Symmetry - CAS

Symmetry Tom Suk Other symmetries ? Symmetry to skew f(x,y)=f(x+ky,y) Terminological remark:

symmetry to skew skew symmetry f(x,y)= f(y,x) Unusual symmetries Projective symmetry a0 a1 x a2 y x c0 c1 x c2 y

b0 b1 x b2 y y c0 c1 x c2 y Unusual symmetries Symmetry to Mbius transform projection of sphere to plane Complex plane z x yi

az b z cz d Real plane ac( x 2 y 2 ) (ad bc) x bd x c 2 ( x 2 y 2 ) 2cdx d 2

(ad bc) y y 2 2 c ( x y 2 ) 2cdx d 2 Unusual symmetries Symmetry to Mbius transform