{"uid":"cap_XWV6D4C9PM5T5qpfPvqB_","slug":"numora-continued-fraction-expansion-f1c5d7a0","name":"Numora Continued Fraction Expansion","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numorapoi.orbonomy.xyz/api/number/continued-fraction","method":"POST","headers":{},"bodySchema":{"type":"object","required":["x"],"properties":{"x":{"type":"number"},"depth":{"type":"integer"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.03/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.03","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.03","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_rGhXY3io3FEhCSZ6cIPWw","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.03","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the continued fraction representation of a real number to a specified depth","exampleAgentPrompt":"What is the continued fraction expansion of 3.14159265358979 to depth 10?","exampleUseCases":null,"resultDescription":"Returns a JSON object with success flag, a result object containing the continued fraction coefficients (the partial quotients) for the input number, and a human-readable computation string describing what was calculated.","failureModes":["Missing required field 'x' returns validation error","Non-numeric value for x causes schema rejection","Payment not included or insufficient triggers 402 Payment Required","Extremely large depth values may cause timeout or truncation","Negative depth integer may return error or default behavior"],"whenToPreferThis":"Use this endpoint when you need the exact continued fraction decomposition of a real number — for example to find rational approximations, analyze the periodicity of quadratic irrationals, or study the number-theoretic properties of a value. Prefer this over general-purpose math libraries when you want a zero-dependency micropayment API call without spinning up a compute environment.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T00:43:32.615Z","isFirstParty":false}