Work

Cutting random triangles with random lines

Year: 2026

Type: article

Abstract: In this research we investigate randomly generated triangles partitioned with randomly generated lines which separates the triangle into 2 shapes. We calculate the expected value of the ratio of the areas of these 2 shapes.With Integrative geometry and elliptic parametrization We get that the answer is (5/8) * (𝛑^2 / 6 - 1).This answer is interesting because by observing quadrilaterals and triangles we somehow arrive at an answer that contains 𝛑, a seemingly unrelated constant.This research is the first step to a generalization where a formula is found not just for triangles but for any polygons.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.19984719

Authors: Gumberidze, Giorgi, Elizbarashvili, Vano, Chelidze, Giorgi

Institution: Kutaisi International University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7159868239

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