### BARS::Pi Approximation Off-By-One Near Congress, Arizona

This road sign is located along AZ Hwy-89A ten miles north of Congress, Arizona.

```   +-----------------+
| Congress     10 |
| Jct SR 71    10 |
| Wickenburg   25 |
+-----------------+
```
```   the numbers are:  10  71  10  25

the off-by-one math is:  (71 - sqrt(25)) / (10 + 10 + 1)

observe...
sqrt(25) = 5
71 - 5 = 66
10 + 10 = 20
66 / 21 approximates Pi (3.14)
off-by-one:  20 is 1 less than 21
66 / 20 is 3.3
3.3 is 5.1% higher than 3.14
```
##### Update::2006.09.24

RoadHacker drove past this road sign again on 22 September 2006. A re-examination of the numbers resulted in another off-by-one find.

```   the numbers are:  10  10  25  71

the off-by-one math is:  sqrt(sqrt(71 + 10)) = (10 / sqrt(25)) + 1

observe...
71 + 10 = 81
sqrt(81) = 9
sqrt(9) = 3
sqrt(25) = 5
10 / 5 = 2
```
##### Update::2007.11.26

The spf function was added to the BARS toolbox on 26 November 2007. The spf calculates the sum of the prime factors for a composite number.

```   the numbers are:  10  10  25  71

the math is:  sqrt(25) + spf(spf(sqrt(71 - spf(10)))) = 10

observe...
spf(10) = 7      [prime factors for 10:  2, 5]
71 - 7 = 64
sqrt(64) = 8
spf(8) = 6       [prime factors for 8:  2, 2, 2]
spf(6) = 5       [prime factors for 6:  2, 3]
sqrt(25) = 5
5 + 5 = 10
```

Creator: Gerald D. Thurman [gthurman@gmail.com]
Created: 28 May 2006 