[Jprogramming] Continued Fraction Challenge

[Rob Hodgkinson]

Agree, very nice solution Raul.

> On 13 Mar 2016, at 10:02 AM, Kip Murray <thekipmurray at gmail.com> wrote:
> 
> Very nice, Raul!  Much shorter than my Rube Goldberg approach.  --Kip
> 
> On Saturday, March 12, 2016, Raul Miller <rauldmiller at gmail.com> wrote:
> 
>>   cv=: ([: (+`%/) 1 }.,)\@|:
>> 
>> I hope this helps...
>> 
>> --
>> Raul
>> 
>> 
>> On Sat, Mar 12, 2016 at 1:21 PM, Kip Murray <thekipmurray at gmail.com
>> <javascript:;>> wrote:
>>> Here you go:
>>> 
>>>    nume =: 1 , 1 % 4x * _1 + 4 * [: *:@>:@i. <:
>>> 
>>>    dene =: 1 1r2 , 1 $~ _2 + ]
>>> 
>>> I think I got those from Abramowitz and Stegun.
>>> 
>>>   (_1 , nume 6),: dene 7
>>> _1   1 1r12 1r60 1r140 1r252 1r396
>>>   1 1r2    1    1     1     1     1
>>> 
>>> --Kip
>>> 
>>> 
>>> On Saturday, March 12, 2016, Raul Miller <rauldmiller at gmail.com
>> <javascript:;>> wrote:
>>> 
>>>> How do you compute the first two rows?
>>>> 
>>>> Thanks,
>>>> 
>>>> --
>>>> Raul
>>>> 
>>>> On Saturday, March 12, 2016, Kip Murray <thekipmurray at gmail.com
>> <javascript:;>
>>>> <javascript:;>> 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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>>> 
>>> 
>>> 
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> 
> 
> 
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