如何计算Continued Fraction
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Continued fractions express numbers as nested fractions: x = a₀ + 1/(a₁ + 1/(a₂ + ...)); useful for rational approximations.
分步指南
- 1Input decimal or fraction
- 2Generate continued fraction expansion
- 3Calculate convergents (increasingly accurate approximations)
例题解析
输入
Pi ≈ 3.14159
结果
CF = [3; 7, 15, 1, 292, ...], convergent 355/113 ≈ 3.14159 (extremely accurate)
常见错误注意事项
- ✕Terminating before accurate enough
- ✕Confusing with decimal fractions
常见问题
Why continued fractions?
Best rational approximations; pi convergents used in engineering.
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