Introduction
Ramanujan’s Continued Fractions and the Icosahedron
Dear Sir,
I beg to introduce myself as a clerk... I have had no University education... employing the spare time at my disposal to work at Mathematics... and the results I get are termed by the local mathematicians as “startling.”
The letter contained nine pages of around 50 results with no proofs. Some of the results were known, some were false, and some (like the red and blue continued fraction identities above) were both new and nontrivial. In fact, Hardy remarked of Ramanujan’s continued fraction results that “They must be true because, if they were not true, no one would have the imagination to invent them.”
In January of 1913, an Indian clerk named Srinivasa Ramanujan sent a letter to the well-known English mathematician G. H. Hardy...