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golden_ratio_approximation_output.txt
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--------------------------------
Start Of Program
--------------------------------
The following statements describe the data capacities of various primitive C++ data types:
sizeof(int) = 4 byte(s).
sizeof(unsigned int) = 4 byte(s).
sizeof(long) = 8 byte(s).
sizeof(unsigned long) = 8 byte(s).
sizeof(long long) = 8 byte(s).
sizeof(unsigned long long) = 8 byte(s).
sizeof(bool) = 1 byte(s).
sizeof(char) = 1 byte(s).
sizeof(float) = 4 byte(s).
sizeof(double) = 8 byte(s).
sizeof(long double) = 16 byte(s).
--------------------------------
The value which was entered for N is 92.
N := 92.
--------------------------------
Computing the first N Golden Ratio approximations by dividing adjacent terms of the Fibonacci Sequence:
golden_ratio_approximation(1) = fibonacci(1) / fibonacci(0).
golden_ratio_approximation(1) = 1 / 1.
golden_ratio_approximation(1) = 1.
G = golden_ratio_approximation(1) = 1.
golden_ratio_approximation(2) = fibonacci(2) / fibonacci(1).
golden_ratio_approximation(2) = 2 / 1.
golden_ratio_approximation(2) = 2.
G = golden_ratio_approximation(2) = 2.
golden_ratio_approximation(3) = fibonacci(3) / fibonacci(2).
golden_ratio_approximation(3) = 3 / 2.
golden_ratio_approximation(3) = 1.5.
G = golden_ratio_approximation(3) = 1.5.
golden_ratio_approximation(4) = fibonacci(4) / fibonacci(3).
golden_ratio_approximation(4) = 5 / 3.
golden_ratio_approximation(4) = 1.666666666666666666630526594250483185533084906637668609619140625.
G = golden_ratio_approximation(4) = 1.666666666666666666630526594250483185533084906637668609619140625.
golden_ratio_approximation(5) = fibonacci(5) / fibonacci(4).
golden_ratio_approximation(5) = 8 / 5.
golden_ratio_approximation(5) = 1.600000000000000000021684043449710088680149056017398834228515625.
G = golden_ratio_approximation(5) = 1.600000000000000000021684043449710088680149056017398834228515625.
golden_ratio_approximation(6) = fibonacci(6) / fibonacci(5).
golden_ratio_approximation(6) = 13 / 8.
golden_ratio_approximation(6) = 1.625.
G = golden_ratio_approximation(6) = 1.625.
golden_ratio_approximation(7) = fibonacci(7) / fibonacci(6).
golden_ratio_approximation(7) = 21 / 13.
golden_ratio_approximation(7) = 1.615384615384615384623724632096042341800057329237461090087890625.
G = golden_ratio_approximation(7) = 1.615384615384615384623724632096042341800057329237461090087890625.
golden_ratio_approximation(8) = fibonacci(8) / fibonacci(7).
golden_ratio_approximation(8) = 34 / 21.
golden_ratio_approximation(8) = 1.619047619047619047624210486535645259209559299051761627197265625.
G = golden_ratio_approximation(8) = 1.619047619047619047624210486535645259209559299051761627197265625.
golden_ratio_approximation(9) = fibonacci(9) / fibonacci(8).
golden_ratio_approximation(9) = 55 / 34.
golden_ratio_approximation(9) = 1.617647058823529411758328222514791150388191454112529754638671875.
G = golden_ratio_approximation(9) = 1.617647058823529411758328222514791150388191454112529754638671875.
golden_ratio_approximation(10) = fibonacci(10) / fibonacci(9).
golden_ratio_approximation(10) = 89 / 55.
golden_ratio_approximation(10) = 1.618181818181818181824095648213557296912767924368381500244140625.
G = golden_ratio_approximation(10) = 1.618181818181818181824095648213557296912767924368381500244140625.
golden_ratio_approximation(11) = fibonacci(11) / fibonacci(10).
golden_ratio_approximation(11) = 144 / 89.
golden_ratio_approximation(11) = 1.61797752808988764042751051785984373054816387593746185302734375.
