Ireland

Shane Browne (17)

City/Region: Bray, County Wicklow E-mail: madforit52@hotmail.com Hobbies: Playing soccer, Gaelic football, basketball, snooker Career: Electronic engineer School: St.Kilians Community School

Michael O'Toole (17)

City/Region: Bray, County Wicklow E-mail: Hobbies: Snooker and playing football Career: Architect School: St.Kilians Community School

Peter Taylor (16)

City/Region: Bray, County Wicklow E-mail: goldengloves@eircom.net Hobbies: Playing football, do boxing. listening to music and playing snooker Career: Electronic engineer or maths/science researcher School: St.Kilians Community School

Symmetrical Shapes formed by Polygons

Shane, Michael and Peter read about an investigation of heptagons in a mathematical magazine. Heptagons are shapes which have seven straight sides. They decided to take a look at the general question of objects with many straight sides (polygons). The three boys proved that every regular polygon, regardless of the number of sides, can be arranged in a perfect symmetrical shape whereby it will have the same number of rotational symmetries as axial symmetries. That is, all regular polygons can be arranged in a perfect circular shape. They proved their hypothesis using a combination of algebra, geometry and technical drawing. In addition to this they developed an elementary relationship between the number of sides of the regular polygon and the number of polygons used to form the circular arrangement.