Dynamic investigation of triangles inscribed in a circle, which tend to an equilateral triangle

• Moshe Stupel ^[2] ; Victor Oxman ^[1] ; Avi Sigler ^[2]
  1. [1] Western Galilee College

     Western Galilee College

     Israel

     
  2. [2] Shaanan College
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 1, 2017, págs. 149-161
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.