-------------------------------- Start Of Program -------------------------------- The following statements describe the data capacities of various primitive C++ data types: sizeof(int) = 4 byte(s). sizeof(unsigned long long int) = 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 45. N := 45. -------------------------------- 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) = 1.6666666666666667406815349750104360282421112060546875. 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) = 1.600000000000000088817841970012523233890533447265625. 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) = 1.615384615384615418776093065389432013034820556640625. 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) = 1.619047619047619068766152850002981722354888916015625. 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) = 1.617647058823529437887600579415448009967803955078125. 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) = 1.61818181818181816566948327817954123020172119140625. 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) = 1.617977528089887595541540576959960162639617919921875. 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) = 1.6180555555555555802271783250034786760807037353515625. 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) = 1.6180257510729614267575016128830611705780029296875. 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) = 1.6180371352785145599995075826882384717464447021484375. 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) = 1.6180327868852459882731409379630349576473236083984375. 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) = 1.6180344478216819315008478952222503721714019775390625. 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) = 1.6180338134001253092009164902265183627605438232421875. 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) = 1.6180340557275540991355455844313837587833404541015625. 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) = 1.618033963166706445946374515187926590442657470703125. 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) = 1.6180339985218032961000744762714020907878875732421875. 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) = 1.61803398501735795633749148692004382610321044921875. 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) = 1.61803399017559712547154049389064311981201171875. 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) = 1.6180339882053249578319764623302035033702850341796875. 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) = 1.6180339889579020695720146250096149742603302001953125. 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) = 1.6180339886704431240360690935631282627582550048828125. 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) = 1.618033988780242626859262600191868841648101806640625. 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) = 1.6180339887383030639256276117521338164806365966796875. 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) = 1.61803398875432247194794399547390639781951904296875. 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) = 1.6180339887482035887700249077170155942440032958984375. 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) = 1.6180339887505408302814657872659154236316680908203125. 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) = 1.6180339887496482109696671614074148237705230712890625. 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) = 1.618033988749989049438227084465324878692626953125. 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) = 1.618033988749858931299741016118787229061126708984375. 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) = 1.618033988749908669291244223131798207759857177734375. 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) = 1.618033988749889573455220670439302921295166015625. 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) = 1.6180339887498969009271831964724697172641754150390625. 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) = 1.61803398874989401434731917106546461582183837890625. 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) = 1.6180339887498951245703437962220050394535064697265625. 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) = 1.6180339887498946804811339461593888700008392333984375. 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) = 1.6180339887498949025257388711906969547271728515625. 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) = 1.6180339887498949025257388711906969547271728515625. 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) = 1.6180339887498949025257388711906969547271728515625. 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) = 1.6180339887498949025257388711906969547271728515625. 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) = 1.6180339887498949025257388711906969547271728515625. 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) = 1.6180339887498949025257388711906969547271728515625. -------------------------------- End Of Program --------------------------------