eDay
This week's opening News proposes the idea that mathematics classrooms should celebrate other numbers besides Pi. If you are interested, eday is lurking nearby...February 7th to be "exact"!
But, I hear you ask, what can be done with your students on eday? Eating Pie is of little value, despite the fact that it tastes great. So, consider theses ideas gleaned from multiple sources......
To help you memorize the digits of e = 2.718281828459045235360287471352662497757247093...., 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 "squareshaped" 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 beiung divided into two congruent 45^{o}90^{o}45^{o} 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 = e^{x} is the only nontrivial function where y = y'.
Whatever you do, have some efun!
