calculus-2014-05-21

DRAFT c○ 2014 Julian Fleron, Philip Hotchkiss, Volker Ecke, Christine von Renesse
3. Integration and Art
The idea of Riemann sums seems to be present in many different areas and objects. Look for
instance at the church Hallgrímskirkja in Reykjavik, see Figure 5.4.
52. Where do you see a connection between Riemann sums and the church? Explain.
Figure 5.4. Church Hallgrímskirkja in Reykjavik, Iceland
Robert Smithson (American Artist; 1938 - 1973) was part of the minimalism movement in
which the artist uses minimal forms and concepts to expose more of the essence of a piece of art.
Walker Art Center (http://www.walkerart.org) describes the piece as follows:
Leaning Strata is the visual manifestation of an extensive set of investigations Smithson was
conducting during the mid-1960s, which included geology, astronomy, perspective, mapping, and the
nature of time and matter. The title suggests a geological configuration. The stepping of the elements
in the form, if continued according to the system established (i.e., moving at a regular rate away from
the implied center), would conclude in a spiral.
53. Explain how the “Leaning Strata” by Robert Smithson, see Figure 5.5, is similar and different
from a Riemann sum.
The area under the graph of a function between a and b is called a definite integral and was
denoted by Riemann as
∫ b
a
f(x)dx.
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