Math
Continued fractions
Build continued fractions term by term and inspect convergents, denominators and approximation errors for famous constants and custom decimals.
Try this
Expand π, e, the golden ratio, √2 or a positive decimal into convergents. Each row adds one partial quotient. Computation uses double precision and stops after ten terms or a near-zero remainder; late terms are numerical approximations.
Equations used in the module
Equations x = a₀ + 1/(a₁ + 1/(a₂ + …)) pₙ = aₙpₙ₋₁ + pₙ₋₂; qₙ = aₙqₙ₋₁ + qₙ₋₂ pₙqₙ₋₁ − pₙ₋₁qₙ = (−1)ⁿ⁻¹ π = [3;7,15,1,…] → 3, 22/7, 333/106, 355/113, …
