Arcology

John Nash initiated the study of arcs in algebraic geometry in a quite unusual paper written in 1968, at the beginning of his long illness. This paper raised many interesting and still-open questions that can be investigated using elementary methods. The tone of the Nash article is discursive, and through a series of examples and comments it reports on "some interesting possible truths which were encountered."We also follow this approach and present the intricacies and beauties of this subject using concrete examples. In addition we discuss some recent results and unsolved problems that are accessible to undergraduates.