Tuesday, April 26, 2005


I have had a fondness for curves as far back as I can remember (Yikes! What's that white goo?!). A curve can be defined thus :

In topology, a curve is a one-dimensional continuum.

In analytic geometry, a curve is continuous map from a one-dimensional space to an n-dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve.

There is nothing more exhilarating than matching a naturally occurring phenomenom with a one-line mathematical function. And, dear readers, it is in the spirit of sharing that I present some recent revelations I have had.

The is the bean curve, a variant of the quartic curve. Or a poker table.

A whirl is constructed by nesting a sequence of polygons (each having the same number of sides), each slightly smaller and rotated relative to the previous one. It also resembles my sphincter after an all-in bluff raise.

A butterfly curve is a sextic plane curve. Think all-in bluff raise.

The division of the Fresnel integrals of a Cornu spiral yields the above, or my bankroll as a function of time.

The elliptic logarithm is a generalization of integrals of the form (t²+at). Also a good depiction of my sphincter after opponent folds to my all-in bluff raise.

And finally, the curve that needs no introduction :

The fish curve is a special case of the ellipse negative pedal curve.