The graceful pi-way is the path through the 15 states on the western and northern borders of the contiguous
USA graph, stretching from California to Maine, in a particular graceful
labeling. Its vertex labels are 31, 41, 59, 26, 53, 58, 97, 93, 23, 84, 62, 64,
33, 83, and 27, precisely the first 30 decimal digits of 
. T. Rokicki found the labeling in October 2020, and
Knuth (2025, p. 18) describes it as a "graceful miracle." With apologies
to Gordon Lightfoot's "Carefree Highway," the path
is illustrated in red above.
