Metallic ratios: Difference between revisions

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numeric digits digs + length(.) /*specify number of decimal digs to use*/

metals= 'platinum golden silver bronze copper nickel aluminum iron tin lead'

@decDigs= ' decimal digits past the decimal point:' /*a literal used in SAY.*/

approx= 'the approximate value reached after ' /*literals that are used for SAYs. */

!.= /*the default name for a metallic ratio*/

do k=0 to 9; !.k= word(metals, k+1) /*assign the (ten) metallic ratio names*/

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if n>0 then do; say 'the first ' n " elements are:"; say $

end /*if N is positive, then show N nums.*/

@approx= 'approximate' /*literal (1 word) that is used for SAY*/

say approx #-1 ' iterations with ' digs " decimal digits past the decimal point:"

~~say~~ format(r,,digs); ~~say~~ /*~~display~~ ~~the~~ ~~ration~~ ~~plus~~ a ~~blank~~ ~~line~~.*/

r= format(r,,digs) /*limit decimal digits for R to digs.*/

if datatype(r, 'W') then do; r= r/1; @approx= "exact"; end

say 'the' @approx "value reached after" #-1 " iterations with " digs @DecDigs

say r; say /*display the ration plus a blank line.*/

end /*m*/ /*stick a fork in it, we're all done. */</lang>

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the first 15 elements are:

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

the ~~approximate~~ value reached after 2 iterations with 32 decimal digits past the decimal point:

the exact value reached after 2 iterations with 32 decimal digits past the decimal point:

1

1.00000000000000000000000000000000

══════════════════════════ Lucas sequence for the golden ratio, where B is 1 ═══════════════════════════

the first 15 elements are:

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610

the approximate value reached after 78 iterations with 32 decimal digits past the decimal point:

1.61803398874989484820458683436564

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the first 15 elements are:

1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243

the approximate value reached after 44 iterations with 32 decimal digits past the decimal point:

2.41421356237309504880168872420970

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the first 15 elements are:

1 1 4 13 43 142 469 1549 5116 16897 55807 184318 608761 2010601 6640564

the approximate value reached after 34 iterations with 32 decimal digits past the decimal point:

3.30277563773199464655961063373525

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the first 15 elements are:

1 1 5 21 89 377 1597 6765 28657 121393 514229 2178309 9227465 39088169 165580141

the approximate value reached after 28 iterations with 32 decimal digits past the decimal point:

4.23606797749978969640917366873128

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the first 15 elements are:

1 1 6 31 161 836 4341 22541 117046 607771 3155901 16387276 85092281 441848681 2294335686

the approximate value reached after 25 iterations with 32 decimal digits past the decimal point:

5.19258240356725201562535524577016

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the first 15 elements are:

1 1 7 43 265 1633 10063 62011 382129 2354785 14510839 89419819 551029753 3395598337 20924619775

the approximate value reached after 23 iterations with 32 decimal digits past the decimal point:

6.16227766016837933199889354443272

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the first 15 elements are:

1 1 8 57 407 2906 20749 148149 1057792 7552693 53926643 385039194 2749201001 19629446201 140155324408

the approximate value reached after 22 iterations with 32 decimal digits past the decimal point:

7.14005494464025913554865124576352

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the first 15 elements are:

1 1 9 73 593 4817 39129 317849 2581921 20973217 170367657 1383914473 11241683441 91317382001 741780739449

the approximate value reached after 20 iterations with 32 decimal digits past the decimal point:

8.12310562561766054982140985597408

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the first 15 elements are:

1 1 10 91 829 7552 68797 626725 5709322 52010623 473804929 4316254984 39320099785 358197153049 3263094477226

the approximate value reached after 20 iterations with 32 decimal digits past the decimal point:

9.10977222864644365500113714088140

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