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Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.

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Mystic Rose

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
How many lines are drawn at each stage of construction of the mystic rose?
Now look at the completed mystic rose - can you describe how many lines are drawn from each point?
How do these relate to "Alison's method" and "Charlie's method"?