G = golden_ratio_approximation(11) = 1.61797752808988764042751051785984373054816387593746185302734375.
golden_ratio_approximation(12) = fibonacci(12) / fibonacci(11).
golden_ratio_approximation(12) = 233 / 144.
golden_ratio_approximation(12) = 1.6180555555555555555073687923339775807107798755168914794921875.
G = golden_ratio_approximation(12) = 1.6180555555555555555073687923339775807107798755168914794921875.
golden_ratio_approximation(13) = fibonacci(13) / fibonacci(12).
golden_ratio_approximation(13) = 377 / 233.
golden_ratio_approximation(13) = 1.6180257510729613734147547265962430174113251268863677978515625.
G = golden_ratio_approximation(13) = 1.6180257510729613734147547265962430174113251268863677978515625.
golden_ratio_approximation(14) = fibonacci(14) / fibonacci(13).
golden_ratio_approximation(14) = 610 / 377.
golden_ratio_approximation(14) = 1.61803713527851458883928537080265641634468920528888702392578125.
G = golden_ratio_approximation(14) = 1.61803713527851458883928537080265641634468920528888702392578125.
golden_ratio_approximation(15) = fibonacci(15) / fibonacci(14).
golden_ratio_approximation(15) = 987 / 610.
golden_ratio_approximation(15) = 1.618032786885245901645387356371230680451844818890094757080078125.
G = golden_ratio_approximation(15) = 1.618032786885245901645387356371230680451844818890094757080078125.
golden_ratio_approximation(16) = fibonacci(16) / fibonacci(15).
golden_ratio_approximation(16) = 1597 / 987.
golden_ratio_approximation(16) = 1.6180344478216818642803132011209754637093283236026763916015625.
G = golden_ratio_approximation(16) = 1.6180344478216818642803132011209754637093283236026763916015625.
golden_ratio_approximation(17) = fibonacci(17) / fibonacci(16).
golden_ratio_approximation(17) = 2584 / 1597.
golden_ratio_approximation(17) = 1.61803381340012523482464745772091418984928168356418609619140625.
G = golden_ratio_approximation(17) = 1.61803381340012523482464745772091418984928168356418609619140625.
golden_ratio_approximation(18) = fibonacci(18) / fibonacci(17).
golden_ratio_approximation(18) = 4181 / 2584.
golden_ratio_approximation(18) = 1.61803405572755417958334678285581276213633827865123748779296875.
G = golden_ratio_approximation(18) = 1.61803405572755417958334678285581276213633827865123748779296875.
golden_ratio_approximation(19) = fibonacci(19) / fibonacci(18).
golden_ratio_approximation(19) = 6765 / 4181.
golden_ratio_approximation(19) = 1.618033963166706529538362013820318452417268417775630950927734375.
G = golden_ratio_approximation(19) = 1.618033963166706529538362013820318452417268417775630950927734375.
golden_ratio_approximation(20) = fibonacci(20) / fibonacci(19).
golden_ratio_approximation(20) = 10946 / 6765.
golden_ratio_approximation(20) = 1.618033998521803399858222383134176425301120616495609283447265625.
G = golden_ratio_approximation(20) = 1.618033998521803399858222383134176425301120616495609283447265625.
golden_ratio_approximation(21) = fibonacci(21) / fibonacci(20).
golden_ratio_approximation(21) = 17711 / 10946.
golden_ratio_approximation(21) = 1.6180339850173579389902567271519728819839656352996826171875.
G = golden_ratio_approximation(21) = 1.6180339850173579389902567271519728819839656352996826171875.
golden_ratio_approximation(22) = fibonacci(22) / fibonacci(21).
golden_ratio_approximation(22) = 28657 / 17711.
golden_ratio_approximation(22) = 1.618033990175597086548682501661033938944456167519092559814453125.
G = golden_ratio_approximation(22) = 1.618033990175597086548682501661033938944456167519092559814453125.
golden_ratio_approximation(23) = fibonacci(23) / fibonacci(22).
golden_ratio_approximation(23) = 46368 / 28657.
golden_ratio_approximation(23) = 1.6180339882053250515070441650777866016142070293426513671875.
