Self-affine convex quadrangles are already completely characterized for the particular case that the underlying dissection is a so-called glass-cut dissection [14]. This is explained and …

Oct 15, 2025 · Clearly, for every choice of \ (0< \alpha< \beta < 1\), \ (Q (\alpha ,\beta )\) describes a unique affine type of convex quadrangles, and all non-trapezoidal convex quadrangles are …

Jun 7, 2020 · Convex quadrangles. Ptolemy's theorem (cf. Ptolemeus theorem): For any point $ P $ in the plane of a triangle $ ABC $ the inequality $$ AB \cdot CP + BC \cdot AP \geq AC \cdot …

Let P = A1A2A3A4 and P 0 = B1B2B3B4 be two convex quadrangles in the plane, and let O be one of their common points di erent from the vertices of P 0. Denote by `i the line OBi, and …

Suppose two convex quadrangles in the plane $P$ and $P'$, share a point $O$ such that, for every line $l$ trough $O$, the segment along which $l$ and $P$ meet is longer then the …

Jan 9, 2023 · The paper is devoted to some extremal problems for convex polygons on the Euclidean plane, related to the concept of self Chebyshev radius for the polygon boundary. …

Feb 24, 2025 · If a convex quadrangle Q is dissected into three convex quadrangles Q1, Q2 and Q3, but not based on a glass-cut dissection, every dissecting line segment starting from the …

1 Introduction These are notes to Math 461, a course in plane geometry I sometimes teach at the University of Wisconsin. Students who take this course have com-pleted the calculus …

Apr 18, 2024 · ll convex quadrangles are 5-self-affine. This goes back o Attila P ́or, see [7, Proposition 1]. There exist self-affine convex pentagons [7, Proposition 4], but the regular …

Abstract. The paper is devoted to some extremal problems for convex polygons on the Euclidean plane, related to the concept of self Chebyshev radius for the polygon boundary. We consider …