from basic expressions to quarterionsa two dimensional shape can be simplified as a collection of points. the points can then be complex number represented as well as a well chosen origin for convenient point rotations. the shape is then effectively rotated. the creation of a rotating shape using complex numbers is quite interesting as well as useful. for example in robotics in real-time navigation, the CORDIC FAQ can serve as a super quick means of rotating a spacial image. a google search with keywords "complex number rotation" (no quotes) found the following diverse references For Kids: More Complex Makes Simple! http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/complex/cmplx.html Jim Lesurf is certainly having fun with rotating animations. Complex number - From Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Complex_number Complex Numbers, Trig & Vectors http://whyslopes.com/etc/ComplexNumbers Advanced: Using Quaternions to Represent Rotation By: Laura Downs http://www.genesis3d.com/~kdtop/Quaternions-UsingToRepresentRotation.htm quaternions are a kind of "3D" complex number and great to represent dynamic spacial operations such as cartesian coordinates for trajectory paths (think missile). Complex numbers and similarity constants http://www.math.okstate.edu/mathdept/dynamics/lecnotes/node30.html complex numbers generate sphinx figures and form a neat spiral known as a loxodrome CORDIC FAQ by Grant R. Griffin http://www.dspguru.com/info/faqs/cordic2.htm rotations are done using algorithm quick binary shifts. Cycloids http://www.cut-the-knot.com/pythagoras/cycloids.shtml the term cycloids is also used to refer to epicycloids and hypocycloids. Cycloids 
Epicycloids 
Hypocycloids 
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