{"uid":"cap_9fsv9SL6sNdQ1yR4VHlqn","slug":"numora-continued-fraction-expansion-8521294c","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://numormo.vercel.app/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":"registry","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":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_l-CjhgWsuyun4NKCo6hnj","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the continued fraction representation of a given real number to a specified depth","exampleAgentPrompt":"Can you compute the continued fraction expansion of 3.14159265 to a depth of 8 terms?","exampleUseCases":[{"title":"Approximating irrational constants","prompt":"What is the continued fraction expansion of Euler's number e (2.718281828) to 10 terms? I want to see its partial quotients."},{"title":"Rational approximation of pi","prompt":"Give me the continued fraction representation of pi (3.14159265358979) up to depth 7 so I can find its best rational approximations."},{"title":"Analyzing the golden ratio","prompt":"Can you compute the continued fraction of 1.6180339887 to a depth of 12? I want to verify it's all 1s like the golden ratio should be."}],"resultDescription":"Returns a JSON object with success=true, a result object containing the continued fraction coefficients (partial quotients) array and related data, and a human-readable computation string describing what was computed.","failureModes":["Missing required field x returns an error","Non-numeric x value causes a validation failure","Extremely large depth values may cause timeout or memory issues","Non-finite inputs (NaN, Infinity) may return an error","Payment failure via x402 prevents the call from executing"],"whenToPreferThis":"Use this endpoint when you need a pure server-side continued fraction decomposition with no external library dependencies, especially in agent workflows that require micropayment-gated math computation. Prefer this over client-side JavaScript solutions when you need verifiable, reproducible results in a backend pipeline, or when you need a standardized API response format for downstream agents.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T12:54:03.609Z","isFirstParty":false}