Here are some questions for you to consider.
- What are the important features? What is allowed to change and what must stay the same?
- Given two positive integers, can you produce the corresponding diagram (without the computer)? Compare your diagram with the one obtained from the interactivity.
- Do different pairs of integers necessarily lead to different diagrams?
- Can you start from a diagram and work back to the initial numbers?
- Can you produce some diagrams that are somehow ‘extreme’ examples?
- Can you describe one of these diagrams in words and/or equations?
- What might the diagram illustrate? You might wish to make some conjectures that you can test (and, if necessary, refine). Try to prove your conjectures.