Leibniz’s harmonic triangle (1673). Each little threesome of unit fractions satisfies the “blue rule” below. Leibniz used this construction to calculate certain infinite sums as telescoping series. E.g., the red sum is 1/2 of the sum of reciprocal triangular numbers. pic.twitter.com/fDYO3mCLyn
— Steven Strogatz (@stevenstrogatz) January 12, 2022