Euler's Constant
Categories: Metrics
Euler's constant is one of those numbers that doesn't quite have a number attached to it. Like pi. It's irrational, meaning that, if you try to write all the decimal places, you'll be writing numbers for the rest of eternity.
Just to be confusing, there are two numbers that sometimes get termed "Euler's constant." They are both named after famed (at least as "famed" as it gets in the math world) Swiss mathematician Leonhard Euler, who lived during the 1700s.
The first of Euler's constants is denoted by the Greek letter gamma and is also sometimes known as the Euler-Mascheroni constant, giving some credit to an Italian mathematician named Lorenzo Mascheroni (also a great pasta).
The other number that sometimes gets called "Euler's constant" or "Euler's number" shows up in math as the constant "e." It's the more famous of the two. It roughly equals 2.71828. Technically, it's defined as the limit of (1 +1/n) taken to the nth power, as n approaches infinity.
We know: mind blown.
The gamma version of Euler's constant gets used in complicated number theory and other high-level mathematical gymnastics.
The "e" version is more central to finance because it's derived from the study of compound interest.
You open a bank account that pays an interest rate of 1% a year. You put in $100 and forget about it. In the first year, you earn $1 of interest. So you have $101 entering the second year. But in the second year, you earn interest on your original $100, plus the $1 you earned in the first year. So in year two, you earn $1.01 in interest...1% of $101. So now you have $102.01 in your account. In year three, you earn $1.0201 in interest, giving you $103.0301. That's compound interest...earning interest on the interest you've earned.
The example above is fairly simple, but you can see how this gets complicated after a while, especially when you're talking about non-round numbers and your interest rates compound more often than once a year (monthly or quarterly, for example).
Anyway, "e" comes up in those equations, along with other mathematical situations. Is there then room for a Euler's Occasional?