5 citations · 16 across the 7 of their papers we have counts for
7 papers
The Simplest Flexible Cross-Polytopes
Hellmuth Stachel
According to R. Bricard there exist three types of flexible octahedra. The octahedra of Type 3 are unsymmetric and admit two flat poses. With regard to higher-dimensional analogues…
Geometric analysis of Bennett's spherical 8-bar linkage and its spatial counterpart
Hellmuth Stachel
We provide a geometric approach to two combinatorically symmmetric overconstrained spatial linkages. Both contain eight bodies and twelve revolute joints and collapse in aligned po…
On the Motion of Billiards in Ellipses
H. Stachel
For billiards in an ellipse with an ellipse as caustic, there exist canonical coordinates such that the billiard transformation from vertex to vertex is equivalent to a shift of co…
The Geometry of Billiards in Ellipses and their Poncelet Grids
H. Stachel
The goal of this paper is an analysis of the geometry of billiards in ellipses, based on properties of confocal central conics. The extended sides of the billiards meet at points w…
Isometric Billiards in Ellipses and Focal Billiards in Ellipsoids
H. Stachel
Billiards in ellipses have a confocal ellipse or hyperbola as caustic. The goal of this paper is to prove that for each billiard of one type there exists an isometric counterpart o…
Area-Invariant Pedal-Like Curves Derived from the Ellipse
Dan Reznik, Ronaldo Garcia, Hellmuth Stachel
We study six pedal-like curves associated with the ellipse which are area-invariant for pedal points lying on one of two shapes: (i) a circle concentric with the ellipse, or (ii) t…
Steiner's Hat: a Constant-Area Deltoid Associated with the Ellipse
Ronaldo Garcia, Dan Reznik, Hellmuth Stachel +1
The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary point M is a 3-cusp closed-curve which is the affine image of the Steiner Deltoid. Over all M the family ha…