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arXiv · 1611.06658

Revisiting the quadrisection problem of Jacob Bernoulli

Carl Eberhart
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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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Carl Eberhart. 2016-11-21. Revisiting the quadrisection problem of Jacob Bernoulli. https://arxiv.org/abs/1611.06658

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