Geodesic
A Spatial Version of the Theorem of the Angle of Circumference
Journal for geometry and graphics, Tome 23 (2019) no. 2, pp. 147-156.

Voir la notice de l'article provenant de la source Heldermann Verlag

The presented spatial version of the theorem of the angle of circumference in three-dimensional Euclidean space deals with pairs of planes $(\epsilon,\phi)$ passing through two skew straight lines $e$ and $f$, respectively, such that the angle $\alpha$ enclosed by $\epsilon$ and $\phi$ is constant. It turns out that the set of intersection lines $r = \eps\cap\phi$ is a quartic ruled surface $\Phi$ with $e\cup f$ being its double curve. We analyse the properties of $\Phi$ and discuss the special cases showing up for special values of some shape parameters such as the slope of $e$ and $f$ (with respect to a fixed plane) or the angle $\alpha$.
Classification : 51N20, 51N35, 51M30, 14J16
Mots-clés : Ruled surface, angle of circumference, quartic ruled surface, Thaloid, isoptic surface 
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     author = {G. Glaeser and B. Odehnal and H. Stachel },
     title = {A {Spatial} {Version} of the {Theorem} of the {Angle} of {Circumference}},
     journal = {Journal for geometry and graphics},
     pages = {147--156},
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G. Glaeser; B. Odehnal; H. Stachel . A Spatial Version of the Theorem of the Angle of Circumference. Journal for geometry and graphics, Tome 23 (2019) no. 2, pp. 147-156. http://geodesic.mathdoc.fr/item/JGG_2019_23_2_JGG_2019_23_2_a0/