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Nature’s Frugal Beauty
By John Adam
Nature’s productions are shoestring operations, encumbered by the
constraints of three-dimensional space, the necessary relations among the
size of things, and an eccentric sense of frugality.
There is a formal system of thought for recognizing, classifying and
exploiting natural patterns.
It is called mathematics.
Ian Stewart has observed that mathematics helps us to organize and systemize our
ideas about patterns. In so doing, we not only admire and enjoy, but also draw
conclusions about the underlying principles that govern the world around us.
A rainbow is formed by
sunlight scattered in preferential
directions by near-spherical
raindrops. A related phenomenon is
that of the “glory,” a set of colored,
concentric rainbow-like rings that
can surround the shadow of an
airplane on a cloud below.
The beautiful circular arcs
known as halos, seen best in arctic
climes, are formed by the refraction
of sunlight through ice crystals of
various shapes in the upper
atmosphere. Colored splotches of
light known as sundogs, often seen
on both sides of the sun when high
cirrus clouds are present, are
similarly formed.
Branching patterns in trees, leaves, river
networks, lungs and blood vessels exhibit similar features.
No river, regardless of size, runs straight for more
than ten times its average width. As a river meanders,
it does the least work in turning, which then defines its probable form.
Whether formed in drying mud, tree bark, or
rapidly-cooling rock, cracks have their own
distinctive mathematical patterns.
The arrangement of leaves
around a stem, or seeds in a
sunflower or daisy face form
recurring numerical patterns,
studied since medieval times. The
spiral arrangement of seeds in the
daisy head is present in the sweeping
curve of the chambered nautilus
shell. The curl of a drying fern and
the rolled-up tail of a chameleon all
exhibit this type of spiral arc.
“There is much beauty in nature’s clues, and we can all recognize it
without any mathematical training . . . Mathematics is to nature as
Sherlock Holmes is to evidence.”
Ian Stewart, writing in Nature’s Numbers
John Adam is an Old Dominion professor of mathematics and statistics.
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