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| number | math::e = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274 |
| | \(e\) number. The natural rate of exponential growth \(f(x) = f'(x) = e^x\). $$e = \lim\limits_{n \to \infty} \left(1 + \frac{1}{n}\right)^n$$
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| number | math::pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 |
| | \(\pi\) number. The ratio of a circle's circumference to its diameter. \(\pi\) radians represent a half rotation ( \(180°\)). $$\pi = \frac{C}{d} = 2 \prod _{n=1}^{\infty}{ \left(1 + \frac{1}{n}\right)^{\left(-1\right)^{n+1}} }$$
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| number | math::tau = 6.283185307179586476925286766559005768394338798750211641949889184615632812572417997256069650684234136 |
| | \(\tau\) number. The ratio of a circle's circumference to its radius. \(\tau\) radians represent a full rotation ( \(360°\)). $$\tau = \frac{C}{r} = 2\pi$$
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| number | math::sqrt2 = 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727 |
| | \(\sqrt{2}\). Square root of 2
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| number | math::sqrt3 = 1.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756 |
| | \(\sqrt{3}\). Square root of 3
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| number | math::sqrt5 = 2.2360679774997896964091736687312762354406183596115257242708972454105209256378048994144144083787822749 |
| | \(\sqrt{5}\). Square root of 5
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| number | math::sqrt6 = 2.4494897427831780981972840747058913919659474806566701284326925672509603774573150265398594331046402348 |
| | \(\sqrt{6}\). Square root of 6
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| number | math::sqrt7 = 2.6457513110645905905016157536392604257102591830824501803683344592010688232302836277603928864745436106 |
| | \(\sqrt{7}\). Square root of 7
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| number | math::sqrt8 = 2.8284271247461900976033774484193961571393437507538961463533594759814649569242140777007750686552831454 |
| | \(\sqrt{8}\). Square root of 8
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| number | math::sqrt10 = 3.1622776601683793319988935444327185337195551393252168268575048527925944386392382213442481083793002951 |
| | \(\sqrt{10}\). Square root of 10
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| number | math::sqrt11 = 3.3166247903553998491149327366706866839270885455893535970586821461164846426090438467088433991282906509 |
| | \(\sqrt{11}\). Square root of 11
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| number | math::sqrt12 = 3.4641016151377545870548926830117447338856105076207612561116139589038660338176000741622923735144971513 |
| | \(\sqrt{12}\). Square root of 12
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| number | math::sqrt13 = 3.6055512754639892931192212674704959462512965738452462127104530562271669482930104452046190820184907176 |
| | \(\sqrt{13}\). Square root of 13
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| number | math::cbrt2 = 1.2599210498948731647672106072782283505702514647015079800819751121552996765139594837293965624362550941 |
| | \(\sqrt[3]{2}\). Cube root of 2
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| number | math::cbrt3 = 1.4422495703074083823216383107801095883918692534993505775464161945416875968299973398547554797056452566 |
| | \(\sqrt[3]{3}\). Cube root of 3
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| number | math::cbrt4 = 1.5874010519681994747517056392723082603914933278998530098082857618252165056242191732735442132622209570 |
| | \(\sqrt[3]{4}\). Cube root of 4
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| number | math::cbrt5 = 1.7099759466766969893531088725438601098680551105430549243828617074442959205041732162571870100201890022 |
| | \(\sqrt[3]{5}\). Cube root of 5
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| number | math::cbrt6 = 1.8171205928321396588912117563272605024282104631412196714813342979313097394593018656471417041264170721 |
| | \(\sqrt[3]{6}\). Cube root of 6
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| number | math::cbrt7 = 1.9129311827723891011991168395487602828624390503458757662106476404472342761792307560075254414772857099 |
| | \(\sqrt[3]{7}\). Cube root of 7
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| number | math::cbrt9 = 2.0800838230519041145300568243578853863378053403732621096975910802001063113972687736060566367907574867 |
