lines, circles, and cubes. And, there are two types of planes: two-dimensional planes and three-dimensional planes. Objects, such as circles and squares, are the domain of plane geometry; cubes and spheres are the domain of solid geometry. Geometric perspective is a way of displaying three-dimensional objects on a two-dimensional plane. Visual arts, such as drawing and painting display objects and use perspective and, therefore, are rooted in geometry. [1] [2]

History

Geometry dates back to antiquity. The Babylonians, the Chinese, the Egyptians, and the Indians all dwelt in geometry. But, Euclides, the Greek philosopher and mathematician, in a book titled The Elements of Geometry, set forth, in great detail, the foundations of modern geometry. Euclid dwelt in both plane and solid geometry. [2]
Throughout history, artists, consciously, or subconsciously, have used geometry for art design. Figure 1 (Black and Violet by Wassily Kandinsky. Public domain [3]) displays an obvious use of geometry in art composition.

Figure 1

And, oftentimes, in modern drawing textbooks, such as Drawing for the Absolute Beginner by Mark and Mary Willenbrink, the authors advise art students, to first use simple geometric shapes to compose drawings. [4]

Geometric Perspective

Geometric perspective, from the Latin perspicere (to see through) is a way of drawing a three-dimensional object on a two-dimensional surface. A one point perspective has one vanishing point. A two-point perspective has two vanishing points. And, a three-point perspective has three vanishing points.[5] Figure 2 (Types of Perspective. © Dr. 2019 Anthony Rodriguez) displays the three types of perspective.

Figure 2

Perspective has been used by artists from Before Christ. Figure 3 (The Healing of Thabitha by Masolino. Public domain [6]) displays the use of perspective.

Figure 3

Geometric Objects

Figures 4 (Landscape by Ivan Kliun. Public domain [7]), Figure 5 (Architectonics by Liubov Popova. Public domain. [8]), Figure 6 (Seated Woman by Maria Blanchard. Public domain. [9]), and Figure 7 (Geometric Composition by Georges Valmier. Public domain. [10]) display a few examples of the conscious or subconscious use of geometry in art composition.

Figure 4
Figure 5
Figure 6
Figure 7

Summary

Artists have long used geometric objects and perspective. This brief Blog Post presented but a few examples of such usage.

Endnotes

[1] Mathematics and art. (2018). From Wikipedia. URL: https://en.wikipedia.org/wiki/Mathematics_and_art

[2] History of geometry. (2019). From Wikipedia. URL: https://en.wikipedia.org/wiki/History_of_geometry

[3] Kandinsky, W. (1923). Black and violet. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Vasily_Kandinsky_-_Black_and_Violet.jpg

[4] Willenbrink, M. and Willenbrink, M. Drawing for the absolute beginner. Cincinnati, OH: North Light Books.

[5] Masolino. (1420s). The healing of Tabitha. From Wikimedia Commoms. URL: https://commons.wikimedia.org/wiki/File:Masolino_Brancacci_Chapel_01.jpg

[6] Perspective. (2018). From Wikipedia. URL: https://en.wikipedia.org/wiki/Perspective_(graphical)

[7] Kliun, I. (n.d.). Landscape. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Landscape_Racing_By.png

[8] Popova, L. (1916). Architectonics. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:1916_Popova_Die_bildliche_Architektonik_anagoria.JPG

[9] Blanchard, M. (1917). Seated Woman. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Femme_Assise_(Seated_Woman),_by_Maria_Blanchard,_Spanish,_c._1917,_oil_on_canvas_-_Meadows_Museum_-_Southern_Methodist_University_-_DSC05425.jpg

[10] Valmier, G. (1930). Geometric composition. From Wikimedia Commons. URL: https://commons.wikimedia.org/wiki/File:Georges_Valmier_geometric-composition-1930.jpg