📐 黄金矩形Golden Rectangle Calculator
黄金比 φ = (1 + √5)/2 ≈ 1.618。已知长边或短边，求另一边、面积和周长。本地处理。Golden ratio φ = (1 + √5)/2 ≈ 1.618. From the long or short side, get the other side, area and perimeter. Processed locally.
使用说明与常见问题How-to & FAQ
「黄金矩形」是什么？What is the Golden Rectangle Calculator tool?
黄金比 φ = (1 + √5)/2 ≈ 1.618。已知长边或短边，求另一边、面积和周长。本地处理。Golden ratio φ = (1 + √5)/2 ≈ 1.618. From the long or short side, get the other side, area and perimeter. Processed locally.
如何使用「黄金矩形」？How do I use the Golden Rectangle Calculator tool?
在「黄金矩形」中，填写「已知边长」、「这条边是」等参数，结果会随输入实时计算并显示在下方。In the Golden Rectangle Calculator: Fill in "Known side", "This side is"; results are recalculated instantly as you type.
切出正方形？Cut off a square?
从黄金矩形切掉一个以短边为边长的正方形，剩下的仍是黄金矩形。Removing a square on the short side leaves another golden rectangle.
能举个计算实例吗？Can you show a worked example?
例如在「黄金矩形」中填 已知边长 = 10，这条边是 = 长边，结果区显示：长边：10；短边：6.18034；面积：61.803399；周长：32.36068For example, entering Known side = 10, This side is = Long side in the Golden Rectangle Calculator gives: Long side: 10; Short side: 6.18034; Area: 61.803399; Perimeter: 32.36068
哪些输入会被检查？Which inputs are validated?
「黄金矩形」会检查这些输入——「已知边长」：必须填写，须大于 0；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 Golden Rectangle Calculator checks its inputs — "Known side": required, must be greater than 0; 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?
「黄金矩形」的设置：「已知边长」默认 10；「这条边是」可选 长边、短边（默认 长边）。每次生成结果都按当前设置处理。Settings in the Golden Rectangle Calculator — "Known side" default 10; "This side is": Long side, Short side (default Long side). The result always uses the current settings.
计算精度如何？How precise are the results?
「黄金矩形」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 Golden Rectangle Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「黄金矩形」免费吗？需要注册吗？Is the Golden Rectangle Calculator free? Do I need an account?
「黄金矩形」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 Golden Rectangle 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.