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It's Soon e-Day!

A previous Math News proposed the idea that mathematics classrooms should celebrate other numbers besides Pi. If you are interested, e-day is lurking nearby...February 7th to be "exact"! But, I hear you ask, what can be done with your students on e-day? Eating Pie is of little value, despite the fact that it tastes great. So, consider theses ideas gleaned from multiple sources......

To memorize the digits of e = 2.71828182845904523536028747135266249775...., consider menumonics where each word has the number of letters equal to the digits of e in order:

  • By omnibus I traveled to Brooklyn.
  • We require a mnemonic to remember e whenever we scribble math.
  • In showing a painting to probably a critical or venomous lady, anger dominates. 0 take guard, or she raves and shouts! (NOTE: The problem of the zeroes arises.)
  • It appears a maneuver to remember e although it shouldn’t. When truly justified, 0 just carry it out until you falter. 0, it possibly induces pain. However, I can truly do thirty paces or more correctly without slipping.
Or, as another mneumonic, Elroy Boldoc (University of Flrida) suggests using a "square-shaped" picture of President Andrew Jackson, with a diagonal drawn bewteen two corners. A variation of Boldoc's mneumoic goes as follows:
  • Andrew Jackson had two marriages, thus the 2.
  • Andrew Jackson was the seventh President, thus the 7.
  • Andrew Jackson was elected President in 1828, thus the 1828.
  • The "square" shape of the photo reminds us square the 1828, thus getting the digit string 18281828
  • The diagonal across the photo reminds us of the square shape being divided into two congruent 45o-90o-45o triangles, hence the next digit string 459045.
The odd thing is that this last mnemonic works, as I know know the first 16 digits of e quite well. Challenge your students to creatively extend the Andrew Jackson story for the additional digits.

What are the best fractions or other numerical expressions that approximate e? Try these:

  • 878/323 =
  • 2721/1001 =
  • 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! +... =
  • 2[(5/2)(2/5)]=
Or, even this sequence of computations, which can easily lead to discussions of compounding interest:
  • (1+1/1)1=
  • (1+1/2)2=
  • (1+1/3)3=
  • (1+1/4)4=
  • (1+1/5)5=
  • (1+1/6)6=
  • (1+1/7)7=
  • (1+1/8)8=
  • (1+1/9)9=
  • (1+1/10)10=
  • (1+1/100)100=
  • (1+1/1000)1000=
  • (1+1/10000)10000=
  • (1+1/1000000)1000000=
  • Other options include looking at e via the continued fractions <2,1,2,1,1,4,1,1,6,1,...>, its defining integral, or the special fact that y = ex is the only non-trivial function where y = y'.

    Whatever you do, have some e-fun!