I never knew that you could calculate fractional approximations for irrational numbers. I thought they just happened to find that 22/7 was a very accurate estimation. It's neat to see the process of how to calculate those approximations.
I didn't understand the relationship between the continued fractions and the greatest common factor. I also didn't catch how they found the fractions 1, 10/9,
2461/2215, 2471/2224 from 12345/11111.
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