How to construct a regular polygon with 15 sides

To feed your curiosity, today we will look at a compass and straightedge construction of the regular polygon with 15 sides and we will show that there is a connection between this construction problem with the measuring liquid puzzle that we have learned from our previous post.

Measuring liquid puzzle

Today we will look at a brainteaser puzzle: "how to measure out exactly 1 liter of water using a 3-liter jug and a 5-liter jug." We will analyse this puzzle to see that, despite its innocent look, this puzzle has a close connection with the linear Diophantine equation.