Rational Quintics Autopolar with Respect to a Finite Number of Conics |
Common terms and phrases
Accordingly acnodes admit linear determination asymptotes admit autopolar with respect bitangent centroid circular points collinear completely symmetric quintic conic is established conics with respect coordinates curve cuspidal tangents cusps and three cyclo-symmetric quintic cyclo-symmetric rational double points equilateral triangle FINITE NUMBER four conics Hence infinity of cyclo-symmetric inflexional tangents inscribed circle intermediate quartic Inverse of quintic lemma line locus located linearly Note figure noting twenty conditions NUMBER OF CONICS obtain the quartic point at infinity point locus point of inflection points of inflexion Polar reciprocation converts possible conics quadratic transformation quintic about circle quintic becomes quintic is autopolar quintic pass quintic referred quintic with respect quintic with three RATIONAL QUINTICS AUTOPOLAR rational self-dual quintic reciprocation with respect respect to conics rhamphoid cusp second triangle single infinity sixty degrees three conics three crunodes three cusps tri-rhamphoid-cuspidal quintic tri-rhamphoidal quintic triangle of reference triangle RST unit point vertices