Gelfand's Problem and Poncelet's closure theorem

Part of the beauty of mathematics is in discovering that two very dissimilar problems have, in fact, the same underlying mechanisms. This paper will describe the relations between two problems that have this property. These problems are Poncelet's closure theorem and Gelfand's question. The first of these is a theorem about tangents to conic sections, and the second is a series of questions about the first digit of powers of integers. The relations between both problems is not a new discovery, it is in fact the subject of a paper by J. L. King. This paper was the starting point of this present work. The aim of this thesis is to make the relations given by King more explicit, and to actually answer the questions posed by Gelfand.