secretsanta
Take a stand.
And Now, For Something Incompletely Sane
fi It's never been done before.
It should never be done again.
Ladies and gentlemen of the blogosphere, I give you:
THE ENTIRE FIBONACCI SEQUENCE.
As it reaches theoretical infinity at about the fourteen-hundred-and-seventy-eighth term, this is only the first 1477.
But first, a little history.
The Fibonacci sequence comes from a problem in a book by Leonardo Bigollo: If one pair of rabbits makes a new pair each month, which are ready to procreate within a month, how many functioning pairs will there be each month?
As confusing a statement as that is (and I'm sure I made it more difficult), you simply start with 1 and 1, add them, get 2, add that to 1, get 3, add that to 2 (5), add that 5 to the 3 (8), and so on, and so forth.
Each term is the sum of the two before it. Fairly simple, eh? XP
And now, the moment you all should be dreading, and most definitely creating the easiest huge-butt entry ever...
THE SEQUINS. Er, SEQUENCE.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099, 53316291173, 86267571272, 139583862445, 225851433717, 365435296162, 591286729879, 956722026041, 1548008755920, 2504730781961, 4052739537881, 6557470319842, 10610209857723, 17167680177565, 27777890035288, 44945570212853, 72723460248141, 117669030460994, 190392490709135, 308061521170129, 498454011879264, 806515533049393, 1304969544928657, 2111485077978050, 3416454622906707, 5527939700884757, 8944394323791464, 14472334024676220, 23416728348467684, 37889062373143900, 61305790721611580, 99194853094755490, 160500643816367070, 259695496911122560, 420196140727489660, 679891637638612200, 1100087778366101900, 1779979416004714000, 2880067194370816000, 4660046610375530000, 7540113804746346000, 12200160415121877000, 19740274219868226000, 31940434634990100000, 51680708854858330000, 83621143489848430000, 135301852344706760000, 218922995834555200000, 354224848179262000000, 573147844013817200000, 927372692193079200000, 1.5005205362068963e+21, 2.4278932283999755e+21, 3.9284137646068717e+21, 6.356306993006848e+21, 1.028472075761372e+22, 1.6641027750620568e+22, 2.6925748508234288e+22, 4.356677625885486e+22, 7.049252476708914e+22, 1.14059301025944e+23, 1.8455182579303315e+23, 2.9861112681897715e+23, 4.831629526120103e+23, 7.817740794309875e+23, 1.2649370320429978e+24, 2.0467111114739851e+24, 3.3116481435169827e+24, 5.358359254990968e+24, 8.670007398507951e+24, 1.402836665349892e+25, 2.269837405200687e+25, 3.6726740705505786e+25, 5.942511475751265e+25, 9.615185546301844e+25, 1.555769702205311e+26, 2.5172882568354952e+26, 4.0730579590408064e+26, 6.590346215876301e+26, 1.0663404174917107e+27, 1.7253750390793408e+27, 2.791715456571052e+27, 4.5170904956503927e+27, 7.308805952221445e+27, 1.1825896447871837e+28, 1.9134702400093282e+28, 3.096059884796512e+28, 5.009530124805841e+28, 8.105590009602353e+28, 1.3115120134408193e+29, 2.1220710144010545e+29, 3.4335830278418734e+29, 5.5556540422429276e+29, 8.989237070084801e+29, 1.454489111232773e+30, 2.353412818241253e+30, 3.807901929474026e+30, 6.161314747715279e+30, 9.969216677189305e+30, 1.6130531424904583e+31, 2.6099748102093888e+31, 4.223027952699847e+31, 6.8330027629092365e+31, 1.1056030715609085e+32, 1.788903347851832e+32, 2.8945064194127406e+32, 4.683409767264573e+32, 7.577916186677313e+32, 1.2261325953941887e+33, 1.98392421406192e+33, 3.2100568094561087e+33, 5.193981023518028e+33, 8.404037832974137e+33, 1.3598018856492165e+34, 2.20020566894663e+34, 