Revisiting the quadrisection problem of Jacob Bernoulli

2016/11/21 by Carl Eberhart, Eberhart, Carl
Mathematics · #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #math.HO

paper · pdf · doi:10.48550/arxiv.1611.06658

arxiv created 2016/11/21 · openalex publication_date 2016/11/21 · arxiv updated 2016/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two perpendicular segments which divide a given triangle into 4 regions of equal area is called a quadrisection of the triangle. Leonhard Euler proved in 1779 that every scalene triangle has a quadrisection with its triangular part on the middle leg. We provide a complete description of the quadrisections of a triangle. For example, there is only one isosceles triangle which has exactly two quadrisections.

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