$$\phi={1+\sqrt5\over2}=1+{1\over\phi}$$
$$-\phi-1={1-\sqrt5\over2}=-{1\over\phi}$$
Binet's formula $$B_n={({1+\sqrt5\over2})^n-({1-\sqrt5\over2})^n\over\sqrt5}$$
$$\phi^2=\phi+1$$
$$\phi=1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over{1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over1+{1\over._{._.}}}}}}}}}}}}}}}}}}}}}}}}}}$$
Something about $$\phi$$ is $$[1,1,1,1,1,1,1,1...]$$ (Please tell me what it is if you know)
By the way, if you want to make these LaTeX expressions, check out latexeditor.lagrida.com. Just make sure you wrap what you make in double-dollar-signs like this:
$$expression here$$
Not seen that symbol before - where is used? - what sort of discussions does it come up in?
It's phi, the golden ratio. The $$n^{th}$$ Fibonacci number divided by the $$(n-1)^{th}$$ approaches $$\phi$$ as $$n$$ approaches $$\infty$$, which is written mathematically as (I think) $$\lim_{n\to\infty}{F_n\over F_{n-1}}=\phi$$
(I'm not sure how to get the "$$n\to\infty$$" to be under the "$$\lim$$".)
$$\phi\approx$$
1.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137484754088075386891752126633862223536931793180060766726354433389086595939582905638322661319928290267880675208766892501711696207032221043216269548626296313614438149758701220340805887954454749246185695364864449241044320771344947049565846788509874339442212544877066478091588460749988712400765217057517978834166256249407589069704000281210427621771117778053153171410117046665991466979873176135600670874807101317952368942752194843530567830022878569978297783478458782289110976250030269615617002504643382437764861028383126833037242926752631165339247316711121158818638513316203840052221657912866752946549068113171599343235973494985090409476213222981017261070596116456299098162905552085247903524060201727997471753427775927786256194320827505131218156285512224809394712341451702237358057727861600868838295230459264787801788992199027077690389532196819861514378031499741106926088674296226757560523172777520353613936210767389376455606060592165894667595519004005559089502295309423124823552122124154440064703405657347976639723949499465845788730396230903750339938562102423690251386804145779956981224457471780341731264532204163972321340444494873023154176768937521030687378803441700939544096279558986787232095124268935573097045095956844017555198819218020640529055189349475926007348522821010881946445442223188913192946896220023014437702699230078030852611807545192887705021096842493627135925187607778846658361502389134933331223105339232136243192637289106705033992822652635562090297986424727597725655086154875435748264718141451270006023890162077732244994353088999095016803281121943204819643876758633147985719113978153978074761507722117508269458639320456520989698555678141069683728840587461033781054443909436835835813811311689938555769754841491445341509129540700501947754861630754226417293946803673198058618339183285991303960720144559504497792120761247856459161608370594987860069701894098864007644361709334172709191433650137157660114803814306262380514321173481510055901345610118007905063814215270930858809287570345050780814545881990633612982798141174533927312080928972792221329806429468782427487401745055406778757083237310975915117762978443284747908176518097787268416117632503861211291436834376702350371116330725869883258710336322238109809012110198991768414917512331340152733843837234500934786049792945991582201258104598230925528721241370436149102054718554961180876426576511060545881475604431784798584539731286301625448761148520217064404111660766950597757832570395110878230827106478939021115691039276838453863333215658296597731034360323225457436372041244064088826737584339536795931232213437320995749889469956564736007295999839128810319742631251797141432012311279551894778172691415891177991956481255800184550656329528598591000908621802977563789259991649946428193022293552346674759326951654214021091363018194722707890122087287361707348649998156255472811373479871656952748900814438405327483781378246691744422963491470815700735254570708977267546934382261954686153312095335792380146092735102101191902183606750973089575289577468142295433943854931553396303807291691758461014609950550648036793041472365720398600735507609023173125016132048435836481770484818109916024425232716721901893345963786087875287017393593030133590112371023917126590470263494028307668767436386513271062803231740693173344823435645318505813531085497333507599667787124490583636754132890862406324563953572125242611702780286560432349428373017255744058372782679960317393640132876277012436798311446436947670531272492410471670013824783128656506493434180390041017805339505877245866557552293915823970841772983372823115256926092995942240000560626678674357923972454084817651973436265268944888552720274778747335983536727761407591712051326934483752991649980936024617844267572776790019191907038052204612324823913261043271916845123060236278935454324617699757536890417636502547851382463146583363833760235778992672988632161858395903639981838458276449124598093704305555961379734326134830494949686810895356963482817812886253646084203394653819441945714266682371839491832370908574850266568039897440662105360306400260817112665995419936873160945722888109207788227720363668448153256172841176909792666655223846883113718529919216319052015686312228207155998764684235520592853717578076560503677313097519122397388722468258057159744574048429878073522159842667662578077062019430400542550158312503017534094117191019298903844725033298802450143679684416947959545304591031381162187045679978663661746059570003445970113525181346006565535203478881174149941274826415213556776394039071038708818233806803350038046800174808220591096844202644640218770534010031802881664415309139394815640319282278548241451050318882518997007486228794215589574282021665706218809057808805032467699129728721038707369740643566745892025865657397856085956653410703599783204463363464854894976638853510455272982422906998488536968280464597457626514343590509383212437433338705166571490059071056702488798580437181512610044038148804072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I remember now 
What is this symbol???
See warped_wart_wars reply three posts back
It's somewhat like $$\pi$$, for example it's irrational, etc.
φ = 1.618033988749895
How I did it.
$$\phi$$ is only approximately equal to that.
It's infinitely long, but you got the first few digits.
And doesn't repeat. Which means it's irrational.
Okay..? I know that, I feel like you're just showing off right now...
I just like math. I knew you almost definitely knew, but I like giving mathematical facts.
$$\phi$$ is also called "the golden ratio" because ancient Greek architects thought that a rectangle whose sides are proportional to 1 and $$\phi$$ was the most aesthetically pleasing shape for a building, or a room in a building. WIkipedia says that people used to think the Parthenon was built in a golden ratio, but more recent scholarship has debunked that idea.
But that post was a bit far up. Plus you gave a link to Wikipedia.
To your whole post:
There are other ratios like the golden ratio, collectively called "metallic ratios". (Numberphile has a video on them.)
Sigh.
Why the sigh? (BTW that rhymes.)