I am very interested in the various mathematical patterns
and ratios that show up in nature and can be used to make art realistic and
aesthetically pleasing. One of these patterns that Professor Vesna described
was the Fibonacci sequence. When I was little, my Grandpa showed me that
pine cones and sunflowers have Fibonacci patterns in them, so it was interesting
to see their relationship to the world of art.
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| The Fibonacci Sequence in a Plant |
The golden ratio, phi, was also interesting to learn about. Although
it is not widely used in math (compared to pi, or e), it has been used in arts
and architecture for thousands of years. Professor Vesna discussed how the
Parthenon was designed using the golden ratio so that it would be timelessly
aesthetically pleasing.
 |
| The Parthenon with the Golden Ratio |
The Parthenon itself is a work of art, and thus clearly
shows how mathematics can influence the artistic world. If the Parthenon was
designed without knowledge of the golden ratio, I doubt that it would be as
iconic and timeless. In the past, architects have needed to have some knowledge
of math, so that they could design proportional and aesthetically pleasing
buildings. I think it’s safe to say that this fact will continue into the future.
Flatland: A Romance of
Many Dimensions, by Edwin Abbott Abbott seems to be a very original
(although somewhat convoluted and outdated) piece of literature. I’ve never read
anything quite like it, as the author pretends to be a square and uses other
geometric figures to describe society.
M. C. Escher’s Waterfall
is another interesting application of mathematics in art. He uses two Penrose
triangles, which are physically impossible figures (and thus ignore the laws of
perspective) to draw a perpetual motion machine. Water flows from the base of a
waterfall to the top, without appearing to travel higher in elevation, and therefore abiding by the first law of conservation of energy.
 |
| Waterfall lithograph, 1961 |
Abbott, Edwin Abbott. Flatland: A Romance of Many Dimensions.
New York: Barnes & Noble, 1963. Print.
"Fibonacci in Nature."
Fibonacci in Nature. N.p., n.d. Web.
12 Apr. 2015.
"The Golden Section /
Golden Ratio - Phi 1.618: The Golden Number." Phi 1618 The Golden Number. N.p., 14 May 2012. Web. 12 Apr. 2015.
"The Mathematical Art of
M.C. Escher." The Mathematical Art
of M.C. Escher. N.p., n.d. Web. 12 Apr. 2015.
"Pics For The Parthenon
Golden Ratio." Pics For The
Parthenon Golden Ratio. N.p., n.d. Web. 12 Apr. 2015.
The
Story of 1. YouTube. YouTube, n.d. Web. 12 Apr.
2015.
Hi Thomas,
ReplyDeleteI also found M.C. Escher's artwork extremely fascinating, especially in regard to his application of mathematics--a discipline that has been traditionally characterized as wholly rational and logical--in order to create his impossible constructs. For example, I think it's so interesting that in the piece Waterfall that you mentioned, Escher managed to incorporate mathematically inspired elements such as geometrical polyhedrons and precise symmetry in order to form a paradoxical picture.