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Logarithmic Spirals
Image Credit: M101 -
NASA,
ESA,
CFHT, NOAO;
Typhoon Rammasun -
MODIS,
NASA
Comparison: Lawrence Anderson-Huang (Ritter
Astrophysical Obs., Univ. Toledo)
Explanation: Uncomfortably close
Typhoon Rammasun (right) and 25 million light-year distant
galaxy M101 don't seem to have much in common. For starters, Rammasun
was only a thousand kilometers or so across while M101 (aka the Pinwheel
Galaxy) spans about 170,000 light-years, making them vastly dissimilar in
scale, not to mention the different physical environments that control
their
formation and
development. But they do look amazingly alike: each with arms
exhibiting the shape of a simple and beautiful mathematical curve known as
a
logarithmic spiral, a spiral whose separation grows in a
geometric way with increasing distance from the center. Also known as
the
equiangular spiral, growth spiral, and Bernoulli's spiral or
spira mirabilis, this curve's
rich properties have fascinated
mathematicians since its discovery by 17th century philosopher
Descartes. Intriguingly, this abstract shape is much more abundant in
nature than suggested by the striking visual comparison above. For
example, logarithmic spirals can also describe the tracks of subatomic
particles in a
bubble chamber, the arrangement of
sunflower seeds and, of course,
cauliflower.
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