求问：用于无限计算π的Python函数所采用的数学公式
Hey there! Let's figure out this π code mystery together. It's wild how many ways there are to calculate π—156 total, as you said—and infinite-iteration methods are some of the most fascinating ones. Since you haven't shared the actual Python code snippet yet, I can walk you through the most common infinite-series formulas used for π calculation, along with their typical code traits, so you can match them to your code:
1. Leibniz Series
π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ... (and so on, alternating signs)
- Code telltale signs: You'll see a loop that alternates adding and subtracting the reciprocal of odd numbers (like
1/(2*n + 1)). Heads up though—this series converges super slowly; you'd need millions of terms to get even a handful of accurate π digits.
2. Machin's Formula
π/4 = 4*arctan(1/5) - arctan(1/239)
- Code telltale signs: There will almost certainly be a helper function to calculate arctangent (usually via its own Taylor series or iterative approximation). This one converges way faster than Leibniz and was a go-to for π calculations back in the day.
3. Chudnovsky Algorithm
1/π = (√10005)/4270934400 * Σ(n=0 to ∞) [(6n)!(13591409+545140134n)] / [(3n)!(n!)3*(-640320)(3n)]
- Code telltale signs: This is the heavy hitter for fast π calculation. You'll see big integer operations, factorial calculations (or optimized factorial shortcuts), and each iteration adds roughly 14 new accurate digits of π. Most high-performance π tools use this.
4. BBP Formula (Bailey–Borwein–Plouffe)
π = Σ(k=0 to ∞) [1/(16^k)] * (4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6))
- Code telltale signs: This is unique because it lets you calculate specific digits of π (hexadecimal, usually) without computing all the preceding ones. The code will involve powers of 16 and four separate terms per iteration that get scaled and summed.
If you can share the actual Python code you found, I can pinpoint exactly which formula it's using and break down how the code maps to the math step by step!
内容的提问来源于stack exchange，提问作者Tolga183
