A common algorithm taught at many universities for triangulating a simple polygon is based on partitioning the input polygon into monotone pieces, which are easy to triangulate. The method is described on Wikipedia (https://www.wikiwand.com/en/Polygon_triangulation#/Using_monotone_polygons), lecture notes can also easily be found with a web search.
Yet despite the algorithm's popularity, I was not able to trace the original authors of the method. Could someone link me to the original paper, if it exists?
The original paper seems to be "Triangulating a simple polygon" by Michael R.Garey,David S.Johnson, Franco P.Preparata, and Robert E.Tarjan from 1978. They mention in this work that the two groups (the third author (a) and the rest (b)) obtained this result at the same time. This source is also referenced by another paper, namely "An overview of triangulation algorithms for simple polygons". (In the comments @CyclotomicField references to a table that shows these names as well.)