*Abstract:* This is an expository lecture intended for a general audience.The term `albime' was coined by Jasbir Chahal (BYU, Provo) and refersto ALtitude-BIsector-MEdian. In a lecture during the ''Nationale Wiskunde Dagen" in 2005,F. van der Blij who retired as a mathematics professor from Utrecht University in 1988,discussed an elementary geometry problem: describe the triangles ABC whichhave integral sides, and moreover have the property that a bisector from vertex A, the median through vertex B, and the altitude through C, are concurrent. We call such ABC (rational) albime triangles.The problem turns out to have an amazing history, and the complete solutioninvolves a nice although elementary mixture of geometry, arithmetic, elliptic integrals, and a classical equidistribution result.