feat : add ipywidgets interactive bisection exploration to 10/20

Add slider widget (0–30 iterations) showing how the bisection
bracket narrows around sqrt(10).  Yellow band, vertical lines
for x_L / x_U, and red square for x_m update in real time.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: beachdweller

10_root_finding/20_bisection.ipynb

@@ -356,6 +356,23 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "source": "### 동적 탐색<br>Interactive Exploration\n\n반복 횟수를 바꾸어 가며 구간이 어떻게 좁아지는지 관찰해 보자.<br>\nChange the number of iterations and observe how the interval narrows down.",
+   "metadata": {}
+  },
+  {
+   "cell_type": "code",
+   "source": "from ipywidgets import interact, IntSlider\n\ndef plot_bisection(iterations):\n    x_l, x_u = 0.0, 6.0\n\n    # 이분법 반복\n    # Bisection iterations\n    for k in range(iterations):\n        x_m = (x_l + x_u) * 0.5\n        if f(x_u) * f(x_m) < 0:\n            x_l = x_m\n        elif f(x_l) * f(x_m) < 0:\n            x_u = x_m\n        else:\n            break\n\n    x_m = (x_l + x_u) * 0.5\n\n    # f(x) 곡선\n    # f(x) curve\n    x_plot = py.linspace(0, 6, 200)\n    py.plot(x_plot, f(x_plot), 'k-', label='$f(x)=x^2-10$')\n    py.axhline(y=0, color='r', linestyle='--', alpha=0.5)\n\n    # 현재 구간 표시\n    # Show current interval\n    py.axvline(x=x_l, color='blue', linestyle='--', alpha=0.7, label=f'$x_L$ = {x_l:.6f}')\n    py.axvline(x=x_u, color='green', linestyle='--', alpha=0.7, label=f'$x_U$ = {x_u:.6f}')\n    py.axvspan(x_l, x_u, alpha=0.15, color='yellow')\n\n    # 중점 표시\n    # Show midpoint\n    py.plot(x_m, f(x_m), 'rs', markersize=10, label=f'$x_m$ = {x_m:.6f}')\n\n    interval = x_u - x_l\n    py.title(f'Iteration {iterations},  Interval = {interval:.6f},  f($x_m$) = {f(x_m):.2e}')\n    py.xlabel('x')\n    py.ylabel('f(x)')\n    py.legend(loc='upper left')\n    py.grid(True)\n    py.show()\n\ninteract(plot_bisection, iterations=IntSlider(min=0, max=30, step=1, value=0,\n                                               description='Iterations:'));",
+   "metadata": {},
+   "execution_count": null,
+   "outputs": []
+  },
+  {
+   "cell_type": "markdown",
+   "source": "반복 횟수를 0에서 30까지 바꾸어 보자. 구간의 폭과 $f(x_m)$이 어떻게 줄어드는가?<br>\nTry changing the number of iterations from 0 to 30. How do the interval width and $f(x_m)$ decrease?",
+   "metadata": {}
+  },
   {
    "cell_type": "markdown",
    "metadata": {},