This is a specific mathematical proof, dating in some form back to antiquity, that the fraction 22 over 7 is greater than the value of pi. A later version of the proof, requiring only elementary calculus, has drawn particular attention for its mathematical elegance and its connection to the theory of how well irrational numbers can be approximated by fractions, with the mathematician Stephen Lucas calling it one of the more beautiful results related to approximating pi. The point of the proof is not simply to establish that 22 over 7 exceeds pi, since that fact follows immediately once pi decimal value is known to be approximately 3.14159, but rather to demonstrate the inequality using far less computation than would be needed to establish pi decimal expansion directly.
Facts
StatementThe integral from 0 to 1 of x^4(1-x)^4/(1+x^2) dx is positive and equals 22/7 minus pi, so 22/7 exceeds pi. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Proof that 22/7 exceeds pi, Wikipedia
Proof section
0<∫₀¹ x⁴(1-x)⁴/(1+x²) dx = 22/7-π
Proof section, historical note
The proof first devised by British electrical engineer Donald Percy Dalzell (1898-1988) in 1944
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