臺灣博碩士論文加值系統

此論文討論有關圓的內外擺線。主要分為兩部分，第一部分為
圓的內外擺線的性質及應用，第二部份討論一個重要外擺線-心臟線。
在此證明了心臟線為拋物線的反演，並提出決定心臟線的一些充分條件。

The epi- and hypo- cycloids are the track described by a point of a circle rolling on a stationary circle
(base-circle). There are two parts in this thesis. The first part, we discuss the properties and applications of epi- and hopi- cycloids. The next part deals with the problems about the epicycloid-cardioid. We prove that a cardioid is the inverse of a parabola and show how a cardioid may be determined by ruler and compass without the knowledge of the base-circle.

1. Introduction.........................................................................................1
2. Properties of epi- and hypo- cycloids..................................................2
3. Properties of the cardioid .................................................................9
4. Construction of the cardioid..............................................................20
5. References.........................................................................................25

[1] E. H. Lockwood, A Book of Curves, (1 nd), University Press, 1961
[2] Howard Eves, A Survery of Geometry, Volume One, Allyn and Bacon, Inc., 1963, U.S.A.
[3] Luigi Cremona, Elements of Projective Geometry, Translated by Charles Leudesdorf, M.A., (3 nd), Dove Publications, Inc.,1960, New York