G = golden_ratio_approximation(23) = 1.6180339882053250515070441650777866016142070293426513671875.
golden_ratio_approximation(24) = fibonacci(24) / fibonacci(23).
golden_ratio_approximation(24) = 75025 / 46368.
golden_ratio_approximation(24) = 1.618033988957902001375697975671386075191549025475978851318359375.
G = golden_ratio_approximation(24) = 1.618033988957902001375697975671386075191549025475978851318359375.
golden_ratio_approximation(25) = fibonacci(25) / fibonacci(24).
golden_ratio_approximation(25) = 121393 / 75025.
golden_ratio_approximation(25) = 1.618033988670443185618752490739780114381574094295501708984375.
G = golden_ratio_approximation(25) = 1.618033988670443185618752490739780114381574094295501708984375.
golden_ratio_approximation(26) = fibonacci(26) / fibonacci(25).
golden_ratio_approximation(26) = 196418 / 121393.
golden_ratio_approximation(26) = 1.6180339887802426828040947004438976364326663315296173095703125.
G = golden_ratio_approximation(26) = 1.6180339887802426828040947004438976364326663315296173095703125.
golden_ratio_approximation(27) = fibonacci(27) / fibonacci(26).
golden_ratio_approximation(27) = 317811 / 196418.
golden_ratio_approximation(27) = 1.61803398873830300689659333901460058768861927092075347900390625.
G = golden_ratio_approximation(27) = 1.61803398873830300689659333901460058768861927092075347900390625.
golden_ratio_approximation(28) = fibonacci(28) / fibonacci(27).
golden_ratio_approximation(28) = 514229 / 317811.
golden_ratio_approximation(28) = 1.61803398875432253765059564809547509867115877568721771240234375.
G = golden_ratio_approximation(28) = 1.61803398875432253765059564809547509867115877568721771240234375.
golden_ratio_approximation(29) = fibonacci(29) / fibonacci(28).
golden_ratio_approximation(29) = 832040 / 514229.
golden_ratio_approximation(29) = 1.6180339887482036212960900822821486144675873219966888427734375.
G = golden_ratio_approximation(29) = 1.6180339887482036212960900822821486144675873219966888427734375.
golden_ratio_approximation(30) = fibonacci(30) / fibonacci(29).
golden_ratio_approximation(30) = 1346269 / 832040.
golden_ratio_approximation(30) = 1.6180339887505408393887640361441526692942716181278228759765625.
G = golden_ratio_approximation(30) = 1.6180339887505408393887640361441526692942716181278228759765625.
golden_ratio_approximation(31) = fibonacci(31) / fibonacci(30).
golden_ratio_approximation(31) = 2178309 / 1346269.
golden_ratio_approximation(31) = 1.618033988749648101573667957620017432418535463511943817138671875.
G = golden_ratio_approximation(31) = 1.618033988749648101573667957620017432418535463511943817138671875.
golden_ratio_approximation(32) = fibonacci(32) / fibonacci(31).
golden_ratio_approximation(32) = 3524578 / 2178309.
golden_ratio_approximation(32) = 1.618033988749989097034702456578969531619804911315441131591796875.
G = golden_ratio_approximation(32) = 1.618033988749989097034702456578969531619804911315441131591796875.
golden_ratio_approximation(33) = fibonacci(33) / fibonacci(32).
golden_ratio_approximation(33) = 5702887 / 3524578.
golden_ratio_approximation(33) = 1.618033988749858848358274820977698027490987442433834075927734375.
G = golden_ratio_approximation(33) = 1.618033988749858848358274820977698027490987442433834075927734375.
golden_ratio_approximation(34) = fibonacci(34) / fibonacci(33).
golden_ratio_approximation(34) = 9227465 / 5702887.
golden_ratio_approximation(34) = 1.618033988749908598926523228822560440676170401275157928466796875.
G = golden_ratio_approximation(34) = 1.618033988749908598926523228822560440676170401275157928466796875.
golden_ratio_approximation(35) = fibonacci(35) / fibonacci(34).
golden_ratio_approximation(35) = 14930352 / 9227465.
golden_ratio_approximation(35) = 1.618033988749889595898205640889244705249438993632793426513671875.
