Geodesic
Singular Fregier Conics in Non-Euclidean Geometry
Journal for geometry and graphics, Tome 21 (2017) no. 2, pp. 201-208 Cet article a éte moissonné depuis la source Heldermann Verlag

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The hypotenuses of all right triangles inscribed into a fixed conic C with fixed right-angle vertex p are incident with the Fr�gier point f to p and C. As p varies on the conic, the locus of the Fr�gier point is, in general, a conic as well. We study conics C whose Fr�gier locus is singular in Euclidean, elliptic and hyperbolic geometry. The richest variety of conics with this property is obtained in hyperbolic plane while in elliptic geometry only three families of conics have a singular Fr�gier locus.
Classification : 51M04, 51M09, 51N35
Mots-clés : Fregier point, Fregier conic, Thales' theorem, hyperbolic geometry, elliptic geometry, singular conic 
@article{JGG_2017_21_2_JGG_2017_21_2_a5,
     author = {H.-P. Schroecker },
     title = {Singular {Fregier} {Conics} in {Non-Euclidean} {Geometry}},
     journal = {Journal for geometry and graphics},
     pages = {201--208},
     year = {2017},
     volume = {21},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2017_21_2_JGG_2017_21_2_a5/}
}
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H.-P. Schroecker . Singular Fregier Conics in Non-Euclidean Geometry. Journal for geometry and graphics, Tome 21 (2017) no. 2, pp. 201-208. http://geodesic.mathdoc.fr/item/JGG_2017_21_2_JGG_2017_21_2_a5/