In triangle geometry, the Bernoulli quadrisection problem asks how to divide a given triangle into four equal-area pieces by two perpendicular lines. Its solution by Jacob Bernoulli was published in 1687. Leonhard Euler formulated a complete solution in 1779.
As Euler proved, in a scalene triangle, it is possible to find a subdivision of this form so that two of the four crossings of the lines and the triangle lie on the middle edge of the triangle, cutting off a triangular area from that edge and leaving the other three areas as quadrilaterals. It is also possible for some triangles to be subdivided differently, with two crossings on the shortest of the three edges; however, it is never possible for two crossings to lie on the longest edge. Among isosceles triangles, the one whose height at its apex is 8/9 of its base length is the only one with exactly two perpendicular quadrisections. One of the two uses the symmetry axis as one of the two perpendicular lines, while the other has two lines of slope
\pm1
\alpha
\alpha
In 2022, the first place in an Irish secondary school science competition, the Young Scientist and Technology Exhibition, went to a project by Aditya Joshi and Aditya Kumar using metaheuristic methods to find numerical solutions to the Bernoulli quadrisection problem.