Dr. Robert Jacobson
Roger Williams University
22 March 2016
Follow along on your device at this address.
where
and
real numbers, and .
are ordinary
The number is called the real part while is called the imaginary part.
Every real number is also a complex number.
Addition:
Multiplication:
"Complexification" of functions:
In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R.
Go check out this other guy's math talk.
Circle Limit III, woodcut, 1959
Upper Half Plan Limit III
It's on Amazon: http://amzn.com/1568814526.
Yellow Fiji Leather Coral
B. de Smit and H. W. Lenstra Jr.
Notices of the AMS, volume 50, number 4, pages 446-451, 2007.
De-Escherization
De-Escherization
"The map \(h(w)\) is given by the easy formula \(h(w)=w^{(2\pi i + \log 256)/(2\pi i)}\)."
Point on sphere to point on plane:
Point on plane to point on sphere: