The Patterson cylindrical, a new projection designed for general-purpose mapmaking, is an alternative to other cylindrical projections. It is positioned between the Plate Carrée projection, which has a 1:2 aspect ratio, and the Miller 1 projection, which excessively exaggerates the size of polar areas. The Patterson cylindrical balances polar exaggeration against maintaining the familiar shape of continents and has a compact height-to-width aspect ratio. Creating the projection started with a graphical template made in Flex Projector that served as a guide for developing the polynomial equations, which are introduced in this article. The reference source code is available in the Java Map Projection Library.