{"uid":"cap_XFGlX6ZNPoIWVW4ROLLBC","slug":"numora-continued-fraction-expansion-2e616a40","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://numormor.netlify.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":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":{"p10Cents":"10.0000","medianCents":"10.0000","p90Cents":"10.0000","minCents":"10.0000","maxCents":"10.0000","p95Cents":"10.0000","sampleCount":1,"varies":false,"failureChargeRate":1},"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_bnm0lDUi5SdXdG4i5EPrW","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","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":"Can you compute the continued fraction expansion of 3.14159265358979 to a depth of 10 terms?","exampleUseCases":[{"title":"Verify rational approximations for engineering tolerances","prompt":"I need to find the best simple fraction approximations of 2.71828182846 for a mechanical design. Can you compute the continued fraction to depth 8 so I can check the convergents?"},{"title":"Analyze mathematical constants for number theory research","prompt":"Help me understand the structure of the golden ratio. What's the continued fraction representation of 1.618033988749895 at depth 12?"},{"title":"Simplify complex decimals into exact fractional forms","prompt":"I have a measurement of 1.41421356237 from an experiment. Can you compute its continued fraction expansion to depth 7 to see if it matches any known mathematical constants?"}],"resultDescription":"Returns a JSON object with success flag, a result object containing the continued fraction coefficients (partial quotients) for the input number at the requested depth, and a human-readable computation description string.","failureModes":["Missing required field x returns validation error","Non-numeric value for x causes parse error","Depth too large may cause timeout or truncation","Payment failure via x402 micropayment returns 402 status","Negative or zero depth may return error or default behavior"],"whenToPreferThis":"Use this endpoint when you need the exact continued fraction decomposition of a specific real number for number theory work, approximation analysis, or studying convergents. Ideal when you need a pure math computation with no external library dependencies and are comfortable with x402 micropayments on Base.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T00:40:17.270Z","isFirstParty":false}