school, but he was, and still is,
admired by mathematicians
for his amazing visualizations
of mathematical principles.
Escher’s interest in math-
ematical patterns began
around 1936, after viewing the
Alhambra Palace’s collection
of Islamic art (see above). He
was fascinated with structures
represented in plane and pro-
jective geometry—both Euclid-
ean and non-Euclidean geome-
try (for more information, see
“Geometry and Trigonome-
try”)—not only using the
geometry of space, but also
the logic of space. For exam-
ple, he used the idea of tessel-
lations, or arrangements of
closed shapes (usually poly-
gons or similar regular
shapes, like those used on a
tiled walkway) that cover the
entire plane without overlaps
or gaps. Not only did he use
regular tessellation shapes,
but also irregular ones, mak-
ing the shapes change and
interact with each other. He
also made many of his amaz-
ing patterns by taking a basic
pattern and either distorting it and/or applying what geometers call reflections, trans-
lations, and rotations. For many other mathematical patterns, he used regular solids,
Platonic solids, and visual aspects of topology in his work. (For more about Platonic
solids, see “Geometry and Trigonometry.”)
What are mathematical sculptures?
Mathematical sculptures are sculptures that represent some mathematical design.
They are usually a geometrical figure and can be made of materials such as metal,
wood, concrete, or stone shaped into squares, triangles, cylinders, specific curves, rec- 377
MATH IN THE HUMANITIES
Using Vedic squares, Islamic artisans could create designs based on
geometric shapes formed by the arrangements of certain numbers.