Most of the time, when people make irrationality jokes, they reference a very well-known constant: pi*. However, an even more exciting number that has a multitude of uses in mathematics and physics is “e”, Euler’s number**. Euler’s number is usually rounded to 2.72 or 2.718†. This fancy number is the base of natural logarithms‡ and is very important to calculus (and often introduced in precalculus). It is fundamental to many areas of mathematics, including complex numbers, logarithms, and exponential growth or decay problems (related to nuclear decay in physics!).
One of the key properties of Euler’s number is that the function f(x) = e^x is its own derivative, which means the slope of the curve at any point is equal to the value of the function at that point. This property is unique to e and is part of what makes it so important in calculus and physics. Euler’s number is also famous for its appearance in Euler’s identity, considered by many to be the most beautiful equation in mathematics (truly a masterpiece). The equation is e^(i*pi) + 1 = 0, combining five of the most important numbers in mathematics: 0, 1, pi, e, and the imaginary unit i, in a simple and elegant relationship.
If you would like to learn more about e, feel free to reach out to your math teacher or use the following resources!
* FYI, this is in reference to pi, the number, 3.14159265358979323846264338327 (not rounded), and not the food. However much our team may wish that pie is a constant, it does, unfortunately, meet an early end due to its deliciousness.
** Euler is difficult to pronounce. It is not pronounced “you-ler.” Rather, it is pronounced “oiler.” Our reference for this is Mr. Mudd in room 234. Please feel free to contact him with any questions about this anomaly.
† A few more digits of this number are 2.718281828459045235!
‡ Another way to say Natural Log is ln (pronounced “ehl – en”), and the British version is “lon” (pronounced “lawn”). If you are in IB Mathematics Higher Level, we highly recommend that you use “lon” aloud in class.
