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Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

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Diophantine N-tuples

Can you explain why a sequence of operations always gives you perfect squares?

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There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Data Chunks

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
Be systematic : start with red rods and try light green, then purple, and so on, working through the rods in order of size.

Next have light green with purple, then yellow, and so on.

Next take purple . . . you get the idea?

Making careful notes and producing tables are essential.