🔮 幻方生成器Magic Square Generator
生成 n 阶幻方（n = 3-20）：奇数阶用暹罗法，4 的倍数用对角线互补法，其余偶数用 LUX 法；每行、每列、两条对角线之和都相等。本地处理。Generate an n×n magic square (n = 3-20): Siamese method for odd n, diagonal complement for multiples of 4 and the LUX method for other even n. Every row, column and both diagonals have the same sum. Processed locally.
使用说明与常见问题How-to & FAQ
「幻方生成器」是什么？What is the Magic Square Generator tool?
生成 n 阶幻方（n = 3-20）：奇数阶用暹罗法，4 的倍数用对角线互补法，其余偶数用 LUX 法；每行、每列、两条对角线之和都相等。本地处理。Generate an n×n magic square (n = 3-20): Siamese method for odd n, diagonal complement for multiples of 4 and the LUX method for other even n. Every row, column and both diagonals have the same sum. Processed locally.
如何使用「幻方生成器」？How do I use the Magic Square Generator tool?
在「幻方生成器」中，填写「阶数 n」等参数，结果会随输入实时计算并显示在下方。In the Magic Square Generator: Fill in "Order n"; results are recalculated instantly as you type.
为什么没有 2 阶幻方？Why is there no order-2 magic square?
2 × 2 的幻方不存在：若 a + b = a + c 则 b = c，数字会重复。所以本页的阶数从 3 开始（3 到 20），1 阶只是平凡的单个数。A 2 × 2 magic square is impossible: a + b = a + c forces b = c, repeating a number. That is why the order here starts at 3 (3 to 20); order 1 is just a single number.
能举个计算实例吗？Can you show a worked example?
例如在「幻方生成器」中填 阶数 n = 3，结果区显示：幻和：15；校验：✔ 行、列、对角线都等于幻和；幻方：8 1 6 3 5 7 4 9 2For example, entering Order n = 3 in the Magic Square Generator gives: Magic constant: 15; Check: ✔ rows, columns and diagonals all match; Square: 8 1 6 3 5 7 4 9 2
哪些输入会被检查？Which inputs are validated?
「幻方生成器」会检查这些输入——「阶数 n」：必须填写，须为整数；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Magic Square Generator checks its inputs — "Order n": required, must be a whole number; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「幻方生成器」的设置：「阶数 n」默认 3。每次生成结果都按当前设置处理。Settings in the Magic Square Generator — "Order n" default 3. The result always uses the current settings.
计算精度如何？How precise are the results?
「幻方生成器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Magic Square Generator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「幻方生成器」免费吗？需要注册吗？Is the Magic Square Generator free? Do I need an account?
「幻方生成器」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 Magic Square Generator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.