I learned the following trick for memorizing the value of e from
my colleague, Gene White. It never fails to impress calculus
students (given a wide enough definition of “impress”). Start by
carefully looking at this picture: That’s a 20 dollar bill, so
memorize “2″ and put down the decimal point. The picture on the
bill is of Andrew Jackson. He was our seventh President, so put
a “7″ after the decimal point to get 2.7. Jackson was elected in
1828, so put down “1828″ next. Since there’s a 2 in front of the
decimal place, put “1828″ a second time. We’re now up to
2.718281828. Now look at the red square over Jackson’s face. The
diagonal creates two congruent right triangles with angle
measures 45, 90, and 45. So, add on 459045 to get
2.718281828459045. And that’s e to 15 places. I’m open to
suggestions on how to memorize more of the digits.