From the 1 of 11 linked papers with an AI index.
11 papers
Joining Two Pairs of Planar Points by Disjoint Arcs: The Sharp Length Bound
George M. Georgiou
Problem F16 of Croft, Falconer, and Guy asks for the least worst-case length needed to join prescribed pairs of points by pairwise disjoint planar arcs, when the distance within ea…
Congruent Triangular Faces, Reflections Allowed: Universal Realization and the Minimum Face Count in Problem B22
George M. Georgiou
Problem B22 in Unsolved Problems in Geometry asks which triangles occur as the common face of a convex polyhedron, how many copies are needed, and how they may be arranged. We sett…
Five-Point Hyperbolas on Power Curves and Near Lamé-Oval Vertices
George M. Georgiou
Problem A33 of Croft--Falconer--Guy records Reznick's question about infinite plane sets for which every five-point subset determines an ellipse or, respectively, a hyperbola, and…
Straightedge-and-Compass Constructibility of the Reciprocal--th-Power Law
George M. Georgiou
The paper determines that a straightedge‑and‑compass construction for the reciprocal‑k‑th‑power relation 1/c^k = 1/a^k + 1/b^k exists exactly when k is a power of two, providing ex…
Reciprocal-Polar Linearization and Two Conic Constructions for the Cone Projection
George M. Georgiou
Let $$ f_R(x)=\frac{x}{1+\norm{x}/R},\qquad R>0, $$ be the radial cone projection of the plane onto the open disk $\DR=\{x:\norm{x}<R\}$. Previous work established the Self-Directr…
Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling
George Georgiou
We determine the type-A Weyl anomaly coefficient , associated with the intrinsic scalar curvature of the defect, for the class of holographically realised co-dimension two defec…