{"uid":"cap_xOFtM5oLRuA33Ytzhkf3A","slug":"numora-continued-fraction-expansion-api-ad959754","name":"Numora Continued Fraction Expansion API","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://numomo.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_EVKiL7rs9oBfXaNr_wo6F","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 real number to a specified depth","exampleAgentPrompt":"What is the continued fraction expansion of 3.14159265 to a depth of 12 terms?","exampleUseCases":[{"title":"Approximating irrational numbers","prompt":"Give me the continued fraction expansion of the square root of 2 to a depth of 15 terms so I can see its partial quotients."},{"title":"Identifying rational approximations","prompt":"Compute the continued fraction of 2.718281828 to depth 10 — I want to understand how well simple fractions can approximate Euler's number."},{"title":"Number theory homework helper","prompt":"What are the continued fraction coefficients for 355 divided by 113, computed to a depth of 8 terms?"}],"resultDescription":"Returns a JSON object with a boolean success flag, a result object containing the continued fraction coefficients (partial quotients) as an array or structured representation, and a human-readable computation string describing what was computed.","failureModes":["Missing required field x returns a validation error","Non-numeric value for x causes a parsing failure","Extremely large depth values may hit computation limits or timeout","Depth of 0 or negative integers may return an error or empty result","Very large or very small floating-point values may produce precision-limited results"],"whenToPreferThis":"Choose this endpoint when you need a pure-math, dependency-free computation of a number's continued fraction expansion without building the algorithm yourself. Ideal for number theory tasks, finding rational approximations of irrationals, or educational/analytical pipelines that need fast, structured continued fraction data on demand via micropayment.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:50:40.846Z","isFirstParty":false}