Möbius transformations (also called linear fractional transformations) are maps from the complex plane to itself of the form

\[

f(z) = \frac{a z + b}{c z + d}

\]

where \(a, b, c, d \in \mathbf{C}\) and \(a d – b c \neq 0\). This definition extends to functions on the Riemann sphere, where the geometry of such transformations becomes more apparent. The following short video shows off a remarkable correspondence between symmetries of the sphere and Möbius transformations.

### Tags

algorithms communication complexity computational complexity cooking counterexamples cryptography dropbox emacs essays geometry hikes iPad LaTeX lectures linear algebra logic M3A M32A M32AH M32B M32BH M61 M115AH M131A M167 number theory online algorithms pedagogy physics PIC10A pictures probabilistic method probability puzzles python recipes set theory stable marriage streaming algorithms videos### Archives

- January 2017
- November 2016
- January 2016
- December 2015
- November 2015
- June 2015
- May 2015
- April 2015
- March 2015
- February 2015
- January 2015
- November 2014
- October 2014
- September 2014
- August 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012