From the legendary Delian problem in
antiquity to modern freeway construction, spirals have attracted great
mathematical talent. Among the more famous are Archimedes,
Descartes, Bernoulli, Euler, and Fermat, but there are many more whose
work has enormously influenced pure mathematics, science and
engineering.
The name
spiral, where a curve winds outward from a fixed
point, has been extended to curves where the tracing point moves
alternately toward and away from the pole, the so-called
sinusoidal
type. We find Cayley's Sextic, Tschirnhausen's Cubic, and
Lituus' shepherd's (or a bishop's) crook. Maclaurin, best known
for his
work on series, discusses spirals in
Harmonia Mensurarum (1722).
We find parabolic spirals. In architecture there is the
Ionic capital on a column. In nature, the spiraled chambered
nautilus is associated with the Golden Ratio, which again is associated
with the Fibonacci Sequence.
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