There is reason to believe that van Gogh
actually played with non-Euclidean spaces in his paintings, in particular,
the painting of the Room at Arles. Patrick Heelan’s article Toward a
New Analysis of the Pictorial Space of Vincent Van Gogh states the
possibility of van Gogh’s use of non-Euclidean space in the Amsterdam
version of this painting. He says:
“When the Amsterdam painting is viewed at about arm’s length, or at the
distance at which the artist would have been working at his easel, one
receives an overwhelming impression of realism. One must, however, look at
the full-sized painting, not a smaller reproduction. An analysis of the
actual forms as represented in pictorial space by van Gogh reveals strange
incongruities vis-a-vis Euclidean anticipations. A tracing of the
perspective lines in the painting shows that he maintained neither the fixed
viewpoint nor the fixed eye-level necessary for a conventional
representation of Euclidean space; even single objects have multiple
convergence points.”
