Studies in Turbine Geometry I-The Concepts of Turbine Geometry

This paper is devoted to the creation oi the necessary concepts required for the building up of what promises to be an important extension of circle and sphere geometries with the help of a fruitful idea due to Prof. Edward Kasner-the TURBINE. I have, however, changed somewhat the significance of this term so that the two-dimensional turbine may have the same features as its confreres in higher space, and Kasner's turbine is here called a "semi-turbine", since two of them go to make up a turbine according to my terminology.