G = golden_ratio_approximation(35) = 1.618033988749889595898205640889244705249438993632793426513671875.
golden_ratio_approximation(36) = fibonacci(36) / fibonacci(35).
golden_ratio_approximation(36) = 24157817 / 14930352.
golden_ratio_approximation(36) = 1.618033988749896854414909996844329498344450257718563079833984375.
G = golden_ratio_approximation(36) = 1.618033988749896854414909996844329498344450257718563079833984375.
golden_ratio_approximation(37) = fibonacci(37) / fibonacci(36).
golden_ratio_approximation(37) = 39088169 / 24157817.
golden_ratio_approximation(37) = 1.618033988749894081893114516912390854486147873103618621826171875.
G = golden_ratio_approximation(37) = 1.618033988749894081893114516912390854486147873103618621826171875.
golden_ratio_approximation(38) = fibonacci(38) / fibonacci(37).
golden_ratio_approximation(38) = 63245986 / 39088169.
golden_ratio_approximation(38) = 1.618033988749895140941796600753121992966043762862682342529296875.
G = golden_ratio_approximation(38) = 1.618033988749895140941796600753121992966043762862682342529296875.
golden_ratio_approximation(39) = fibonacci(39) / fibonacci(38).
golden_ratio_approximation(39) = 102334155 / 63245986.
golden_ratio_approximation(39) = 1.6180339887498947364259660464114176647854037582874298095703125.
G = golden_ratio_approximation(39) = 1.6180339887498947364259660464114176647854037582874298095703125.
golden_ratio_approximation(40) = fibonacci(40) / fibonacci(39).
golden_ratio_approximation(40) = 165580141 / 102334155.
golden_ratio_approximation(40) = 1.618033988749894890924775625595799510847427882254123687744140625.
G = golden_ratio_approximation(40) = 1.618033988749894890924775625595799510847427882254123687744140625.
golden_ratio_approximation(41) = fibonacci(41) / fibonacci(40).
golden_ratio_approximation(41) = 267914296 / 165580141.
golden_ratio_approximation(41) = 1.618033988749894831944177442384358300841995514929294586181640625.
G = golden_ratio_approximation(41) = 1.618033988749894831944177442384358300841995514929294586181640625.
golden_ratio_approximation(42) = fibonacci(42) / fibonacci(41).
golden_ratio_approximation(42) = 433494437 / 267914296.
golden_ratio_approximation(42) = 1.6180339887498948543871624128343000847962684929370880126953125.
G = golden_ratio_approximation(42) = 1.6180339887498948543871624128343000847962684929370880126953125.
golden_ratio_approximation(43) = fibonacci(43) / fibonacci(42).
golden_ratio_approximation(43) = 701408733 / 433494437.
golden_ratio_approximation(43) = 1.618033988749894845821965250198815056137391366064548492431640625.
G = golden_ratio_approximation(43) = 1.618033988749894845821965250198815056137391366064548492431640625.
golden_ratio_approximation(44) = fibonacci(44) / fibonacci(43).
golden_ratio_approximation(44) = 1134903170 / 701408733.
golden_ratio_approximation(44) = 1.618033988749894849074571767655328358159749768674373626708984375.
G = golden_ratio_approximation(44) = 1.618033988749894849074571767655328358159749768674373626708984375.
golden_ratio_approximation(45) = fibonacci(45) / fibonacci(44).
golden_ratio_approximation(45) = 1836311903 / 1134903170.
golden_ratio_approximation(45) = 1.618033988749894847881949377921273480751551687717437744140625.
G = golden_ratio_approximation(45) = 1.618033988749894847881949377921273480751551687717437744140625.
golden_ratio_approximation(46) = fibonacci(46) / fibonacci(45).
golden_ratio_approximation(46) = 2971215073 / 1836311903.
golden_ratio_approximation(46) = 1.6180339887498948483156302469154752543545328080654144287109375.
