Minimum Area Venn Diagrams Whose Curves Are Polyominoes

Abstract

While working at the Berlin Academy, the renowned Swiss mathematician Leonard Euler was asked to tutor Frederick the Great's niece, the of Anhalt-Dessau, in all matters of natural science and philosophy [17]. Euler's tutelage of the princess continued from 1760 to 1762 and culminated in the publishing of the popular and widely-translated Letters to a German Princess [9]. In the letters, Euler eloquently wrote about diverse topics ranging from why the sky was blue to free will and deter minism. In his lesson on categorical propositions and syllogisms, Euler used diagrams com prised of overlapping circles; these diagrams became known as Eulerian circles, or simply Euler diagrams. In an Euler diagram, a proposition's classes are represented as circles whose overlap depends on the relationship established by the proposition. For example, the propositions