[Jprogramming] Continued Fraction Challenge

[Raul Miller]

How do you compute the first two rows?

Thanks,

-- 
Raul

On Saturday, March 12, 2016, Kip Murray <thekipmurray at gmail.com> wrote:

> The challenge is at the end.  First a table for a finite continued fraction
> that approximates e =: ^ 1 .
>  --Kip Murray
>
>
> The table below summarizes a finite continued fraction which begins
>
>          1
>  1 + -------------
>              1r12
>      1r2 + --------
>                 1r60
>            1 + ------
>
>                1 + .
>                      .
>                        .
>
>     table
>  _1   1 1r12   1r60     1r140       1r252          1r396
>   1 1r2    1      1         1           1              1
>   1   3 19r7 193r71 2721r1001 49171r18089 1084483r398959
>
>
> You must ignore the _1 in the upper left corner. You see how the first row
> identifies numerators and the second row numbers on the "diagonal" of the
> continued fraction.
>
>
> The third row gives the "convergents", results of terminating the continued
> fraction at a diagonal number.  The first four convergents are
>
>  1 , (1 + 1 % 1r2) , (1 + 1 % 1r2 + 1r12 % 1) , (1 + 1 % 1r2 + 1r12 % 1 +
> 1r60 % 1)
>
>
> The convergents of this continued fraction approximate the number  e =: ^ 1
> .
>
>     2 * 0.5 * {: table
>  1 3 2.714285714 2.718309859 2.718281718 2.718281829 2.718281828
>
>
> Now, how would you write verb cv which provides the third row of the table
> given the first two?
>
>     2 {. table
>  _1   1 1r12 1r60 1r140 1r252 1r396
>   1 1r2    1    1     1     1     1
>
>     cv 2 {. table
>  1 3 19r7 193r71 2721r1001 49171r18089 1084483r398959
>
>
> --Kip Murray
>
>
>
> --
> Sent from Gmail Mobile
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