Metallic ratios: Difference between revisions
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the approximate value reached after 615 iterations with 256 decimal digits past the decimal point: |
the approximate value reached after 615 iterations with 256 decimal digits past the decimal point: |
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1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144 |
1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144 |
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</pre> |
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=={{header|Sidef}}== |
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<lang ruby>func metalic(f, places = 32) { |
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1..Inf -> reduce {|t,n| |
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var r = (f(n+1)/f(n)).round(-places) |
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return(n, r.as_dec(places + r.abs.int.len)) if (r == t) |
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r |
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} |
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} |
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for k,v in (%w(Platinum Golden Silver Bronze Copper Nickel Aluminum Iron Tin Lead).kv) { |
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next if (k == 0) # undefined ratio |
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say "Lucas sequence U_n(#{k},-1) for #{v} ratio" |
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var f = {|n| lucasu(k, -1, n) } |
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say ("First 15 elements: ", 15.of(f).join(', ')) |
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var (n, r) = metalic(f) |
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say "Approximated value: #{r} reached after #{n} iterations" |
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say '' |
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} |
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with (metalic({|n| fib(n) }, 256)) {|n,v| |
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say "Golden ratio to 256 decimal places:" |
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say "Approximated value: #{v}" |
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say "Reached after #{n} iterations" |
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}</lang> |
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{{out}} |
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<pre> |
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Lucas sequence U_n(1,-1) for Golden ratio |
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First 15 elements: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 |
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Approximated value: 1.61803398874989484820458683436564 reached after 79 iterations |
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Lucas sequence U_n(2,-1) for Silver ratio |
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First 15 elements: 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782 |
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Approximated value: 2.4142135623730950488016887242097 reached after 45 iterations |
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Lucas sequence U_n(3,-1) for Bronze ratio |
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First 15 elements: 0, 1, 3, 10, 33, 109, 360, 1189, 3927, 12970, 42837, 141481, 467280, 1543321, 5097243 |
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Approximated value: 3.30277563773199464655961063373525 reached after 33 iterations |
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Lucas sequence U_n(4,-1) for Copper ratio |
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First 15 elements: 0, 1, 4, 17, 72, 305, 1292, 5473, 23184, 98209, 416020, 1762289, 7465176, 31622993, 133957148 |
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Approximated value: 4.23606797749978969640917366873128 reached after 28 iterations |
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Lucas sequence U_n(5,-1) for Nickel ratio |
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First 15 elements: 0, 1, 5, 26, 135, 701, 3640, 18901, 98145, 509626, 2646275, 13741001, 71351280, 370497401, 1923838285 |
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Approximated value: 5.19258240356725201562535524577016 reached after 26 iterations |
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Lucas sequence U_n(6,-1) for Aluminum ratio |
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First 15 elements: 0, 1, 6, 37, 228, 1405, 8658, 53353, 328776, 2026009, 12484830, 76934989, 474094764, 2921503573, 18003116202 |
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Approximated value: 6.16227766016837933199889354443272 reached after 23 iterations |
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Lucas sequence U_n(7,-1) for Iron ratio |
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First 15 elements: 0, 1, 7, 50, 357, 2549, 18200, 129949, 927843, 6624850, 47301793, 337737401, 2411463600, 17217982601, 122937341807 |
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Approximated value: 7.14005494464025913554865124576352 reached after 21 iterations |
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Lucas sequence U_n(8,-1) for Tin ratio |
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First 15 elements: 0, 1, 8, 65, 528, 4289, 34840, 283009, 2298912, 18674305, 151693352, 1232221121, 10009462320, 81307919681, 660472819768 |
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Approximated value: 8.12310562561766054982140985597408 reached after 20 iterations |
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Lucas sequence U_n(9,-1) for Lead ratio |
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First 15 elements: 0, 1, 9, 82, 747, 6805, 61992, 564733, 5144589, 46866034, 426938895, 3889316089, 35430783696, 322766369353, 2940328107873 |
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Approximated value: 9.1097722286464436550011371408814 reached after 19 iterations |
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Golden ratio to 256 decimal places: |
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Approximated value: 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144 |
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Reached after 616 iterations |
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</pre> |
</pre> |
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