# IJPAM: Volume 25, No. 1 (2005)

**THE POLYGON CASE OF THE THETA-CURVE THEOREM**

Department of Mathematics and Informatics

Faculty of Sciences

University of Novi Sad

4, Trg Dositeja Obradovica

Novi Sad, 21000, SERBIA AND MONTENEGRO

e-mail: bodroza@im.ns.ac.yu

e-mail: ratosic@im.ns.ac.yu

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 , 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