M.C. Escher was an artist during the early to mid 1900's that primarily focused on woodcuts and lithographs that had a small contribution the world in mathematics. His most famous being the lithograph Print Gallery in 1956. However, the focus of this thesis is on his works that exhibit characteristics found in the properties of self-similar sets of fractal geometry and properties of projective geometry. The works include two woodcuts, that exhibit self-similar sets, and three lithographs, all of which use projective geometry to create optical illusions. Mathematically speaking, in fractal geometry, Hausdorff dimension is discussed using multiple examples that are also self-similar sets. Following, projective geometry is discussed providing the axioms and function of projectivities. Lastly, the connections between these two subjects and Escher's art are explored as to how extensive each of the properties are exhibited in the woodcuts and lithographs.
Trontz, Adam J., "Similarly Intriguing and Perspectively Odd: Fractal and Projective Geometry Explored in M.C. Escher's Art" (2012). Senior Independent Study Theses. Paper 932.
fractals, projectivities, escher
Bachelor of Arts
Senior Independent Study Thesis
© Copyright 2012 Adam J. Trontz