This works so well because while 22/7 is a well-known approximation for pi, 19/7 does a pretty good job with e.
<br /><a href='https://en.wikipedia.org/wiki/Simple_continued_fraction#/media/File:Diophantine_approximation_graph.svg'>https://en.wikipedia.org/wiki/Simple_continued_fraction#/media/File:Diophantine_approximation_graph.svg</a>