Bernoulli discovered e by studying a question about compound interest

There is more than one famous Bernoulli. This is the work of Jacob Bernoulli; Daniel Bernoulli, of Bernoulli's principle, is arguably better known.

Funny how the calculation seems to be done backwards

(For an initial 100% interest) "If the interest is credited twice in the year, the interest rate for each 6 months will be 50%"

And of course this is wrong, because the interest is not 50% but (2^1/2) - 1 (that is, 41%) since x * 1.4142(first interest payment) * 1.4142(second interest payment) should be 2*x

There is a great book out there called ' Against the Gods ' by Peter Bernstein. http://www.amazon.com/Against-Gods-Remarkable-Story-Risk/dp/... It has the fantastic story of how a lot of mathematical computations are a product of the effort to quantify risk.

This reminds me of something a professor told me in my first Calculus course that the famous L'Hospital's rule, named after the French mathematician Guillaume de l'Hôpital, was actually discovered and proved by Bernoulli. The saying is that l'Hospital bought the rights to Bernoulli's mathematical discovery in order to publish it in his book Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes[1]

[1] http://www.stewartcalculus.com/data/ESSENTIAL%20CALCULUS%20E...

So, XKCD. http://xkcd.com/947/

Here's my "e bookshelf" http://imgur.com/YBB33 , which uses the 1/n! definition. It only goes up to 1/3!, but ideally would approach 1/infinity!. e grows as the total area of the clear books on the left. For example, for the bottom shelf, 1/3! is the same as having all possible arrangements of three objects, and choosing one.

Calculus 101?

I recall that learning that lim(1 - 1/n)^n with n->inf is 1/e, was one of the first things learned in Calculus. I think we even briefly touched this in highschool.

What can't compound interest teach us....

In other breaking news of interest to the digitally connected elite, e follows d and precedes f. It is also generally not used as a grade in American educational institutions.