[1] Line PA

[2] Line (e) is the polar of the Fregier point F

That H is a homography can be seen by reducing it to the product of two reflexions at two lines passing through P and forming there an angle of half omega. This kind of homography was studied in ReflexionOnConics.html .

Take A

Notice that for Y = H(X) and X on the conic (c) the line XY is tangent to member of the family of conics generated by (c) and (e). Thus, by selecting omega to be of the form pi/n, where n a natural number n>2, we easily construct examples of polygons inscribed in (c) and circumscribing another conic (c') (see Poncelet.html ).

FregierPolar.html

InvolutiveHomography.html

Poncelet.html

ReflexionOnConics.html

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