Questions

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.