φ 计算黄金比例 φ 的位数Calculate Phi Digits
用 φ=(1+√5)/2 和大整数开方精确计算 φ 的小数点后位数。本地处理。可设置「小数位数」。Compute decimal places of φ=(1+√5)/2 with an exact big-integer square root. Processed locally. Settings: Decimal places.
使用说明与常见问题How-to & FAQ
「计算黄金比例 φ 的位数」是什么？What is the Calculate Phi Digits tool?
用 φ=(1+√5)/2 和大整数开方精确计算 φ 的小数点后位数。本地处理。可设置「小数位数」。Compute decimal places of φ=(1+√5)/2 with an exact big-integer square root. Processed locally. Settings: Decimal places.
如何使用「计算黄金比例 φ 的位数」？How do I use the Calculate Phi Digits tool?
在「计算黄金比例 φ 的位数」中，按需设置「小数位数」，结果会实时显示在下方，点击「复制结果」即可复制。In the Calculate Phi Digits: Adjust "Decimal places"; the result appears below instantly — click "Copy result" to copy it.
显示的小数是四舍五入还是截断？Are the digits rounded or truncated?
截断。本页用大整数平方根精确计算 φ = (1 + √5) / 2，再直接截取所需的位数，所以每一位都与 φ 的真实小数展开一致，最后一位不会因四舍五入而进位。最多 5000 位小数。Truncated. φ = (1 + √5) / 2 is computed exactly with a big-integer square root and then cut at the requested length, so every digit matches the true expansion and the last digit is never rounded up. Up to 5,000 decimal places.
输入和输出是什么样的？What does the input and output look like?
例如在「计算黄金比例 φ 的位数」中把「小数位数」设为 10，输出为：1.6180339887。For example, in the Calculate Phi Digits with "Decimal places" set to 10, the output is: 1.6180339887.
有哪些选项可以调整？What options can I adjust?
「计算黄金比例 φ 的位数」的设置：「小数位数」默认 50。每次生成结果都按当前设置处理。Settings in the Calculate Phi Digits — "Decimal places" default 50. The result always uses the current settings.
计算精度如何？How precise are the results?
「计算黄金比例 φ 的位数」中的整数都用大整数（BigInt）精确计算，不经过浮点，所以再长的项也不会丢失位数；输入超出页面说明的范围时会给出提示，而不是悄悄截断。Integers in the Calculate Phi Digits are computed exactly with big integers (BigInt), with no floating-point step, so even very long terms keep every digit; values outside the stated ranges give a message instead of being silently cut off.
「计算黄金比例 φ 的位数」免费吗？需要注册吗？Is the Calculate Phi Digits free? Do I need an account?
「计算黄金比例 φ 的位数」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 Calculate Phi Digits is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.