Odds Third
- Author:
- John Golden
- Topic:
- Fractions
Saw this fabulous fraction at the Futility Closet, with a link to Roger Nelson's triangular proof without words. When I was making sense of it myself, I thought about how the sum of the odds is a square number, so the first n odds 1, ..., 2n-1 sum to n^2, But then the first 2n odds sum to (2n)^2, so the 2nd n odds, 2n+1, ..., 4n-1 sum to 3n^2 and I had to make this visual.
That it goes back to Galileo is just gravy!
