Standard Tier Module
Mathematical Coincidence Checker
Paste two expressions (e.g.
See it run - a worked example, 100% in this browser tab
What it is
Paste two expressions (e.g. "pi^4 + pi^5" and "e^6") and see the TRUTH to arbitrary precision. The honest antidote to viral fake math-coincidence posts: it computes each side with BigInt fixed-point arithmetic (not doubles), then reports the REAL agreement - how many significant figures actually match, a log-space view, and an openly-disclosed heuristic surprise score. Ships a gallery of famous coincidences with their real numbers, several of which debunk the clickbait version (pi^4 + pi^5 = e^6 agrees to about 7 figures, NOT 12), one deep Ramanujan almost-integer that needs the extra precision to see, and one TRUE identity to prove the tool tells a genuine identity apart from a near-miss. A near-miss is not a hidden law.
Honest scope
Deterministic and citation-backed: every figure is exact arithmetic or a cited rule. Any year- or jurisdiction-indexed value is a confirmable input, never an eternal hardcode. This is a computation tool, not professional (legal, tax, medical, or financial) advice - confirm against the controlling authority for your context.
Authorities cited
- Weisstein, Eric W. "Almost Integer." MathWorld. https://mathworld.wolfram.com/AlmostInteger.html - near-integer log-combinations of constants are expected by density.
- Weisstein, Eric W. "Ramanujan Constant." MathWorld. exp(pi*sqrt(163)) = 262537412640768743.99999999999925... , a famous almost-integer requiring high precision to reveal.
- Baker, A. (1975). Transcendental Number Theory. Cambridge Univ. Press. (Gelfond-Schneider: e^pi is transcendental; pi and e are believed algebraically independent.)
- pi and e reference digits: OEIS A000796 (pi) and A001113 (e). ln 2: A002162. sqrt 2: A002193.
- Euler-Mascheroni constant gamma (stored 100-digit literal): OEIS A001620. Catalan constant G (stored literal): OEIS A006752.
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Run it on your own data
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