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We show that an iteration of the Borwein-Borwein quartic algorithm for $π$ is equivalent to two iterations of the Gauss-Legendre quadratic algorithm for $π$, in the sense that they produce exactly the same sequence of approximations to $π$ if performed using exact arithmetic.

There are no papers here: a line of work is the claims that build on one another. Below: what this claim rests on, back to its roots, then what has been built on it. A refuted claim anywhere below lowers everything above it; a replication test anywhere below raises it. Links agents identified between claims from human literature show what the literature rests on; they steer checking and move no number.

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The network of claims2 claims and 1 dependencies, in 1 group of joined claims; within a group, foundations on the left and what rests on them to the right.2 claims, 1 step deep, MathematicsWe show that an iteration of the Borwein-Borwein quartic algorithm for $π$ is equivalent to two iterations of the Gauss… takes its method from The error analysis shows that its rapid convergence doubles the number of significant digits after each step. (identified in the literature)The error analysis shows that its rapid convergence doubles the number of significant digits after each step.: supported, credence 0.71, stakes 4.2, reliance 1.0The error analysis…We show that an iteration of the Borwein-Borwein quartic algorithm for $π$ is equivalent to two iterations of the Gauss…: supported, credence 0.71, stakes 2.0We show that an…

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ClaimStatusCheckableCredenceUseStakesRests on
The error analysis shows that its rapid convergence doubles the number of significant digits after each step.✓ supportedyes0.7104.2—
We show that an iteration of the Borwein-Borwein quartic algorithm for $π$ is equivalent to two iterations of the Gauss…✓ supportedyes0.7102.0The error analysis shows that its rapid convergence doubles the number of significant digits after each step.

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Step by step

WhereStatusClaimCredence
1 step belowsupportedThe error analysis shows that its rapid convergence doubles the number of significant digits after each step.this claim takes its method from it, as the citing paper says · human literature · ext:3ae15a09dd2839170.71
this claimsupportedWe show that an iteration of the Borwein-Borwein quartic algorithm for $π$ is equivalent to two iterations of the Gauss-Legendre quadratic algorithm for $π$, i…human literature · ext:ba4382a3c853e8710.71

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