| | \(\sqrt[3]{8}\). Cube root of 9
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| number | math::cbrt10 = 2.1544346900318837217592935665193504952593449421921085824892355063464111066483408001854415035432432761 |
| | \(\sqrt[3]{10}\). Cube root of 10
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| number | math::lnhalf = -0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875 |
| | \(\ln\left(\frac{1}{2}\right)\). Natural logarithm of \(\frac{1}{2}\)
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| number | math::ln2 = 0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875 |
| | \(\ln(2)\). Natural logarithm of 2
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| number | math::ln3 = 1.0986122886681096913952452369225257046474905578227494517346943336374942932186089668736157548137320887 |
| | \(\ln(3)\). Natural logarithm of 3
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| number | math::ln4 = 1.3862943611198906188344642429163531361510002687205105082413600189867872439393894312117266539928373750 |
| | \(\ln(4)\). Natural logarithm of 4
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| number | math::ln5 = 1.6094379124341003746007593332261876395256013542685177219126478914741789877076577646301338780931796107 |
| | \(\ln(5)\). Natural logarithm of 5
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| number | math::ln10 = 2.302585092994045684017991454684364207601101488628772976033327900967572609677352480235997205089598298 |
| | \(\ln(10)\). Natural logarithm of 10
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| number | math::phi = 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374 |
| | \(\varphi = \frac{1 + \sqrt{5}}{2}\)
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| number | math::psi = -0.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374 |
| | \(\psi = \frac{1 - \sqrt{5}}{2} = - \varphi^{-1}\)
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| number | math::invphi = -psi |
| | \(\varphi^{-1} = \frac{-1 + \sqrt{5}}{2} = -\psi\)
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| number | math::invpsi = -phi |
| | \(\psi^{-1} = \frac{-1 - \sqrt{5}}{2} = -\varphi\)
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| number | math::golden = phi |
| | Golden ratio \(\varphi\). 1° metallic mean. \(\frac{1 + \sqrt{5}}{2}\). Continued fraction \([1;\overline{1}]\) and positive solution to the equation \(x^2 = x + 1\).
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| number | math::silver = 2.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727 |
| | Silver ratio. 2° metallic mean. \(1 + \sqrt{2}\). Continued fraction \([2;\overline{2}]\) and positive solution to the equation \(x^2 = 2x + 1\).
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| number | math::bronze = 3.302775637731994646559610633735247973125648286922623106355226528113583474146505222602309541009245359 |
| | Bronze ratio. 3° metallic mean. \(\frac{3 + \sqrt{13}}{2}\). Continued fraction \([3;\overline{3}]\) and positive solution to the equation \(x^2 = 3x + 1\).
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| number | math::copper = 4.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275 |
| | Copper ratio. 4° metallic mean. \(2 + \sqrt{5}\). Continued fraction \([4;\overline{4}]\) and positive solution to the equation \(x^2 = 4x + 1\).
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| number | math::nickel = 5.192582403567252015625355245770164778147560080822394418840194335008322981413829346438316890839917742 |
| | Nickel ratio. 5° metallic mean. \(\frac{5 + \sqrt{29}}{2}\). Continued fraction \([5;\overline{5}]\) and positive solution to the equation \(x^2 = 5x + 1\).
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| number | math::super_golden = 1.4655712318767680266567312252199391080255775684722857016431831112492629966850178404781258011949092701 |
| | Supergolden ratio. Real solution to the equation \(x^3 = x^2 + 1\).
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| number | math::plastic = 1.324717957244746025960908854478097340734404056901733364534015050302827851245547594054699347981787280 |
| | Plastic ratio. Real solution to the equation \(x^3 = x + 1\).
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| number | math::tribonacci = 1.839286755214161132551852564653286600424178746097592246778758639404203222081966425738435419428307014 |
| | Tribonacci constant. Real solution to the equation \(x^3 = x^2 + x + 1\).
