Date of Award

Summer 1941

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)

Department

Mathematics

Abstract

As expressed in the title, the purpose of this thesis is to projectively generalize certain well-known curves. These curves, which are the cissoid of diocles and the conchoid of Nicomedes, are ordinarily associated with metric geometry. Their equations and the curves themselves are almost always expressed and shown in the terms of non-homogeneous cartesian coordinates. The problem at hand, then is to obtain the projective analogs of these curves and by means of algebraic analysis in the terms of homogeneous projective coordinates, to generalize their geometric construction and their algebraic expressions. No particular example of such a conversion of these curves, as developed in this thesis, has come to the author's attention. In that sense, the work of this thesis is original. However, numerous references, those listed in the bibliography, were consulted for the development of the method of projective generalization and for the formulation of projective analytical expressions.

Share

COinS