Cutting random triangles with random lines

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 (19/32) * (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.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-02
DOI
https://doi.org/10.5281/zenodo.19984720
Primary Topic
Point processes and geometric inequalities
Type
article
Field-Weighted Citation Impact
0.00
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article

Cutting random triangles with random lines

Giorgi Gumberidze, Giorgi Chelidze, Vano Elizbarashvili
Zenodo (CERN European Organization for Nuclear Research)
Point processes and geometric inequalities
article

Cutting random triangles with random lines

Giorgi Gumberidze, Giorgi Chelidze, Vano Elizbarashvili
article en

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 (19/32) * (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.

Zenodo (CERN European Organization for Nuclear Research)
Kutaisi International University (GE)
Openalex Percentile: Top 4%
Point processes and geometric inequalities
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