BARS::Rio Salado Phi Trail Sign in Phoenix, Arizona

This trail sign is on the northside of the Rio Salado near the Central Avenue parking lot in Phoenix, Arizona.

The trail sign says...

   +-------------------------------+
   |          Rio Salado           |
   |  Central Avenue Gateway to:   |
   | 7th Street Bridge   0.5 miles |
   | 16th Street Bridge  1.4 miles |
   +-------------------------------+

[side-bar] In the above trail sign, should 0.5 miles be 0.5 mile? And, should 1.4 miles be 1.4 mile?

To help when it comes to doing BARS (Basic Arithmetic Road Signs), MathBabbler has memorized the following equation.

   (1 + sqrt(5))/2 = Phi

Let's do the math...

   the numbers are:  7  0.5  16  1.4

   the Phi math is:  0.5 + sqrt(floor(7 - 1.4) / sqrt(16)) = Phi

   observe...
      Phi golden ratio = 1.61803399
      7 - 1.4 = 5.6
      floor(5.6) = 5
      sqrt(16) = 4
      sqrt(5/4) = sqrt(5)/sqrt(4) = sqrt(5)/2
      0.5 = 1/2
      1/2 + sqrt(5)/2 = (1 + sqrt(5))/2

   more math:  ceil(1.4 / 0.5) = sqrt(16 - 7)

   observe...
      1.4 / 0.5 = 2.8
      ceil(2.8) = 3
      16 - 7 = 9
      sqrt(9) = 3

   more math:  ceil(1.4 / 0.5) = 7 - sqrt(16)

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 24 December 2007

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This work is licensed under a Creative Commons Attribution 3.0 United States License.