foci of bicircular quartics
 | this activity is a page of geogebra-book elliptic functions & bicircular quartics & . . .(07.08.2023) |
07.08.2023
Four different points in the complex plane can always be mapped by a suitable Möbius transformation to 4 points in normal form with . Depending on the order of the points the complex double ratio . Absolutely invariant is .- 4 distinct points are the foci of confocal bicircular quartics, if their absolute invariant is real.
- If is real and non-negative, the foci are concyclic.
- If is real and not positiv, then the foci in 2 pairs lie mirror-inverted on 2 orthogonal circles.
- If , then both are true: the foci lie harmonically.