The minor change in the transformation representation changes radically its behaviour. Lines XY (Y = f(X)) do not pass through a fixed point any more. Instead, they are tangent to some curve which is rational of degree seven (quotient of two polynomials of degree at most seven).

- Besides, one can easily see that (f) restricted on line t

- On line t

- These two remarks suffice to construct projectivity (f) through a recipe on the vertices of square ADEG. It is the unique projectivity mapping A-->G, E--> and G-->E, D-->A.

-The connection between the two maps can be easily seen by multiplying the matrices A'*A

representing the reflexion on the x-axis. Thus A' = W*A, where W is an isometry of the circle. One could generalize by taking W to be an arbitrary isometry of the circle.

A slightly modified configuration, producing a hyperbola from an ellipse is studied in HyperbolaFromEllipse.html .

HyperbolaGeneration.html

ParabolaProjectFromCircle.html

Projectivity.html

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