Curves103 of 113
Hyperbolic spiral
P. Nicolas, 1696; Pierre Varignon, 1704
Read the hyperbola xy = a in polar coordinates, as rθ = a, and the result is this spiral, which Pierre Varignon studied in 1704. Its turns close in on the centre without reaching it, and its outer arm flattens toward the line y = a. A spiral staircase seen along its axis shows the curve, and the staggered starts of a 400 m race are placed on one.
r = a/φ
On mathcurve.com as Spirale hyperbolique