|Jacob Bernoulli, Leonhard Euler mathematics|
- The first irrational constant was π,
- known as Archimedes’ constant.
- The second was √2,
- known as Pythagoras’ constant.
- The third was e,
- known as Euler’s number.
- Jacob Bernoulli was the first
- to find Euler’s number
- as the result of compounding interest
- when the interval approaches zero,
- known as continuous compounding.
- Leonhard Euler identified e
- as a base for logarithms
- because the number 1
- is common to all counting systems,
- because the logarithm base e of 1 is 1,
- and because the derivative
- of logarithm base e of 1 is 1.
- For something characterized as transcendental,
- it’s odd that e pops up so frequently.
- as the result of continuous compounding
- as the probability of always losing
- in integral expressions for bell curves
- in expressions for the rate of radioactive decay
- in the formula for distances on a Mercator map
- as the area under the hyperbola 1/x
- between 1 and a is the natural log of a.
- Euler’s number is approximately equal to
- but it is exactly equal to
- the limit as n approaches infinity
- of 1 plus 1 over n to the power of n,
- but go ahead and try to write that out.
- Without being subject
- to the law of diminishing returns,
- you may get as close as you like.