Abstract
Finding a point lying at one-kth of given segment is well-known plane geometry task. Restriction to Euclidean constructions using straightedge and compasses alone makes the problem more interesting and effort to find the shortest possible construction is even more challenging.
We demonstrate several Euclidean constructions of dissection of segment in given ratio (well-known as well as not-well-known constructions) and prove their correctness in this paper.