G = golden_ratio_approximation(46) = 1.6180339887498948483156302469154752543545328080654144287109375.
golden_ratio_approximation(47) = fibonacci(47) / fibonacci(46).
golden_ratio_approximation(47) = 4807526976 / 2971215073.
golden_ratio_approximation(47) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(47) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(48) = fibonacci(48) / fibonacci(47).
golden_ratio_approximation(48) = 7778742049 / 4807526976.
golden_ratio_approximation(48) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(48) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(49) = fibonacci(49) / fibonacci(48).
golden_ratio_approximation(49) = 12586269025 / 7778742049.
golden_ratio_approximation(49) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(49) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(50) = fibonacci(50) / fibonacci(49).
golden_ratio_approximation(50) = 20365011074 / 12586269025.
golden_ratio_approximation(50) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(50) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(51) = fibonacci(51) / fibonacci(50).
golden_ratio_approximation(51) = 32951280099 / 20365011074.
golden_ratio_approximation(51) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(51) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(52) = fibonacci(52) / fibonacci(51).
golden_ratio_approximation(52) = 53316291173 / 32951280099.
golden_ratio_approximation(52) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(52) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(53) = fibonacci(53) / fibonacci(52).
golden_ratio_approximation(53) = 86267571272 / 53316291173.
golden_ratio_approximation(53) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(53) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(54) = fibonacci(54) / fibonacci(53).
golden_ratio_approximation(54) = 139583862445 / 86267571272.
golden_ratio_approximation(54) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(54) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(55) = fibonacci(55) / fibonacci(54).
golden_ratio_approximation(55) = 225851433717 / 139583862445.
golden_ratio_approximation(55) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(55) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(56) = fibonacci(56) / fibonacci(55).
golden_ratio_approximation(56) = 365435296162 / 225851433717.
golden_ratio_approximation(56) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(56) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(57) = fibonacci(57) / fibonacci(56).
golden_ratio_approximation(57) = 591286729879 / 365435296162.
golden_ratio_approximation(57) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(57) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(58) = fibonacci(58) / fibonacci(57).
golden_ratio_approximation(58) = 956722026041 / 591286729879.
golden_ratio_approximation(58) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(58) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(59) = fibonacci(59) / fibonacci(58).
golden_ratio_approximation(59) = 1548008755920 / 956722026041.
golden_ratio_approximation(59) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(59) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(60) = fibonacci(60) / fibonacci(59).
golden_ratio_approximation(60) = 2504730781961 / 1548008755920.
golden_ratio_approximation(60) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(60) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(61) = fibonacci(61) / fibonacci(60).
golden_ratio_approximation(61) = 4052739537881 / 2504730781961.
golden_ratio_approximation(61) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(61) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(62) = fibonacci(62) / fibonacci(61).
golden_ratio_approximation(62) = 6557470319842 / 4052739537881.
golden_ratio_approximation(62) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(62) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(63) = fibonacci(63) / fibonacci(62).
golden_ratio_approximation(63) = 10610209857723 / 6557470319842.
golden_ratio_approximation(63) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(63) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(64) = fibonacci(64) / fibonacci(63).
golden_ratio_approximation(64) = 17167680177565 / 10610209857723.
golden_ratio_approximation(64) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(64) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(65) = fibonacci(65) / fibonacci(64).
golden_ratio_approximation(65) = 27777890035288 / 17167680177565.
golden_ratio_approximation(65) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(65) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(66) = fibonacci(66) / fibonacci(65).
golden_ratio_approximation(66) = 44945570212853 / 27777890035288.
golden_ratio_approximation(66) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(66) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(67) = fibonacci(67) / fibonacci(66).
golden_ratio_approximation(67) = 72723460248141 / 44945570212853.
golden_ratio_approximation(67) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(67) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(68) = fibonacci(68) / fibonacci(67).
golden_ratio_approximation(68) = 117669030460994 / 72723460248141.
golden_ratio_approximation(68) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(68) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(69) = fibonacci(69) / fibonacci(68).
golden_ratio_approximation(69) = 190392490709135 / 117669030460994.
golden_ratio_approximation(69) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(69) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(70) = fibonacci(70) / fibonacci(69).
golden_ratio_approximation(70) = 308061521170129 / 190392490709135.
golden_ratio_approximation(70) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(70) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(71) = fibonacci(71) / fibonacci(70).
golden_ratio_approximation(71) = 498454011879264 / 308061521170129.
