Category Archives: Mathematics

Which is better, e or π?

Top ln(e10) reasons why e is better than pi : e is easier to spell than pi. pi ≒ 3.14 while e ≒ 2.718281828459045. The character for e can be found on a keyboard, but pi sure can't. Everybody fights for their piece of the pie. ln(pi1) is a really nasty number, but ln(e1) = 1. e is… Read More »

Euler Phi-Function is a Multiplicative Function

Let \(n\) be a positive integer. Recall that the Euler phi-function \(\phi(n)\) is defined as the number of positive integers less than or equal to \(n\) and relatively prime to \(n.\) Note that \(\phi(1)=1.\) We have seen that Euler used this function to generalize the Fermat's Little Theorem. It is sometimes needed to calculate the value \(\phi(n)\) of… Read More »