Irrational Numbers

In some of your calculations it is possible that you will need to use various irrational numbers.  Here we show you how to get them.  We could have programmed them in, however how do we identify them?  The values for e and phi cannot be labeled “e” and “phi”, as there are stocks that use those symbols.  Thus we let you choose you own names for the macros.  Here’s how to generate the values:

pi:         2 * arcsin 1

e:          exp 1

phi:       (1 + sqrt 5)/2

“pi” is used in various trigonometric functions.

“e” can be used to continuously compound a nominal interest rate, which is necessary in various options calculations.

“phi” is the value which Fibonacci ratios converge to.  Although Fibonacci numbers are digital (1, 1, 2, 3, 5, 8, 13, 21, 34, …), the Fibonacci Ratio is the ratio of each number to the prior one.  As you keep extending the series, the ratio converges to “phi”.  “phi” is also the “golden mean” of Classical Greece.