On February 7, 2018, several math classes celebrate a special day known as “e day.” It is a day that coincides with the mathematical constant e, which starts out 2.718 and goes on forever. The day, month, and year correspond with the digits, which makes the day a very rare and special occasion.
Many math classes learned about e, its uses, and celebrate with food. Mrs. Tavel’s AP Calculus class feasted on many “e foods,” which included egg rolls, empanadas, (deviled) eggs, edamame, “e” cookies, eclairs, and much more.
How should you celebrate “e day”? Well, the first place students usually encounter the number e is in the formula for continuously compounded interest. That formula is A=Pert, where A is the amount of money in the account, P is the principal amount invested, r is the interest rate, and t is the length of time the money has been there. Leonhard Euler named the constant e and found that it was the limit of another expression, the infinite sum 1+1/1+1/2+1/6+1/24+1/120+… . That helped him compute e to 18 decimal places and show that, like π, it is irrational, that is, it can’t be written as a fraction. Though Euler didn’t actually choose the letter e to name it after himself, we now call it the Euler constant.
The focus of e‘s application to Tavel’s AP Calculus class revolves around the derivative of ex. The derivative is a measure of how quickly a function is changing at a particular point. Any exponential function has a derivative that is a multiple of itself. For example, the derivative of the function y=2x is approximately (0.69)2x. Only when the base is e do you get to discard the number at the beginning: The derivative of ex is just ex. To know how quickly this function is increasing at any given point, you just have to look at the value of the function at that point.
This mathematical occasion was celebrated by scholars around the globe on Wednesday, including those at St. Patrick. Students learned a thing or two about e and were able to enjoy some delicious food on its behalf, too.
Story by Richard Springer