3.5600075545958467e+34, 5.760213223542477e+34, 9.320220778138323e+34, 1.50804340016808e+35, 2.4400654779819122e+35, 3.9481088781499925e+35, 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1.8691056866520183e+251, 3.024276529568676e+251, 4.893382216220695e+251, 7.917658745789371e+251, 1.2811040962010066e+252, 2.0728699707799435e+252, 3.35397406698095e+252, 5.4268440377608935e+252, 8.780818104741844e+252, 1.4207662142502737e+253, 2.298848024724458e+253, 3.719614238974731e+253, 6.01846226369919e+253, 9.738076502673921e+253, 1.575653876637311e+254, 2.549461526904703e+254, 4.125115403542014e+254, 6.674576930446717e+254, 1.079969233398873e+255, 1.7474269264435447e+255, 2.827396159842418e+255, 4.574823086285962e+255, 7.40221924612838e+255, 1.1977042332414342e+256, 1.937926157854272e+256, 3.135630391095706e+256, 5.073556548949979e+256, 8.209186940045685e+256, 1.3282743488995665e+257, 2.149193042904135e+257, 3.4774673918037014e+257, 5.626660434707837e+257, 9.104127826511539e+257, 1.4730788261219376e+258, 2.3834916087730915e+258, 3.856570434895029e+258, 6.24006204366812e+258, 1.0096632478563149e+259, 1.633669452223127e+259, 2.643332700079442e+259, 4.277002152302569e+259, 6.920334852382011e+259, 1.119733700468458e+260, 1.811767185706659e+260, 2.9315008861751174e+260, 4.7432680718817765e+260, 7.674768958056894e+260, 1.2418037029938671e+261, 2.0092805987995564e+261, 3.2510843017934235e+261, 5.26036490059298e+261, 8.511449202386403e+261, 1.3771814102979384e+262, 2.2283263305365785e+262, 3.6055077408345165e+262, 5.833834071371095e+262, 9.439341812205611e+262, 1.5273175883576705e+263, 2.4712517695782316e+263, 3.998569357935902e+263, 6.469821127514133e+263, 1.0468390485450036e+264, 1.6938211612964169e+264, 2.7406602098414205e+264, 4.434481371137837e+264, 7.175141580979258e+264, 1.1609622952117095e+265, 1.8784764533096354e+265, 3.0394387485213448e+265, 4.9179152018309806e+265, 7.957353950352325e+265, 1.2875269152183306e+266, 2.083262310253563e+266, 3.3707892254718936e+266, 5.454051535725457e+266, 8.82484076119735e+266, 1.4278892296922807e+267, 2.3103733058120157e+267, 3.7382625355042964e+267, 6.048635841316312e+267, 9.786898376820609e+267, 1.5835534218136922e+268, 2.5622432594957532e+268, 4.145796681309445e+268, 6.708039940805197e+268, 1.0853836622114642e+269, 1.756187656291984e+269, 2.841571318503448e+269, 4.597758974795432e+269, 7.43933029329888e+269, 1.2037089268094313e+270, 1.9476419561393193e+270, 3.151350882948751e+270, 5.0989928390880705e+270, 8.250343722036821e+270, 1.3349336561124892e+271, 2.159968028316171e+271, 3.4949016844286605e+271, 5.654869712744832e+271, 9.149771397173493e+271, 1.4804641109918323e+272, 2.3954412507091816e+272, 3.875905361701014e+272, 6.271346612410196e+272, 1.014725197411121e+273, 1.6418598586521405e+273, 2.6565850560632613e+273, 4.298444914715402e+273, 6.955029970778663e+273, 1.1253474885494065e+274, 1.8208504856272727e+274, 2.946197974176679e+274, 4.7670484598039515e+274, 7.713246433980631e+274, 1.2480294893784583e+275, 2.0193541327765214e+275, 3.2673836221549794e+275, 5.286737754931501e+275, 8.55412137708648e+275, 1.3840859132017982e+276, 2.2394980509104464e+276, 3.6235839641122446e+276, 5.863082015022691e+276, 9.486665979134936e+276, 1.5349747994157627e+277, 2.4836413973292562e+277, 4.0186161967450185e+277, 6.502257594074275e+277, 1.0520873790819292e+278, 1.7023131384893566e+278, 2.754400517571286e+278, 4.4567136560606425e+278, 7.211114173631929e+278, 1.1667827829692572e+279, 1.8878942003324502e+279, 