Course: Discrete Mathematics
Institution: Saint Mary's College
Faculty: Ranjan Rohatgi

Assignment

Triangles on Grids

• Suppose you have a square grid of 9 points (I’m going to call this a “3 by 3” grid) as shown below.

• How many different triangles can we draw on this grid assuming the vertices of the triangles are on points of the grid?
• What if you have a 4 by 4 grid?
• What if you have a 5 by 5 grid?
• Discuss how you would answer the question for a 6 by 6 (or larger) grid.
• Ask an interesting question based on these scenarios, generalizing or slightly changing them in some way. Discuss this new problem and how you could attempt to solve it. Maybe solve a special case or two.
• Curiosity: Pick your favorite topic that we have covered up to this point. Mathematically, why do you find it interesting? What makes you curious to know more about it?