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

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

The road sign says...

   +-----------------+
   | 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

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