Containing a Regular Polygon by Extending Sides

Key Points

• This research aims to determine the number of ways to select k sides from an n-sided polygon to create a k-gon that contains the n-gon.
• Analyzed ways to select k sides from a regular n-sided polygon.
• Developed formulas based on distinguishable sides and indistinguishable factors.
• Considered cases of rotations and reflections in the polygon arrangements.
• Formulas were derived for distinguishable sides, resulting in specific combinatorial counts.
• Established forms for indistinguishable rotations that adjust the total based on symmetries.
• Identified outcomes for cases where both rotations and reflections are treated as identical.