Tag Archives: complex

Apollonian gaskets and Descartes’ Theorem II

In a few previous posts I wrote about “kissing sets” of four mutually tangent circles, and the fact that their signed bends satisfy Descartes’ Theorem, (Remember that the signed bend of a circle is like the curvature , except that … Continue reading

Posted in geometry, pattern, pictures, recursion | Tagged , , , , , , , | 1 Comment

Mystery curve, animated

As a follow-on to my previous post, here’s an animation (17MB) showing how the “mystery curve” arises as a sum of circular motions: Recall that the equation for the curve is . The big blue circle corresponds to the term—it … Continue reading

Posted in complex numbers, geometry, programming | Tagged , , , , , , , | 6 Comments

Random cyclic curves

Princeton Press just sent me a review copy of a new book by Frank Farris called Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. It looks amazing and I’m super excited to read it. Apparently John Cook has been reading … Continue reading

Posted in complex numbers, geometry, programming | Tagged , , , , , | 24 Comments

Monday Math Madness #31

This week’s Monday Math Madness is a nice little problem involving complex exponentiation. Go check it out, and maybe win a prize!

Posted in challenges, complex numbers, links | Tagged , , , ,