Year: 2017
Type: preprint
Abstract: We extend the notion of triangle to "imaginary triangles" with complex valued sides and angles, and parametrize families of such triangles by plane algebraic curves. We study in detail families of triangles with two commensurable angles, and apply the theory of plane Cremona transformations to find "Pythagorean theorems" for them, which are interpreted as the implicit equations of their parametrizing curves.
Source: arXiv (Cornell University)
Author: Koshkin, Sergiy
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2775922765