balanced-numbers.json

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9382 bytes, as of the version from 2026-10-27 01:07 (current). Recorded here, not run.

{
  "0": {
    "number": "0"
  },
  "sqrt(2)": {
    "number": "0.7139722140219396136290864445540744192342533790480201933811346920912513446963638290807381025179679407",
    "param-latex": "$\\sqrt{2}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "2": {
    "number": "0.3434156783636982421953008159580684568865418122025247675792689204494767226635844744099255427628399726",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(6)": {
    "number": "0.6289396585401117728184466575898857835874301338936196998637469273323838305080700340663560956522276463",
    "param-latex": "$\\sqrt{6}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(8)": {
    "number": "0.3879689926370840423209953257839401150018733339393444152152127756611889373032020868579735141144298043",
    "param-latex": "$\\sqrt{8}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(10)": {
    "number": "0.6003623872514163464779588105343786203600684863438193020577173987264135270737114835527168827742940624",
    "param-latex": "$\\sqrt{10}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(12)": {
    "number": "0.4083013319319968570379499122099649942978256588378485617160563073987127479917838335555500988093646671",
    "param-latex": "$\\sqrt{12}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(14)": {
    "number": "0.5849422386136541946868267916839699121961824205281904499357795383487733235914215476562012442766841036",
    "param-latex": "$\\sqrt{14}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "4": {
    "number": "0.4205157542469284244453431407430670454544259302864021845554070415663643292186552030928116047704261302",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(18)": {
    "number": "0.5749567208876167799931603659147529666048873790377506055172862103995629335255432934215582284021834083",
    "param-latex": "$\\sqrt{18}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(20)": {
    "number": "0.4288773650821645290696683451403967023839926508586979752457802425779177214065409837210050940399018833",
    "param-latex": "$\\sqrt{20}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(22)": {
    "number": "0.5678215816628569341150982648203626622941759718028589348540872907775714240624968279649289143067358422",
    "param-latex": "$\\sqrt{22}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(24)": {
    "number": "0.4350593471289110965049178989093155295073294649502747174279547759943820670655513323157249296453731065",
    "param-latex": "$\\sqrt{24}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(26)": {
    "number": "0.5623977800501405327456753471952112038685322742519742929638418685727195406822260146952488455276330837",
    "param-latex": "$\\sqrt{26}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(28)": {
    "number": "0.4398683042084832856073014250571730763360476471780328030302272835044351972717823267421940526678955363",
    "param-latex": "$\\sqrt{28}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(30)": {
    "number": "0.5580956171490010672785171184348441602130753347160347476803279836081552584665452675365664513631747049",
    "param-latex": "$\\sqrt{30}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(32)": {
    "number": "0.4437468760363048524201111322404436987723092003962895510148114661587833289900239189764184624205075748",
    "param-latex": "$\\sqrt{32}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(34)": {
    "number": "0.5545753847289788636977468556487570590149290201425765148013079619708216148319234519267217496410269646",
    "param-latex": "$\\sqrt{34}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "6": {
    "number": "0.4469607612369302776239202878407789191062455470831531284957966923293313013942181764645977320961782948",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(38)": {
    "number": "0.5516258390307205989322703581893023061982391186240658964944412567888346734474818098199650297421255342",
    "param-latex": "$\\sqrt{38}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "sqrt(40)": {
    "number": "0.4496803282386250622499088906389720100133757472398374737225140262248550140297305944553645525759220908",
    "param-latex": "$\\sqrt{40}$",
    "comment": "The argument is specified by CITE{argument-selection}."
  },
  "1": {
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4382591473903547660767566966251526374937865724524165673344073262658059382112998771734606741411548457"
  },
  "sqrt(3)": {
    "param-latex": "$\\sqrt{3}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5173051218636263692865268341903558004908133781956532570786082207998195831074112372552057974477605276"
  },
  "sqrt(5)": {
    "param-latex": "$\\sqrt{5}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4913925389676197244898030041321475744945508032451102284731633810662074267559242146613869308212418187"
  },
  "sqrt(7)": {
    "param-latex": "$\\sqrt{7}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5053187400454302931243238882155469598340715189174239330898240136406119544839547009484947263853019955"
  },
  "3": {
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4963129989673750360976122652991121038564670345832411060867864797255800015977318607582479312692337430"
  },
  "sqrt(11)": {
    "param-latex": "$\\sqrt{11}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5027439987156609692253284278140212642193522490029064823362984686378981537916294828492829177479882176"
  },
  "sqrt(13)": {
    "param-latex": "$\\sqrt{13}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.4978571112962106184277526444403698652816675246600007998938489752127164164510747353592429112831382469"
  },
  "sqrt(15)": {
    "param-latex": "$\\sqrt{15}$",
    "comment": "The other coordinate at an axis-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.5017326018844271236175481903437571521237023306669420539000452089034640536155130360410471239129964652"
  },
  "sqrt(1/2)": {
    "param-latex": "$\\sqrt{1/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.1771219699791394139583863788921418849485832604950947617630038904394809417932690012063221991163564907"
  },
  "1*sqrt(2/pi)": {
    "param-latex": "$1\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.2475582876516108426099050144052166355678178520505607433029455487383778682978538406490113083526747232"
  },
  "sqrt(3/2)": {
    "param-latex": "$\\sqrt{3/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.6416988905685876555386160768886808197986603362322564210426885087684141849303626152728441350292573586"
  },
  "2*sqrt(2/pi)": {
    "param-latex": "$2\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.6421187357445146953318002859307074484957773008887281670851493375808421115681758776309379344297222532"
  },
  "sqrt(5/2)": {
    "param-latex": "$\\sqrt{5/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.6528316466610344384981099211184946284077567439713134421345108170156171348770379077471801522012700249"
  },
  "3*sqrt(2/pi)": {
    "param-latex": "$3\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.6172135970241896124400929011078847161701404510433965710768269050712555055410471690686542627762873057"
  },
  "sqrt(7/2)": {
    "param-latex": "$\\sqrt{7/2}$",
    "comment": "A diagonal-tangent point of Cornu's spiral; see CITE{balanced-cornu}.",
    "number": "0.3920993952502802379065070005989045767225246071522609779108043953645512623032170588527719323598715926"
  },
  "4*sqrt(2/pi)": {
    "param-latex": "$4\\sqrt{2/\\pi}$",
    "comment": "A unit-quadratic-phase reference; see CITE{balanced-quadratic}.",
    "number": "0.5961265594980171973648629640371573960022357548787927199570128930780753240127125371453396930460013208"
  },
  "1/2": {
    "comment": "A bounded arc-length reference; see CITE{balanced-simple}.",
    "number": "0.06473243285999927761148051223061476765072591849351249278758894564828689767392197589943934122214205058"
  }
}