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| number | math::lemniscate = 2.622057554292119810464839589891119413682754951431623162816821703800790587070414250230295532961429093 |
| | \(\varpi\) Lemniscate constant. The ratio of a Bernoulli's lemniscate's perimeter to its diameter. $$\varpi = \frac{p}{d} = 2 \prod _{n=1}^{\infty}{ \left(1 + \frac{1}{2n}\right)^{\left(-1\right)^{n+1}} }$$
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| number | math::parabolic = 2.295587149392638074034298049189490387597832203638583483929975346644109662684133126684094426237897616 |
| | \(P\) Universal parabolic constant. The ratio of a parabola's latus rectum arc to its semi latus rectum. $$P = \sqrt{2} + \ln{\left(1 + \sqrt{2}\right)}$$
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| number | math::gauss = 0.8346268416740731862814297327990468089939930134903470024498273701036819927095264118696911603512753241 |
| | \(G\) Gauss constant. $$G = \frac{\varpi}{\pi}$$
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| number | math::golden_angle = 2.399963229728653322231555506633613853124999011058115042935112750731307338239438790779962060660583964 |
| | Golden angle in radians \(g\). The smaller angle that sections a circles's circumference according to the golden ratio \(\varphi\).
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| number | math::euler_gamma = 0.57721566490153286060651209 |
| | Euler–Mascheroni constant.
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| number | math::catalan = 0.9159655941772190150546035149323841107741934 |
| | Catalan constant.
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| number | math::twopi = tau |
| | \(2\pi = \tau\)
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| number | math::fourpi = 12.56637061435917295385057353311801153678867759750042328389977836923126562514483599451213930136846827 |
| | \(4\pi\)
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| number | math::halfpi = 1.570796326794896619231321691639751442098584699687552910487472296153908203143104499314017412671058534 |
| | \(\frac{\pi}{2}\)
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| number | math::quartpi = 0.7853981633974483096156608458198757210492923498437764552437361480769541015715522496570087063355292670 |
| | \(\frac{\pi}{4}\)
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| number | math::invpi = 0.3183098861837906715377675267450287240689192914809128974953346881177935952684530701802276055325061719 |
| | \(\frac{1}{\pi}\)
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| number | math::twoinvpi = 0.6366197723675813430755350534900574481378385829618257949906693762355871905369061403604552110650123438 |
| | \(\frac{2}{\pi}\)
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| number | math::fourinvpi = 1.273239544735162686151070106980114896275677165923651589981338752471174381073812280720910422130024688 |
| | \(\frac{4}{\pi}\)
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| number | math::inv2pi = 0.1591549430918953357688837633725143620344596457404564487476673440588967976342265350901138027662530860 |
| | \(\frac{1}{2\pi}\)
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| number | math::inv4pi = 0.07957747154594766788444188168625718101722982287022822437383367202944839881711326754505690138312654298 |
| | \(\frac{1}{4\pi}\)
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| number | math::sqrtpi = 1.772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665 |
| | \(\sqrt{\pi}\)
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| number | math::sqrt2pi = 2.506628274631000502415765284811045253006986740609938316629923576342293654607841974946595838378057266 |
| | \(\sqrt{2\pi}\)
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| number | math::sqrt4pi = 3.544907701811032054596334966682290365595098912244774256427615579705822569182064362749901313477089331 |
| | \(\sqrt{4\pi}\)
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| number | math::sqrthalfpi = 1.253314137315500251207882642405522626503493370304969158314961788171146827303920987473297919189028633 |
| | \(\sqrt{\frac{\pi}{2}}\)
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| number | math::invsqrt2 = 0.7071067811865475244008443621048490392848359376884740365883398689953662392310535194251937671638207864 |
| | \(\frac{1}{\sqrt{2}}\)
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| number | math::invsqrtpi = 0.5641895835477562869480794515607725858440506293289988568440857217106424684414934144867436602021073634 |
| | \(\frac{1}{\sqrt{\pi}}\)
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| number | math::invsqrt2pi = 0.3989422804014326779399460599343818684758586311649346576659258296706579258993018385012523339073069364 |
| | \(\frac{1}{\sqrt{2\pi}}\)
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| number | math::lnpi = 1.144729885849400174143427351353058711647294812915311571513623071472137769884826079783623270275489708 |
| | \(\ln{(\pi)}\). Natural logarithm of \(\pi\)
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| number | math::ln2pi = 1.837877066409345483560659472811235279722794947275566825634303080965531391854520795389486597271908395 |
| | \(\ln{(2\pi)}\). Natural logarithm of \(2\pi\)
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| number | math::ln4pi = 2.531024246969290792977891594269411847798295081635822079754983090458925013824215510995349924268327083 |
| | \(\ln{(4\pi)}\). Natural logarithm of \(4\pi\)
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1.10.0