# Curve with ever increasing radius

by bobbobwhite
 P: 53 Cannot remember the name of a curve that begins with a lesser radius and tangents off into an ever increasing radius until it is almost a straight line. Very commonly used in art deco design. Thanks for your help.
 P: 53 You see it on the more complex mechanical drawing templates, which I don't have.
 PF Patron HW Helper Sci Advisor P: 4,082 Are you thinking of a spiral?
P: 53

## Curve with ever increasing radius

or not and this site won't let me draw it to show it to you. It starts like a spiral with a tighter curve but the second curve swings open eventually to almost a straight line as it progresses to infinity(becoming an nearly imperceptible curve as it progresses away from the first curve due its much larger and ever increasing radius). Perhaps I should ask the physics folks as this curve is commonly seen in astronomy.
 PF Patron HW Helper Sci Advisor P: 4,082 You might find it among http://local.wasp.uwa.edu.au/~pbourke/surfaces_curves/ http://xahlee.org/SpecialPlaneCurves...aneCurves.html Please post the answer to your question when you find it.
 Sci Advisor P: 2,347 He might mean the "hyperbolic spiral" http://mathworld.wolfram.com/HyperbolicSpiral.html which in polar coordinates has the equation $r \, \theta = a$, and which is asymptotic to $y=a$. But if so, "begins with a lesser radius" doesn't sound right. The more familiar logarithmic spiral http://mathworld.wolfram.com/LogarithmicSpiral.html $r = \exp(a \, \theta)$ has no such asymptote, and has the property that the curve intersects each ray infinitely often but makes the same angle each time it intersects a given ray. As for "commonly seen in astronomy", I guess he might mean the "parabolic spiral" http://mathworld.wolfram.com/FermatsSpiral.html $(r-a)^2 = 4 a \, k \, \theta$, which to some eyes vaguely resembles the arm of a spiral galaxy (but physicists know that these "arms" are to some extent optical illusions). Finally, it is possible he is confusing the clothoid or "Euler-Cornu spiral" http://mathworld.wolfram.com/CornuSpiral.html with the hyperbolic spiral.

 Related Discussions Introductory Physics Homework 2 Calculus & Beyond Homework 0 Special & General Relativity 9 Introductory Physics Homework 6 General Math 21