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

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