## Projective rotations

Here we continue the discussion initiated in TriangleProjectivitiesPlay.html - [8]. Start with a point A1 on the outer conic e''(x) and draw tangents to the inner one e'(x). The second intersection points on these tangents with e''(x) form a triangle A1B1C1 which is simultaneously inscribed in e''(x) and circumscribed in e'(x).

All the triangles constructed in this way have the same trilinear polar L(x) w.r. to x. They are simply the images of the other equilateral triangles inscribed in the same circle with the original one A0B0C0. Thus they correspond to a sort of projective rotations of triangle ABC about the point x. Notice the locus of intersection points (like points C', B') of tangents at vertices A1, B1, C1 which is a conic c1 belonging to the family of conics generated by e'(x) and e''(x).
The term projective rotation is suggested from the fact that we build projectivities of the form Ht = H*Rt, which are compositions of H and a usual rotation Rt by an angle (t) about M0. Thus Ht*H-1 is conjugate to a usual rotation.

CircumcircleConjugate.html
CrossRatio.html
CrossRatio0.html
CrossRatioLines.html
GoodParametrization.html
Harmonic.html
Harmonic_Bundle.html
HomographicRelation.html
HomographicRelationExample.html
IncircleConjugate.html
Pascal.html
PascalOnTriangles.html
ProjectivityFixingVertices.html
Steiner_Ellipse.html
TriangleCircumconics.html
TriangleCircumconics2.html
TriangleProjectivitiesPlay.html
TrilinearPolar.html