Quiz: Infinite Continued fractions


At the SouthWest Fox speaker dinner we were talking about continued (or infinite) fractions.


 


I posed this question:


 


What does this expression evaluate to?


 


 


       1 +            1


                  _________


                   1 +     1


                          ________


                           1 +   1


                                 _______


                                  1 +    1


                                         ______


                                          1 +    1


                                             


 


 


Clue: It’s adding some positive value to 1, so it must be larger than one. The thing it’s adding is the reciprocal of some number larger than 1 so….

Comments (5)

  1. Thierry says:

    The golden ratio : 1.618034

  2. Anonoymous says:

    x = 1 + 1/x

    ==>

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

    ==> 1.618034

  3. Raj Kaimal says:

    1.618034 or -0.618034 (the golden ratio is an irrational number)

  4. kfarmer says:

    Raj:

    Never assume that the fact that the expression contains sqrt(5) somewhere in it implies that both positive and negative roots are correct for the answer.

    The answer must be positive in this case, and so you cannot take the negative root.

  5. Theo Huenestein says:

    http://www.mlahanas.de/Greeks/GoldenSection.htm

    It always helps if you have read "The Da Vinci Code"

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