A non-standard approach to the Euclidean study of plane curves (Q1380846)

Using Nelson Internal Set theory the author considers the formalization of various notions from the elementary geometry of curves and tangents. A limit concept appears in this paper but is not defined. Since he is working within monads of points, this limit concept cannot be a translation of the standard concept. It appears more likely that it is somewhat intuitive in character and appears to be what seems to happen when one point within a monad ``moves'' along a curve. Further, the author seems to assume that the standard concepts associated with Euclidean geometry hold in the nonstandard structure and his transformed diagrams have meaning within a monad. His proofs appear to be based strongly upon what is perceived from the diagrams and as such are less rigorous than one would expect using nonstandard analysis. His results are relative to what are infinitesimal arcs, curvature, the circle of curvature, tangent segments and similar concepts.