Many people don't realize that what we now call "algorithm design"
actually dates back to the ancient Greeks! Of course, if you think
about it, there's always the "Euclidean Algorithm". A more dubious
example might be Theseus's use of a ball of string to solve the
"Labyrinth Problem". (Google "Theseus, Labyrinth, string".)
Solutions to this problem got a lot less dubious after graph theory
was invited, since a graph turns out to be a good way of representing
a maze mathematically. We will examine the classical solutions to
this problem, and then throw in a twist --- a Twisted Painting Machine
that puts restrictions on which paths we can take to explore the maze.
Applications to sewing may also appear, depending on the presence of
audience interest and string.