Three Closed Problems on the Jonah Triangle: Non-isosceles Fixed Points, Analytic Stability, and Kendall Latitude
Year: 2026
Type: article
Abstract: We resolve three open problems from the companion paper "The Jonah Triangle" (Zenodo, 2026). (1) We prove that every fixed triangle of the pedal map F_t with natural vertex correspondence is isosceles, via the equivalence P_t=O and a barycentric proof that O,I,N are collinear iff the triangle is isosceles. (2) We prove that F_t is real analytic on the interior of shape space, hence the local stable manifold at the Jonah triangle is analytic by the analytic stable manifold theorem. (3) We derive the explicit formula sin(phi) = sqrt(3)sin(theta)/(2-cos(theta)) for the Kendall-sphere latitude of isosceles triangles, yielding sin(phi_J) = 4sqrt(15)/19 exactly for the Jonah triangle. All proofs are exact and self-contained; no numerical verification is relied upon.
Authors: Schloss Jonah, Schloss Jonah
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225578522