3.054676983301707e+279, 4.942571183634157e+279, 7.997248166935864e+279, 1.2939819350570022e+280, 2.0937067517505885e+280, 3.3876886868075906e+280, 5.4813954385581795e+280, 8.869084125365771e+280, 1.435047956392395e+281, 2.321956368928972e+281, 3.757004325321367e+281, 6.078960694250339e+281, 9.835965019571706e+281, 1.5914925713822045e+282, 2.575089073339375e+282, 4.1665816447215794e+282, 6.741670718060955e+282, 1.0908252362782534e+283, 1.7649923080843489e+283, 2.855817544362602e+283, 4.620809852446951e+283, 7.476627396809553e+283, 1.2097437249256505e+284, 1.957406464606606e+284, 3.1671501895322564e+284, 5.124556654138862e+284, 8.291706843671119e+284, 1.3416263497809983e+285, 2.1707970341481102e+285, 3.5124233839291085e+285, 5.683220418077219e+285, 9.195643802006327e+285, 1.4878864220083546e+286, 2.4074508022089873e+286, 3.895337224217342e+286, 6.302788026426329e+286, 1.019812525064367e+287, 1.650091327707e+287, 2.6699038527713674e+287, 4.3199951804783675e+287, 6.989899033249734e+287, 1.1309894213728102e+288, 1.8299793246977837e+288, 2.960968746070594e+288, 4.790948070768378e+288, 7.751916816838971e+288, 1.254286488760735e+289, 2.029478170444632e+289, 3.283764659205367e+289, 5.313242829649999e+289, 8.597007488855366e+289, 1.3910250318505364e+290, 2.250725780736073e+290, 3.641750812586609e+290, 5.892476593322682e+290, 9.53422740590929e+290, 1.5426703999231972e+291, 2.496093140514126e+291, 4.038763540437323e+291, 6.53485668095145e+291, 1.0573620221388773e+292, 1.7108476902340223e+292, 2.7682097123728997e+292, 4.479057402606922e+292, 7.247267114979821e+292, 1.1726324517586743e+293, 1.8973591632566564e+293, 3.0699916150153306e+293, 4.967350778271987e+293, 8.037342393287317e+293, 1.3004693171559304e+294, 2.104203556484662e+294, 3.4046728736405925e+294, 5.508876430125255e+294, 8.913549303765847e+294, 1.4422425733891103e+295, 2.333597503765695e+295, 3.7758400771548054e+295, 6.109437580920501e+295, 9.885277658075306e+295, 1.5994715238995807e+296, 2.5879992897071113e+296, 4.187470813606692e+296, 6.775470103313804e+296, 1.0962940916920496e+297, 1.77384110202343e+297, 2.870135193715479e+297, 4.643976295738909e+297, 7.514111489454388e+297, 1.2158087785193297e+298, 1.9672199274647685e+298, 3.1830287059840983e+298, 5.150248633448867e+298, 8.333277339432965e+298, 1.3483525972881832e+299, 2.1816803312314797e+299, 3.530032928519663e+299, 5.7117132597511424e+299, 9.241746188270806e+299, 1.495345944802195e+300, 2.4195205636292755e+300, 3.9148665084314706e+300, 6.334387072060746e+300, 1.0249253580492217e+301, 1.6583640652552963e+301, 2.6832894233045177e+301, 4.341653488559814e+301, 7.0249429118643315e+301, 1.1366596400424146e+302, 1.839153931228848e+302, 2.9758135712712625e+302, 4.81496750250011e+302, 7.790781073771373e+302, 1.2605748576271483e+303, 2.0396529650042858e+303, 3.300227822631434e+303, 5.3398807876357195e+303, 8.640108610267153e+303, 1.3979989397902873e+304, 2.2620098008170023e+304, 3.66000874060729e+304, 5.922018541424292e+304, 9.582027282031581e+304, 1.5504045823455874e+305, 2.5086073105487455e+305, 4.059011892894333e+305, 6.567619203443078e+305, 1.062663109633741e+306, 1.7194250299780488e+306, 2.78208813961179e+306, 4.501513169589839e+306, 7.283601309201629e+306, 1.1785114478791467e+307, 1.9068715787993096e+307, 3.085383026678456e+307, 4.992254605477766e+307, 8.077637632156222e+307, 1.3069892237633987e+308, Infinity.
Now, don't go thinking I went through and added all those.
I just whipped up me a lil' applet that generated 'em for me.
