Discussing the geometry of ellipses and hyperbolae
on the sphere we recall here these are the curves which correspond to position lines based on the constant sum or the absolute value of difference of distances from two fixed points.
Rates of root growth are given by the slopes of the hyperbolae
(Eqn 1, Fig.
The hyperbolic curves for mixing of two magmas can be readily extended to three sources by calculating the three hyperbolae
that represent the combination of any two sources and interpolating between these curves (Fig.
Anyone interested in pursuing further aspects of paper folding could investigate folding ellipses and hyperbolae
by using circular paper (Yates, 1943) or turning to any of: Hilton and Pedersen (1983), (1993); Polster (2004); Froemke and Grossman (1988); to investigate a technique that allows the approximation of any rational angle with simple sequences of angle bisections.
That means that it is one which it is very difficult to tell without intrusive hyperbolae
The Wholer's curves are pseudo hyperbolae
displaying a horizontal asymptote corresponding to the endurance limit.
As regards the "inches" expression, it appears from Adagia 406 ("Latum vnguem, ac similes hyperbolae
prouerbiales," ASD 2, 1) that Folly owes it to Plautus, Aulularia 56-57, "Si tu hercle ex isthoc loco digitum transuersum aut vnguem latum excesseris .
5 resemble a family of hyperbolae
approaching a common asymptote that is curved and concave to the time axis.