golden_ratio_approximation(71) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(71) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(72) = fibonacci(72) / fibonacci(71).
golden_ratio_approximation(72) = 806515533049393 / 498454011879264.
golden_ratio_approximation(72) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(72) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(73) = fibonacci(73) / fibonacci(72).
golden_ratio_approximation(73) = 1304969544928657 / 806515533049393.
golden_ratio_approximation(73) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(73) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(74) = fibonacci(74) / fibonacci(73).
golden_ratio_approximation(74) = 2111485077978050 / 1304969544928657.
golden_ratio_approximation(74) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(74) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(75) = fibonacci(75) / fibonacci(74).
golden_ratio_approximation(75) = 3416454622906707 / 2111485077978050.
golden_ratio_approximation(75) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(75) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(76) = fibonacci(76) / fibonacci(75).
golden_ratio_approximation(76) = 5527939700884757 / 3416454622906707.
golden_ratio_approximation(76) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(76) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(77) = fibonacci(77) / fibonacci(76).
golden_ratio_approximation(77) = 8944394323791464 / 5527939700884757.
golden_ratio_approximation(77) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(77) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(78) = fibonacci(78) / fibonacci(77).
golden_ratio_approximation(78) = 14472334024676221 / 8944394323791464.
golden_ratio_approximation(78) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(78) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(79) = fibonacci(79) / fibonacci(78).
golden_ratio_approximation(79) = 23416728348467685 / 14472334024676221.
golden_ratio_approximation(79) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(79) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(80) = fibonacci(80) / fibonacci(79).
golden_ratio_approximation(80) = 37889062373143906 / 23416728348467685.
golden_ratio_approximation(80) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(80) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(81) = fibonacci(81) / fibonacci(80).
golden_ratio_approximation(81) = 61305790721611591 / 37889062373143906.
golden_ratio_approximation(81) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(81) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(82) = fibonacci(82) / fibonacci(81).
golden_ratio_approximation(82) = 99194853094755497 / 61305790721611591.
golden_ratio_approximation(82) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(82) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(83) = fibonacci(83) / fibonacci(82).
golden_ratio_approximation(83) = 160500643816367088 / 99194853094755497.
golden_ratio_approximation(83) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(83) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(84) = fibonacci(84) / fibonacci(83).
golden_ratio_approximation(84) = 259695496911122585 / 160500643816367088.
golden_ratio_approximation(84) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(84) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(85) = fibonacci(85) / fibonacci(84).
golden_ratio_approximation(85) = 420196140727489673 / 259695496911122585.
golden_ratio_approximation(85) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(85) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(86) = fibonacci(86) / fibonacci(85).
golden_ratio_approximation(86) = 679891637638612258 / 420196140727489673.
golden_ratio_approximation(86) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(86) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(87) = fibonacci(87) / fibonacci(86).
golden_ratio_approximation(87) = 1100087778366101931 / 679891637638612258.
golden_ratio_approximation(87) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(87) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(88) = fibonacci(88) / fibonacci(87).
golden_ratio_approximation(88) = 1779979416004714189 / 1100087778366101931.
golden_ratio_approximation(88) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(88) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(89) = fibonacci(89) / fibonacci(88).
golden_ratio_approximation(89) = 2880067194370816120 / 1779979416004714189.
golden_ratio_approximation(89) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(89) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(90) = fibonacci(90) / fibonacci(89).
golden_ratio_approximation(90) = 4660046610375530309 / 2880067194370816120.
golden_ratio_approximation(90) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(90) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(91) = fibonacci(91) / fibonacci(90).
golden_ratio_approximation(91) = 7540113804746346429 / 4660046610375530309.
golden_ratio_approximation(91) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(91) = 1.618033988749894848207210029666924810953787527978420257568359375.
golden_ratio_approximation(92) = fibonacci(92) / fibonacci(91).
golden_ratio_approximation(92) = 12200160415121876738 / 7540113804746346429.
golden_ratio_approximation(92) = 1.618033988749894848207210029666924810953787527978420257568359375.
G = golden_ratio_approximation(92) = 1.618033988749894848207210029666924810953787527978420257568359375.
--------------------------------
End Of Program
--------------------------------