Enclosing the Center
If we randomly select 3 vertices of a regular hexagon to form a triangle, what are the respective probabilities that the center of the hexagon is i) inside, ii) outside, iii) on the edge of the triangle?
Distances to Vertices
In the square below, points that are closer to the center than one of the vertices is coloured yellow. The area of the yellow region is 1/2 of the area of the square.
Area-Bisecting Lines
Every line going through the center of a square bisects its area. Does every line going through the center of an equilateral triangle bisect its area too?
Squares in Squares
Let’s draw a smaller square inside a unit square by dividing out a fixed fraction of each side and connecting the dividing point to an opposite angle.
Two-Colourable Triangles
We start with a polygon and a number of points inside it. We are asked to draw line segments between the points to subdivide the entire polygon into triangles.