In what Knuth (2024, p. 18) describes as a "graceful miracle," as found by T. Rokicki in October 2020, not only does there exist a graceful
labeling for the contiguous USA graph,
but the graceful labeling illustrated above has the property that the 15 states on
the western and northern borders stretching from California to Maine are labeled
with the numbers 31, 41, 59, 26, 53, 58, 97, 93, 23, 84, 62, 64, 33, 83, and 27,
which are precisely the first 30 decimal digits of 
. With apologies to Gordon Lightfoot's "Carefree Highway,"
this miraculous path (shown in red above) might be termed the "graceful pi-way."