I'm not THAT bored. XD
Each and every one of those numbers ties in to the enormous mathematical discovery I made the other day. When any one of those is divided by the term before it, it gives a number around 1.618033989. (More precision shows up as one progresses through the sequence.)
The weird thing is, if you take a rectangle and square off the inside: (not to scale)
__________________
| |__| |
| |__|___|
| | |
|x x| |x
| | |
|______X____|__y___|
The new rectangle bound by x and y is precisely the same proportions as the original, larger rectangle. This process may then continue on and in, infinitely. This can be expressed in ratio form as:
X = Y
X+Y = X
A little cross-multiplication yields the equation
X2 = Y(X+Y).
If we substitute X as 1 (to find the 1:? ratio), we have
1 = Y + Y2 , or Y2 + Y - 1 = 0.
This quadratic equation solves to -0.5 + √(5)/2, or .618033989.
Referring to the original diagram, we plug this in for Y and get a ratio of 1:1.618033989, also known as the Golden Ratio or Golden Section. This number is exactly the same as that derived from the division of adjacent terms in the Fibonacci sequence. It is often referred to as Φ (Phi).
Weird, eh? XD
And I'm not even getting into the Golden Spiral, which is inscribed into the squares and rectangles created by the golden ratio. It can also be graphed with either the parametric equations
X = ΦTcos T
Y = ΦTsin T
or the polar equation
r(θ) = Φθ.
Using some simple calculus, I have proved both of these graphing methods to be true to the golden ratio, thus creating valid spirals.
However, to get these equations I only guessed-and-checked using my knowledge of exponential decay and growth of periodic functions, such as trigonometrics.
I'm not entirely sure how to straight-up derive them yet.
But they work, suckas.
For the bottom line that everyone inevitably skips to, math can do some creepy stuff, man.
THE END.
...for now...
(DISCLAIMER: I don't care if anyone actually reads this, I just wanted to fully document my discovery. So there. Ha.)
It should never be done again.
Ladies and gentlemen of the blogosphere, I give you:
THE ENTIRE FIBONACCI SEQUENCE.
As it reaches theoretical infinity at about the fourteen-hundred-and-seventy-eighth term, this is only the first 1477.
But first, a little history.
The Fibonacci sequence comes from a problem in a book by Leonardo Bigollo: If one pair of rabbits makes a new pair each month, which are ready to procreate within a month, how many functioning pairs will there be each month?
As confusing a statement as that is (and I'm sure I made it more difficult), you simply start with 1 and 1, add them, get 2, add that to 1, get 3, add that to 2 (5), add that 5 to the 3 (8), and so on, and so forth.
Each term is the sum of the two before it. Fairly simple, eh? XP
And now, the moment you all should be dreading, and most definitely creating the easiest huge-butt entry ever...
THE SEQUINS. Er, SEQUENCE.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099, 53316291173, 86267571272, 139583862445, 225851433717, 365435296162, 591286729879, 956722026041, 1548008755920, 2504730781961, 4052739537881, 6557470319842, 10610209857723, 17167680177565, 27777890035288, 44945570212853, 72723460248141, 117669030460994, 190392490709135, 308061521170129, 498454011879264, 806515533049393, 1304969544928657, 2111485077978050, 3416454622906707, 5527939700884757, 8944394323791464, 14472334024676220, 23416728348467684, 37889062373143900, 61305790721611580, 99194853094755490, 160500643816367070, 259695496911122560, 420196140727489660, 679891637638612200, 1100087778366101900, 1779979416004714000, 2880067194370816000, 4660046610375530000, 7540113804746346000, 12200160415121877000, 19740274219868226000, 31940434634990100000, 51680708854858330000, 83621143489848430000, 135301852344706760000, 218922995834555200000, 