The geometry of map equations for trochoids

Author

Sibel Pasali

Abstract

“We will study trochoids and related curves using the representation of these curves as mapping of the unit circle in the complex plane. Points on the unit circle, or turns, and their uses in representing curves will be introduced and developed. Then we will prove several results which illustrate properties of trochoids. Special attention will be given to rosettes, trochoids which pass through the origin many times and have radial symmetry. Necessary and sufficient conditions for a trochoid to be a rosette are given, and we will define and study the petals of a rosette. Some trochoids exhibit cusps, and we give conditions for cusps and relate our work to existing results about cusps for families of curves which involve the use of generalized discriminants. Examples for most of the results will be given”--Abstract, page iii.

Advisor(s)

Hall, Leon M., 1946-

Committee Member(s)

Grimm, L. J.
Randolph, Timiothy W.
Morgan, Ilene H.
Le, Vy Khoi
Nisbett, J. Keith

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

Spring 2002

Pagination

viii, 53 pages

Note about bibliography

Includes bibliographical references (page 52).

Rights

© 2002 Sibel Pasali, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type

text

Language

English

Subject Headings

Epicycloids and hypocycloids

Thesis Number

T 8074

Print OCLC #

51110523

Recommended Citation

Pasali, Sibel, "The geometry of map equations for trochoids" (2002). Doctoral Dissertations. 1424.
https://scholarsmine.mst.edu/doctoral_dissertations/1424