IJPAM: Volume 25, No. 1 (2005)

THE POLYGON CASE OF THE THETA-CURVE THEOREM

Olga Bodroza-Pantic$^1$, Ratko Tošic$^2$, Bogdanka Jakovljev$^{3}$
$^{1,2}$Department of Mathematics and Informatics
Faculty of Sciences
University of Novi Sad
4, Trg Dositeja Obradovica
Novi Sad, 21000, SERBIA AND MONTENEGRO
$^1$e-mail: bodroza@im.ns.ac.yu
$^2$e-mail: ratosic@im.ns.ac.yu
$^{3}$Secondary School ``Jovan Vukanovic"
1, Gagarinova, Novi Sad, 21000, SERBIA AND MONTENEGRO


Abstract.The well known game of Hex uses the following corollary of the Jordan Curve Theorem, so-called theta-Curve Theorem: An open Jordan curve with its endpoints on a closed Jordan curve ${\cal K}$, but otherwise located in the bounded part, divides the closure of the bounded part into two parts.

Some students in a honor class, who have not been previously exposed to homology theory, after being motivated by the game of Hex, may be given direct and elementary proofs of the polygon case of both the Jordan Curve Theorem and the Theta-Curve Theorem.

Received: August 2, 2005

AMS Subject Classification: 40D25, 40D05, 51A20

Key Words and Phrases: Jordan curve, Theta-Curve Theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 1