On the Circle of Apollonius

Autor/in	Ayoub, Ayoub B.
Titel	On the Circle of Apollonius
Quelle	In: Mathematics and Computer Education, 40 (2006) 3, S.198-204 (7 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0730-8639
Schlagwörter	Geometric Concepts; Mathematical Logic; Validity; Computation; Theories + Suchen Sie Ihr Suchwort? Elementare Geometrie; Mathematical logics; Mathematische Logik; Gültigkeit; Theory; Theorie
Abstract	The circle discussed in this paper is named after "The Great Geometer of Antiquity", that is Apollonius of Perga (ca. 262-190 BCE). Among his many contributions to geometry is a book with the title "Plane Loci." This book included, among others, a problem about the locus of a point moving in a plane such that the ratio of its distances from two fixed points is a positive constant different from one. It turned out that the locus is a circle now known as "Circle of Apollonius". The proof of this result is based on the following theorems: (1) The angle bisectors of a triangle; (2) Thales' theorem of the angle inscribed in a semicircle; and (3) The proportion resulting from a line drawn parallel to a side of a triangle. In fact, the proof connects these theorems in a nice way, and provides a refreshing idea about circles. The students can use Circle of Apollonius to tackle interesting, sometimes challenging, problems. (Contains 8 figures.) (ERIC).
Anmerkungen	MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10