🏺 埃及分数计算器Egyptian Fraction Calculator
用斐波那契–西尔维斯特贪心算法把分数 a/b 拆成互不相同的单位分数之和（如 4/13 = 1/4 + 1/18 + 1/468），大于 1 的分数先取出整数部分；用大整数精确计算并验算。Split a fraction a/b into a sum of distinct unit fractions with the Fibonacci–Sylvester greedy algorithm (e.g. 4/13 = 1/4 + 1/18 + 1/468), taking out the whole part first for fractions above 1. Big-integer arithmetic keeps it exact, and the sum is checked.
使用说明与常见问题How-to & FAQ
「埃及分数计算器」是什么？What is the Egyptian Fraction Calculator tool?
用斐波那契–西尔维斯特贪心算法把分数 a/b 拆成互不相同的单位分数之和（如 4/13 = 1/4 + 1/18 + 1/468），大于 1 的分数先取出整数部分；用大整数精确计算并验算。Split a fraction a/b into a sum of distinct unit fractions with the Fibonacci–Sylvester greedy algorithm (e.g. 4/13 = 1/4 + 1/18 + 1/468), taking out the whole part first for fractions above 1. Big-integer arithmetic keeps it exact, and the sum is checked.
如何使用「埃及分数计算器」？How do I use the Egyptian Fraction Calculator tool?
在「埃及分数计算器」中，填写「分子 a」、「分母 b」等参数，结果会随输入实时计算并显示在下方。In the Egyptian Fraction Calculator: Fill in "Numerator a", "Denominator b"; results are recalculated instantly as you type.
什么是埃及分数？What is an Egyptian fraction?
古埃及人把分数写成互不相同的单位分数（分子为 1）之和，例如 3/4 = 1/2 + 1/4。每个正有理数都能这样表示，而且表示法不唯一。Ancient Egyptians wrote fractions as sums of distinct unit fractions (numerator 1), such as 3/4 = 1/2 + 1/4. Every positive rational number can be written this way, and not in just one way.
贪心算法怎么做？How does the greedy algorithm work?
每一步取不超过剩余部分的最大单位分数 1/⌈b/a⌉，减掉后继续，直到余数为 0（斐波那契 1202 年提出，西尔维斯特 1880 年证明一定会结束）。它不一定给出项数最少或分母最小的表示，分母有时会变得非常大，例如 5/121 的最后一项有 25 位。At each step take the largest unit fraction not exceeding what's left, 1/⌈b/a⌉, subtract it and repeat until nothing remains (Fibonacci, 1202; Sylvester proved in 1880 that it always ends). It doesn't always give the fewest terms or smallest denominators, and denominators can grow huge — the last term of 5/121 has 25 digits.
有什么限制？Are there limits?
分子和分母须为 1 到 10¹² 的整数。为防止浏览器卡死，展开最多 30 项，单个分母最多约 2,000 位；超出时会提示结果已截断。Numerator and denominator must be whole numbers from 1 to 10¹². To keep the browser responsive the expansion stops at 30 terms or a denominator of about 2,000 digits, with a warning that it was truncated.
计算精度如何？How precise are the results?
「埃及分数计算器」全程使用精确的大整数（BigInt）运算，不经过浮点近似，所以每一项的分母和最后的求和验算都是精确的。The Egyptian Fraction Calculator computes entirely with exact big-integer (BigInt) arithmetic — no floating-point approximation — so every denominator and the final sum check are exact.
「埃及分数计算器」免费吗？需要注册吗？Is the Egyptian Fraction Calculator free? Do I need an account?
「埃及分数计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Egyptian Fraction Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.