Update tikz-notes.ipynb

chenshuo · Jan 8, 2025 · 0733129 · 0733129
1 parent 5226305
commit 0733129
Showing 1 changed file with 94 additions and 0 deletions.
diff --git a/tikz-notes.ipynb b/tikz-notes.ipynb
@@ -422,6 +422,42 @@
     "  (C) -- ($(A)!(C)!(B)$) coordinate (F) node [left] {$F$} node [midway, left=3pt] {357};"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "6c02fbe3-f7de-49b8-aba0-452a691ebe75",
+   "metadata": {},
+   "source": [
+    "### 坐标分量\n",
+    "\n",
+    "直角三角形与正方形，求蓝线长度。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "5176cab4-3956-4b82-b1b3-c43eaac38faa",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n"
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%%tikz -l calc\n",
+    "\n",
+    "\\draw (62:1) coordinate (B1)\n",
+    "  (0, 0) coordinate (B)\n",
+    "  -- (4, 0) coordinate (C) node [midway, below] {17}\n",
+    "  -- ($(B)!(C)!(B1)$) coordinate (A) -- cycle node [midway,left] {8};\n",
+    "\n",
+    "\\draw let \\p1 = (A) in (B) rectangle (\\y1, \\y1) coordinate (D);\n",
+    "\\draw [blue] (C) -- (D) node [midway,above] {?};"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "e3368435-7992-4c56-bba9-0be9d4cdbae9",
@@ -543,6 +579,64 @@
     "\\draw (1, 0) node [above] {$\\alpha=60^\\circ$} node [below] {$r=?$};"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "7d24c4a6-d423-424a-b450-857a27f05bb2",
+   "metadata": {},
+   "source": [
+    "### 三角函数计算\n",
+    "\n",
+    "直角三角形内接半圆，求半径。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "15a19a3d-8738-4f80-8459-4000343deb29",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n"
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%%tikz -l math\n",
+    "\n",
+    "\\draw (0,0) -- (4, 0) node [midway,below] {$4$}-- (0, 3)\n",
+    "  -- cycle node [midway,left] {$3$};\n",
+    "\\tikzmath {\\r=(3*4)/(3+4);\\a=atan(3/4);}\n",
+    "\\draw (0, \\r) arc (180:360-\\a:\\r)\n",
+    "  (0, \\r) arc (180:180-\\a:\\r)\n",
+    "  (\\r,\\r) node [above right] {$r=?$};"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "10216c0d-6ae5-4dd4-b5ee-f72dd4d7974d",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n"
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%%tikz -l math\n",
+    "\n",
+    "\\tikzmath {\\r=(3*4)/(3+4); \\a=atan(4/3); \\x=(3-\\r)*5/3;}\n",
+    "\n",
+    "\\draw (0, 0) -- (\\a:3) node [midway, left] {6} -- (5, 0) node [midway, above] {8} -- cycle;\n",
+    "\\draw (\\x+\\r, 0) arc (0:180:\\r);"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "1049fe6e-ebb8-44ee-a965-d7ecd9b5fc86",