Guided discovery of the nine-point circle theorem and its proof

• Orly Buchbinder ^[1]
  1. [1] University of New Hampshire

     University of New Hampshire

     Town of Durham, Estados Unidos

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 49, Nº. 1, 2018, págs. 138-153
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through investigation in a dynamic geometry environment, and consequently prove it using a method of guided discovery. The paper concludes with a variety of suggestions for the ways in which the whole set of activities can be implemented in geometry classrooms.