- Phantom Graphs
- Background and low degree polynomials
- Duals: Functions that are PGs of each other when rotated
- Phantom Graph of ellipse is hyperbola (& v.v.)
- Phantom Graph of hyperbola
- Exp, cosine, cosh, sin & sinh are all connected
- Cosine & cosh are PG duals
- Cosh (hyperbolic) and Cos are dual PGs.
- Phantom Graph sine(x)
- Phantom Graph of 1/(1+x^2)
- Phantom Graph of 1/(1-x^2)
- Phantom Graph of 2x^2/(x^2+1)
- Phantom Graph 2x^2/(x^2-1)
- Phantom Graph x^4/(1+x^2)
- Phantom Graph x^4/(1-x^2)
- Phantom Graph (x^2-1)^2
- Phantom Graph (x^2+1)^2
- Phantom Graph cos(x^2/2)
- Phantom Graph cosh(x^2/2)

- Exp and sinh: similar but not duals
- Howard K.Fehr (1951)!!
- Philip Lloyd of New Zealand. All phantom graphs in this chapter come from his notes.
- Some Famous Curves
- Phantom Graph Witch of Agnesi
- Phantom Graph Cissoid of Diocles
- Phantom Graph Devil's Curve
- Phantom Graph Tschirnhaus's Cubic
- Phantom Graph Conchoid de Sluze
- Phantom Graph Figure Eight
- Phantom Graph Trisectrix of Maclaurin
- Phantom Graph Serpentine
- Phantom Graph Pear-shaped Quartic
- Phantom Graphs Newton's Diverging Parabolas
- Phantom Graph Kampyle of Eudoxus
- Phantom Graph Strophoid