### BARS::Phi Sign on Northbound Loop 101 in Tempe, Arizona

This road sign was found on northbound Loop 101 in Tempe, Arizona.

Note: The following expression approximates Phi (`1.61803399+`)...

```   1 + sqrt(5)
-----------
2
```

The road sign says...

```   +--------------------------------------+
| Broadway Rd/Apache Blvd          1/4 |
| University Dr/Rio Salado Pkwy  1 1/4 |
+--------------------------------------+

the numbers are:  (1/4)  (1 1/4)

the math is:  sqrt(1/4) + sqrt(1 1/4) = Phi

observe...
sqrt(1/4) = sqrt(1)/sqrt(4) = 1/2
sqrt(1 1/4) = sqrt(5/4) = sqrt(5)/sqrt(4) = sqrt(5)/2

1    sqrt(5)   1 + sqrt(5)
--- + ------- = -----------
2       2          2
```

The key to finding Phi in this road sign was using the mixed number `1 1/4` as the fraction `5/4`. The square root of `5/4` is square root `5` divided-by square root `4`, which is `2`. Thus, we get a fraction having square root `5` in the numerator and `2` in the denominator. The square root of the fraction `1/4` is `1` divided-by the square root of `4`, which gives `1/2`. We now have two fractions having the common denominator of `2` and we add them together to get `1` plus square root `5` in the numerator.

Wikipedia.org:: Golden ratio

Creator: Gerald D. Thurman [gthurman@gmail.com]
Created: 19 April 2007 