🌳 生成毕达哥拉斯树Generate Pythagoras Tree
生成毕达哥拉斯树：在正方形顶边上搭一个直角三角形，再在两条直角边上各长出一个较小的正方形，反复迭代。可调分叉角，导出 PNG。Generate a Pythagoras tree: a right triangle sits on the top edge of a square and a smaller square grows on each of its two legs, repeated. Set the branch angle; export PNG.
使用说明与常见问题How-to & FAQ
「生成毕达哥拉斯树」是什么？What is the Generate Pythagoras Tree tool?
生成毕达哥拉斯树：在正方形顶边上搭一个直角三角形，再在两条直角边上各长出一个较小的正方形，反复迭代。可调分叉角，导出 PNG。Generate a Pythagoras tree: a right triangle sits on the top edge of a square and a smaller square grows on each of its two legs, repeated. Set the branch angle; export PNG.
如何使用「生成毕达哥拉斯树」？How do I use the Generate Pythagoras Tree tool?
在「生成毕达哥拉斯树」中，按需设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」等选项，然后点击「绘制」、「下载 PNG」按钮即可。In the Generate Pythagoras Tree: Set "Width", "Height", "Padding", "Line width", "Iterations", then click "Draw", "Download PNG".
为何叫毕达哥拉斯树？Why is it called a Pythagoras tree?
每次分叉都在一个直角三角形的斜边（父正方形的顶边）上进行，两条直角边上各长一个正方形。按勾股定理，两个子正方形的面积之和等于父正方形的面积，所以每一层的总面积都相同。Every fork happens on a right triangle whose hypotenuse is the parent square's top edge, with a square on each leg. By the Pythagorean theorem the two child squares together have the same area as the parent, so every level has the same total area.
分叉角有什么作用？What does the branch angle do?
分叉角是左侧直角边与斜边的夹角：45°（默认）时两边一样大，树左右对称；小于 45° 时左侧正方形更大、树向左倾，大于 45° 时向右倾。范围 20°–70°，超出范围会提示。第 n 次迭代共有 2^(n+1) − 1 个正方形，12 次约 8000 个。The branch angle is the angle between the left leg and the hypotenuse: at 45° (the default) both squares are equal and the tree is symmetric; below 45° the left square is larger and the tree leans left, above 45° it leans right. The range is 20°–70° and values outside it give a message. Iteration n has 2^(n+1) − 1 squares, about 8,000 at 12.
有哪些选项可以调整？What options can I adjust?
「生成毕达哥拉斯树」的设置：「宽度」默认 512，范围 64–2048；「高度」默认 512，范围 64–2048；「边距」默认 20，范围 0–256；「线宽」默认 2，范围 0.5–40；「迭代次数」默认 8，范围 1–12；「分叉角 (°)」默认 45，范围 20–70；「背景」默认 #ffffff；「线条」默认 #1e3a8a；「填充」默认 #93c5fd。每次生成结果都按当前设置处理。Settings in the Generate Pythagoras Tree — "Width" default 512, range 64–2048; "Height" default 512, range 64–2048; "Padding" default 20, range 0–256; "Line width" default 2, range 0.5–40; "Iterations" default 8, range 1–12; "Branch angle (°)" default 45, range 20–70; "Background" default #ffffff; "Line" default #1e3a8a; "Fill" default #93c5fd. The result always uses the current settings.
「生成毕达哥拉斯树」免费吗？需要注册吗？Is the Generate Pythagoras Tree free? Do I need an account?
「生成毕达哥拉斯树」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 Generate Pythagoras Tree is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.