354224848179262000000, 573147844013817200000, 927372692193079200000, 1.5005205362068963e+21, 2.4278932283999755e+21, 3.9284137646068717e+21, 6.356306993006848e+21, 1.028472075761372e+22, 1.6641027750620568e+22, 2.6925748508234288e+22, 4.356677625885486e+22, 7.049252476708914e+22, 1.14059301025944e+23, 1.8455182579303315e+23, 2.9861112681897715e+23, 4.831629526120103e+23, 7.817740794309875e+23, 1.2649370320429978e+24, 2.0467111114739851e+24, 3.3116481435169827e+24, 5.358359254990968e+24, 8.670007398507951e+24, 1.402836665349892e+25, 2.269837405200687e+25, 3.6726740705505786e+25, 5.942511475751265e+25, 9.615185546301844e+25, 1.555769702205311e+26, 2.5172882568354952e+26, 4.0730579590408064e+26, 6.590346215876301e+26, 1.0663404174917107e+27, 1.7253750390793408e+27, 2.791715456571052e+27, 4.5170904956503927e+27, 7.308805952221445e+27, 1.1825896447871837e+28, 1.9134702400093282e+28, 3.096059884796512e+28, 5.009530124805841e+28, 8.105590009602353e+28, 1.3115120134408193e+29, 2.1220710144010545e+29, 3.4335830278418734e+29, 5.5556540422429276e+29, 8.989237070084801e+29, 1.454489111232773e+30, 2.353412818241253e+30, 3.807901929474026e+30, 6.161314747715279e+30, 9.969216677189305e+30, 1.6130531424904583e+31, 2.6099748102093888e+31, 4.223027952699847e+31, 6.8330027629092365e+31, 1.1056030715609085e+32, 1.788903347851832e+32, 2.8945064194127406e+32, 4.683409767264573e+32, 7.577916186677313e+32, 1.2261325953941887e+33, 1.98392421406192e+33, 3.2100568094561087e+33, 5.193981023518028e+33, 8.404037832974137e+33, 1.3598018856492165e+34, 2.20020566894663e+34, 3.5600075545958467e+34, 5.760213223542477e+34, 9.320220778138323e+34, 1.50804340016808e+35, 2.4400654779819122e+35, 3.9481088781499925e+35, 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3.6235839641122446e+276, 5.863082015022691e+276, 9.486665979134936e+276, 1.5349747994157627e+277, 2.4836413973292562e+277, 4.0186161967450185e+277, 6.502257594074275e+277, 1.0520873790819292e+278, 1.7023131384893566e+278, 2.754400517571286e+278, 4.4567136560606425e+278, 7.211114173631929e+278, 1.1667827829692572e+279, 1.8878942003324502e+279, 3.054676983301707e+279, 4.942571183634157e+279, 7.997248166935864e+279, 1.2939819350570022e+280, 2.0937067517505885e+280, 3.3876886868075906e+280, 5.4813954385581795e+280, 8.869084125365771e+280, 1.435047956392395e+281, 2.321956368928972e+281, 3.757004325321367e+281, 6.078960694250339e+281, 9.835965019571706e+281, 1.5914925713822045e+282, 2.575089073339375e+282, 4.1665816447215794e+282, 6.741670718060955e+282, 1.0908252362782534e+283, 1.7649923080843489e+283, 2.855817544362602e+283, 4.620809852446951e+283, 7.476627396809553e+283, 1.2097437249256505e+284, 1.957406464606606e+284, 3.1671501895322564e+284, 5.124556654138862e+284, 8.291706843671119e+284, 1.3416263497809983e+285, 2.1707970341481102e+285, 3.5124233839291085e+285, 5.683220418077219e+285, 9.195643802006327e+285, 1.4878864220083546e+286, 2.4074508022089873e+286, 3.895337224217342e+286, 6.302788026426329e+286, 1.019812525064367e+287, 1.650091327707e+287, 2.6699038527713674e+287, 4.3199951804783675e+287, 6.989899033249734e+287, 1.1309894213728102e+288, 1.8299793246977837e+288, 2.960968746070594e+288, 4.790948070768378e+288, 7.751916816838971e+288, 1.254286488760735e+289, 2.029478170444632e+289, 3.283764659205367e+289, 5.313242829649999e+289, 8.597007488855366e+289, 1.3910250318505364e+290, 2.250725780736073e+290, 3.641750812586609e+290, 5.892476593322682e+290, 9.53422740590929e+290, 1.5426703999231972e+291, 2.496093140514126e+291, 4.038763540437323e+291, 6.53485668095145e+291, 1.0573620221388773e+292, 1.7108476902340223e+292, 2.7682097123728997e+292, 4.479057402606922e+292, 7.247267114979821e+292, 1.1726324517586743e+293, 1.8973591632566564e+293, 3.0699916150153306e+293, 4.967350778271987e+293, 8.037342393287317e+293, 1.3004693171559304e+294, 2.104203556484662e+294, 