# Approximations Of Natural Numbers

What with so many people learning hundreds of decimals of pi and other irrational numbers, there's a danger that they might forget the values of the naturals. To solve this problem, I've composed a list of approximations of the first naturals, which could be very handy if you're one of the people who are comfortable with pi, e, and the square root of 2, but stare for hours at the number 7, wondering how much it really is.

An approximation of the natural number "1" hasn't been included; in fact, four of the formulas even use the number 1. I can only recommend that you memorize the value of 1 before you read the rest of this page.

Here are the approximations:

```             _______
/     _
2  =  pi - V e - V2

____________
3  =   /
V e + pi + pi

_
1 - V2
4  =  ------ + e + pi
pi

________
5  =   /      _     _
V pi - V2  * V2 + pi

1
_____
6  =    __  + e + e
Vpi

______________
/ _______    _
7  =  V V 1 + e  - V2  + pi + pi

_________
/ 4_              _
8  =  V  V2 + pi  * e * V2

9  =  e + pi + pi

/  pi - 1            \     _
10 =  |  -------- + pi + pi  | * V2
\    e               /

```

These formulas give good approximations for the first natural numbers; if you remember them, you'll be able to lead a pretty normal life without ever having to memorize the exact values of 2, 3, 4 etc.

I've tried to avoid formulas where elements are squared, since that could be hard to remember. I've also tried to avoid formulas which consist of or include repeated additions of an element.

The approximations vary in quality; I've tried to compromise between precision and simplicity - if the formula is harder to remember than the natural number it represents, then there's really no need for it, is there?

The least correct one is the approximation of 9; it is only correct to two decimal places. However, it's been included anyway because of its simplicity. And if you only use the approximations in your everyday life, does it really matter if you pay someone \$9, or \$9 and 0.1 cents?

• l"auteur