"Capture the Flag"

Kim Seay

EMAT 6680

Suppose three teams, A, B, and C , are to play a game of capture the flag. Each team begins in a different position. The starting points for the team can be connected to form a triangle.

The goal of the game is to capture a flag, and return it to your team's starting point. Assuming the triangle is scalene, where should the flag be placed to ensure a fair game?

Begin by constructing the perpendicular bisectors for all three sides the triangle. The point where these three lines intersect is called the circumcenter, and is equal distance from all three vertices.



By making a script in GSP, I can try this with any three starting positions for the teams. Click here to open the script. Open a new sketch under File in GSP. Choose any three points. Click on the script itself, and then click on play. The computer should find the circumcenter of the triangle for you.


I chose this assignment in part, because of my own memories of playing "Capture the Flag." I think students would really enjoy this assignment, because it ties in with their own background knowledge as well. This shows a very real application of geometry concepts.