Archimedean Spirals and Rational Approximation
Eric Mack • North Idaho College
Born out of the ancient and medieval question of how to match a stack of perfect fifths (`a_n = 1.5^n`) against a stack of perfect octaves (`b_n = 2^n`), we’ll explore the phenomena of emergent spiral behaviors in Christmas lights wrapped tightly around different-diameter trees, then flatten this helix into an Archimedean spiral for a 2D view, before finally relating the phenomena to continued fractions and rational approximation. Geogebra will be used for a visual aid.
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