3.4046728736405925e+294, 5.508876430125255e+294, 8.913549303765847e+294, 1.4422425733891103e+295, 2.333597503765695e+295, 3.7758400771548054e+295, 6.109437580920501e+295, 9.885277658075306e+295, 1.5994715238995807e+296, 2.5879992897071113e+296, 4.187470813606692e+296, 6.775470103313804e+296, 1.0962940916920496e+297, 1.77384110202343e+297, 2.870135193715479e+297, 4.643976295738909e+297, 7.514111489454388e+297, 1.2158087785193297e+298, 1.9672199274647685e+298, 3.1830287059840983e+298, 5.150248633448867e+298, 8.333277339432965e+298, 1.3483525972881832e+299, 2.1816803312314797e+299, 3.530032928519663e+299, 5.7117132597511424e+299, 9.241746188270806e+299, 1.495345944802195e+300, 2.4195205636292755e+300, 3.9148665084314706e+300, 6.334387072060746e+300, 1.0249253580492217e+301, 1.6583640652552963e+301, 2.6832894233045177e+301, 4.341653488559814e+301, 7.0249429118643315e+301, 1.1366596400424146e+302, 1.839153931228848e+302, 2.9758135712712625e+302, 4.81496750250011e+302, 7.790781073771373e+302, 1.2605748576271483e+303, 2.0396529650042858e+303, 3.300227822631434e+303, 5.3398807876357195e+303, 8.640108610267153e+303, 1.3979989397902873e+304, 2.2620098008170023e+304, 3.66000874060729e+304, 5.922018541424292e+304, 9.582027282031581e+304, 1.5504045823455874e+305, 2.5086073105487455e+305, 4.059011892894333e+305, 6.567619203443078e+305, 1.062663109633741e+306, 1.7194250299780488e+306, 2.78208813961179e+306, 4.501513169589839e+306, 7.283601309201629e+306, 1.1785114478791467e+307, 1.9068715787993096e+307, 3.085383026678456e+307, 4.992254605477766e+307, 8.077637632156222e+307, 1.3069892237633987e+308, Infinity.
Now, don't go thinking I went through and added all those.
I just whipped up me a lil' applet that generated 'em for me.
I'm not THAT bored. XD
Each and every one of those numbers ties in to the enormous mathematical discovery I made the other day. When any one of those is divided by the term before it, it gives a number around 1.618033989. (More precision shows up as one progresses through the sequence.)
The weird thing is, if you take a rectangle and square off the inside: (not to scale)
__________________
| |__| |
| |__|___|
| | |
|x x| |x
| | |
|______X____|__y___|
The new rectangle bound by x and y is precisely the same proportions as the original, larger rectangle. This process may then continue on and in, infinitely. This can be expressed in ratio form as:
X = Y
X+Y = X
A little cross-multiplication yields the equation
X2 = Y(X+Y).
If we substitute X as 1 (to find the 1:? ratio), we have
1 = Y + Y2 , or Y2 + Y - 1 = 0.
This quadratic equation solves to -0.5 + √(5)/2, or .618033989.
Referring to the original diagram, we plug this in for Y and get a ratio of 1:1.618033989, also known as the Golden Ratio or Golden Section. This number is exactly the same as that derived from the division of adjacent terms in the Fibonacci sequence. It is often referred to as Φ (Phi).
Weird, eh? XD
And I'm not even getting into the Golden Spiral, which is inscribed into the squares and rectangles created by the golden ratio. It can also be graphed with either the parametric equations
X = ΦTcos T
Y = ΦTsin T
or the polar equation
r(θ) = Φθ.
Using some simple calculus, I have proved both of these graphing methods to be true to the golden ratio, thus creating valid spirals.
However, to get these equations I only guessed-and-checked using my knowledge of exponential decay and growth of periodic functions, such as trigonometrics.
I'm not entirely sure how to straight-up derive them yet.
But they work, suckas.
For the bottom line that everyone inevitably skips to, math can do some creepy stuff, man.
THE END.
...for now...
(DISCLAIMER: I don't care if anyone actually reads this, I just wanted to fully document my discovery. So there. Ha.)
Because She Cooks
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