# Euler’s formula as a model for the universe

Euler’s formula relates imaginary numbers, the natural logarithm, trigonometry, and the ratio of a circle’s diameter and circumference, all in a single equation. I would like to propose that this equation can also describe the potential and kinetic energy of an ideal oscillating system, and, in doing so, provide a useful model for the hypothetical expansion and contraction of the universe.

The equation is written as follows:

If math isn’t your thing, I’ll explain the symbols real quick…

*e*, also known as Euler’s number, is the base of the natural logarithm. Like pi, *e* is an irrational number with decimal places that continue endlessly. Its first digits are 2.718, and it’s defined by the following series:

Perhaps the easiest way to think of *e* is in terms of compound interest…

If I give you a dollar and say that I will pay you 100% interest per year, you would expect to have $2 at the end of the year, presuming that I compute and credit the interest just one time, at the end of the year.

If the interest is credited twice in the year, the interest rate for each 6 months would be 50%… So after 6 months, I’d give you fifty cents, and you’d have $1.50. Then, at the end of the year, I’d be paying you 50% interest on the new sum of 1.50, so you’d get another 75 cents and end up with $2.25 total.

If we keep on increasing the number of intervals, the same rules apply. Quarterly payments would…