Random Triangles and Polygons in the Plane

DOI10.1080/00029890.2019.1535735zbMath1410.52004arXiv1702.01027OpenAlexW2593205548MaRDI QIDQ3120222

Tom Needham, Gavin Stewart, Jason Cantarella, Clayton Shonkwiler

Publication date: 1 March 2019

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.01027

zbMATH Keywords

random triangleGrassmann manifold of 2-planesGrassmannian geometry of planar quadrilateralsGrassmannian geometry of trianglesmoduli space of unordered quadrilateralsplanar \(n\)-gons

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Grassmannians, Schubert varieties, flag manifolds (14M15) Curves in Euclidean and related spaces (53A04) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (3)

Hall's conjecture on extremal sets for random triangles ⋮ Spherical geometry and the least symmetric triangle ⋮ Triangle Inscribed-Triangle Picking

Cites Work

• Unnamed Item
• The symplectic geometry of closed equilateral random walks in 3-space
• The symplectic geometry of polygons in Euclidean space
• A metric on shape space with explicit geodesics
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• Polygon spaces and Grassmannians
• Embeddings of Gromov hyperbolic spaces
• A Lewis Carroll pillow problem: probability of an obtuse triangle
• Kähler structures on spaces of framed curves
• Random triangle theory with geometry and applications
• A flag representation for finite collections of subspaces of mixed dimensions
• Grassmannian Geometry of Scattering Amplitudes
• Probability Theory of Random Polygons from the Quaternionic Viewpoint
• A fast direct sampling algorithm for equilateral closed polygons
• Schubert Calculus
• The Historical Development of J. J. Sylvester's Four Point Problem
• Exact distributions for shapes of random triangles in convex sets
• There Are Three Times as Many Obtuse-Angled Triangles as There Are Acute-Angled Ones
• The Toric Geometry of Triangulated Polygons in Euclidean Space
• The expected total curvature of random polygons

This page was built for publication: Random Triangles and Polygons in the Plane