Dynamic investigation of triangles inscribed in a circle, which tend to an equilateral triangle. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Stupel, Moshe; Oxman, Victor; Sigler, Avi
• Is Part Of: International journal of mathematical education in science and technology. Volume 48:Issue 1(2017)
• Page Start: 149
• Page End: 161
• Publication Date: 2017-01-02
• Subjects: Geometrical investigative problems -- convergence of geometrical properties -- combinations of fields in mathematics; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; 510.07
• DOI: 10.1080/0020739X.2016.1206978
• Languages: English
• ISSNs: 0020-739X

Abstract

ABSTRACT: We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties, after which we present formal proofs that rest on a combination between different fields of mathematics: trigonometry, algebra and geometry, and the use of the concept of standard deviation that is taken from statistics.