A note on a certain property of a family of curves

Albert Wertheimer
1934 Bulletin of the American Mathematical Society  
1. Introduction. In studying methods of constructing alignment charts for sets of empirical curves, it was found necessary to consider a certain property of the curves which we will call the closure property. Let Ci, C 2 , and C 3 be three plane curves such that C 2 lies between C\ and C 3 ; take any point P on C 2 and make the following sequence of projections. Project P vertically on Cz into P 3 , project P 3 horizontally on C\ into Pi, project Pi vertically on C 2 into P 2 , project P 2
more » ... , project P 2 horizontally on Cz into P 3 , project Pi vertically on C\ into P{, finally project Pi on C 2 into P'. If the points P and P' coincide for all points on C 2 , the three curves are said to have the closure property.
doi:10.1090/s0002-9904-1934-05805-1 fatcat:vayoufx7ijbqpmq6g3p6b6fl2u