A Historical Note on the Proof of the Area of a Circle

Autor/inn/en	Wilamowsky, Yonah; Epstein, Sheldon; Dickman, Bernard
Titel	A Historical Note on the Proof of the Area of a Circle
Quelle	In: Journal of College Teaching & Learning, 8 (2011) 3, S.1-5 (5 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1544-0389
Schlagwörter	Calculus; Mathematics Instruction; Mathematical Logic; Validity; History; College Mathematics; Algebra; Problem Solving + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Gültigkeit; Geschichte; Geschichtsdarstellung; Problemlösen
Abstract	Proofs that the area of a circle is nr[superscript 2] can be found in mathematical literature dating as far back as the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges and then fitting the wedges together in a way to approximate a rectangle. Later more sophisticated proofs relied on arguments involving infinite sequences and calculus. Generally speaking, both of these approaches are difficult to explain to unsophisticated non-mathematics majors. This paper presents a less known but interesting and intuitive proof that was introduced in the twelfth century. It discusses challenges that were made to the proof and offers simple rebuttals to those challenges. (Contains 6 diagrams.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10