IJPAM: Volume 66, No. 1 (2011)

THE BEAUTIFUL GEOMETRIC THEOREM OF VAN AUBEL

Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi, Higashiyodogawa, Osaka, 533-8533, JAPAN
e-mail: [email protected]


Abstract.There is much beauty to be found among the theorems of geometry. This article introduces Van Aubel's Theorem (1878), and provides proofs using (i) vectors and complex numbers and (ii) elementary geometry. The beauty of this theorem lies both in the theorem itself and also in its proofs. The appearance of geometry problems in university entrance examinations has declined dramatically since the adoption of mark sheets. Geometry is one of mathematics' great resources, and the author suggests the revival of geometry problems in the mathematics curriculum.

Received: October 27, 2010

AMS Subject Classification: 51M04, 97G50, 97I80

Key Words and Phrases: Van Aubel's Theorem, complex number, vector, elementary geometry

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 1