Editing Conformal map (section)

===Maxwell's equations===
[[Maxwell's equations]] are preserved by [[Lorentz transformation]]s which form a group including circular and [[hyperbolic rotation]]s. The latter are  sometimes called Lorentz boosts to distinguish them from circular rotations. All these transformations are conformal since hyperbolic rotations preserve [[hyperbolic angle]], (called [[rapidity]]) and the other rotations preserve [[angle|circular angle]]. The introduction of translations in the [[Poincaré group]] again preserves angles. 

A larger group of conformal maps for relating solutions of Maxwell's equations was identified by [[Ebenezer Cunningham]] (1908) and [[Harry Bateman]] (1910). Their training at Cambridge University had given them facility with the [[method of image charges]] and associated methods of images for spheres and inversion. As recounted by Andrew Warwick (2003) ''Masters of Theory'':
<ref>{{cite book|last1=Warwick|first1=Andrew|title=Masters of theory : Cambridge and the rise of mathematical physics|url=https://archive.org/details/mastersoftheoryc0000warw|url-access=registration|date=2003|publisher=[[University of Chicago Press]]|pages=[https://archive.org/details/mastersoftheoryc0000warw/page/404 404–424]|isbn=978-0226873756}}</ref>

: Each four-dimensional solution could be inverted in a four-dimensional hyper-sphere of pseudo-radius <math>K</math> in order to produce a new solution.
Warwick highlights this "new theorem of relativity" as a Cambridge response to Einstein, and as founded on exercises using the method of inversion, such as found in [[James Hopwood Jeans]] textbook ''Mathematical Theory of Electricity and Magnetism''.