Socratic · 1

Ramanujan's hidden step

In 1911 Ramanujan asked readers of the Journal of the Indian Mathematical Society for the value of an infinite nest of square roots. This video stops at each step and asks you first. Sound on.

Sources. Question 289, Journal of the Indian Mathematical Society 3 (1911), p. 90; his solution, vol. 4 (1912), p. 226; Collected Papers of Srinivasa Ramanujan (Cambridge, 1927), pp. 323 and 348; A. Herschfeld, "On infinite radicals", American Mathematical Monthly 42 (1935). Chronology: D. J. Jones, arXiv:1707.06139. Every fact on screen is in claims.md.

Prefer a plain video? The MP4 has a "pause and think" countdown at each question instead.