The basic ideas of the theory of manifolds is illustrated using elementary geometry. (MM)

Article gives a brief history and suggestions for the proof of the theorem that of all plane figures with a common perimeter, the circle has the maximum area. (RS)

Criteria for a reasonable axiomatic system are discussed. A discussion of the historical attempts to prove the independence of Euclids parallel postulate introduces non-Euclidean geometries. Poincare's model for a non-Euclidean geometry is defined and analyzed. (LS)