@evmar Update on this thread: I did some deep searching in the literature and did indeed find the result. It's in https://github.com/linebender/linebender.github.io/pull/44 which will shortly be merged to https://linebender.org/wiki/curves/euler-spiral-evolute/ (the gentle reader is invited to contribute a review).

I also updated the Wikipedia articles on Cesàro equation and Evolute to include this result. I was originally worried about "no original research" but I'm on firm ground now, as I cite published papers.