How does this nursery rhyme pertain to power series: “There was a little girl Who had a little curl Right in the middle of her forehead..." This is from _The Way of Analysis_ by Strichartz, chapter $7$, section $7.4$, page $276$. He writes > "In discussing power series it is good to recall a nursery rhyme:" > > "There was a little girl > > Who had a little curl > > Right in the middle of her forehead > > When she was good > > She was very, very good > > But when she was bad > > She was horrid." I don't understand why or how this nursery rhyme is related to power series. * * * Kudos to the comment by Barry Cipra. The rest of the poem can be seen here. I wonder if the rest of the poem can be turned into having some mathematical significance.

The nursery rhyme may be referring to the fact that power series are "very, very good" within their radius of convergence (absolute convergence, term-by-term differentiation and integration, uniform convergence, etc.) while they diverge outside the radius of convergence (which is "horrid" as far as series are concerned).

The curl in the middle of her forehead may be referencing the boundary of convergence; on one side, it's very nice while on the other side, it's horrible. (It's also a possibility that it's simply part of a preexisting rhyme, as @Blue puts it.)