In this article we describe how a group of third year mathematics students of the University of Rome who were following a mathematics education option explored some of the properties of hyperbolic plane geometry before preparing a unit on non-Euclidean geometry to be used with sixth-formers at the Liceo Virgilio, Rome. We recall here that the Mathematical Association considered the possibility of such work in its 1923 report on geometry [1]. Nowadays the report is associated with the three ‘stages’ of geometry teaching, A, B and C, but in fact it proposed two further stages. The fifth stage included non-Euclidean geometry both ‘for a few gifted specialists’ and also because it might interest ‘able boys who are not mathematical specialists’.