The Mystery of e^Pi-Pi (Very Mysterious Number)

If you have a calculator, check out the value of $e^\pi-\pi$. It is 19.99909998…

Why is it so close to the integer 20? Is it a coincidence (few things in Math are coincidence), or is it a sign of something deeper? e and Pi are two very fundamental numbers in Math, and the very fact that $e^\pi-\pi\approx 20$ may well mean something.

This was observed by a few mathematicians (Conway, Sloane, Plouffe, 1988) many years ago, but till this day there is no answer.

Do give it a thought!

Featured book:

Pi: A Biography of the World’s Most Mysterious Number

We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren’t told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird. Mathematicians call it a “transcendental number” because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction.

In this delightful layperson’s introduction to one of math’s most interesting phenomena, Drs. Posamentier and Lehmann review pi’s history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi (including an attempt to legislate its exact value), and useful applications of pi in everyday life, including statistics.

This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.

5 Ways to get Pi on Calculator without pressing the Pi button:

1) 22/7

22/7 is not an exact value for Pi, but it is a pretty good approximation. 22/7=3.142857143… has just a percentage error of 0.04% compared to the actual value of Pi!

Percentage error is calculated by: $\displaystyle\frac{22/7-\pi}{\pi}\times 100\%=0.04\%$

2) 355/113

355/113 is an even better approximation for Pi. 355/113=3.14159292… has merely a percentage error of 0.000008%! This is incredibly accurate for a “relatively” simple fraction like 355/113. 355/113 has a cool Chinese name called “Milü密率, given by the ancient Chinese Mathematician astronomer Zǔ Chōngzhī (祖沖之) who discovered it.

3) 3.14

Using the simple and straightforward 3.14 (0.05% error) may be sufficient for everyday purposes. 🙂

4) $2\sin^{-1}(1)$ or 2 arcsin(1) (Radian Mode)

This relies on the fact that $\sin^{-1}(1)=\pi /2$.

5) $\lim_{n\to\infty}{n\sin(180^\circ/n)}$

We can let n=180 for convenience, and get ${180\sin(1^\circ)\approx 3.14143}$. This is a pretty decent approximation for $\pi$, with just 0.005% error. The approximation gets better as n gets larger.

Featured Book:

Pi: A Biography of the World’s Most Mysterious Number

We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren’t told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird.