Euler_sin_ntheta.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bingsen-wang/Math/blob/main/Euler_sin_ntheta.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAMKoELNpsK-"
      },
      "source": [
        "<center><h1><b>$\\sin(n\\theta)$</h1></b>\n",
        "\n",
        "Dr. Bingsen Wang\n",
        "\n",
        "2/8/2025\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hv0YxDrWU4h8"
      },
      "source": [
        "#Python Code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "XeGsHYTt8IXU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 936
        },
        "outputId": "57093ae9-80e9-4fff-b5b7-eb77288ae905"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1600x900 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "from matplotlib import pyplot,animation,cm\n",
        "import numpy as np\n",
        "pyplot.rcParams.update({\"font.family\":\"sans-serif\", \"mathtext.fontset\":\"cm\"})\n",
        "\n",
        "Nl,Nf,r,x0,y0 = 8,1500,3,[4,8],4.5\n",
        "n = np.linspace(1,Nl,Nl)\n",
        "theta=np.linspace(0,np.pi*2,Nf)\n",
        "cr = r*np.exp(1j*theta)+x0[0]+1j*y0\n",
        "clst = list(cm.tab10.colors) #colors of lines\n",
        "fig = pyplot.figure(figsize=([16,9]))\n",
        "ax = fig.add_axes([0,0,1,1],xlim=[0,16],ylim=[0,9])\n",
        "ax.axis('off')\n",
        "ax.plot(cr.real,cr.imag,lw=3,c='0.3',alpha=.6)\n",
        "[ax.annotate('',(x0[i]+[3.5,7][i],y0),(x0[i]+[-3.5,-.2][i],y0),arrowprops={'arrowstyle':'->','lw':1.5}) for i in range(2)]\n",
        "[ax.annotate('',(x0[i],y0+4),(x0[i],y0-4),arrowprops={'arrowstyle':'->','lw':1.5}) for i in range(2)]\n",
        "[ax.text([x0[0],x0[0]+3.2,x0[1],x0[1]+6.7][i],[y0+4,y0,y0+4,y0][i],\n",
        " ['$Im$','$Re$',rf'$\\sin(n\\theta),n=1,2,...,{Nl}$',r'$\\theta$'][i],size=25,va='top') for i in range(4)]\n",
        "sc=[ax.scatter(n*0,n*0,marker='o',c=clst[:len(n)],s=[150,100][k]) for k in range(2)]\n",
        "lines=[[ax.plot([],[],ls=['--','-'][k],lw=[1,4-2.5*i/(Nl-1)][k],c=clst[i])[0] for i in range(Nl)] for k in range(2)]\n",
        "lines.append(ax.plot([],[],lw=1,c='k')[0])\n",
        "txt = [ax.text(0,0,'',c=clst[i],size=30,ha='center',va='center') for i in range(Nl)]\n",
        "txt.append(ax.text(0,0,'',c='k',size=25))\n",
        "def animate(k):\n",
        "  ejnt = r*np.exp(1j*theta[k]*n)\n",
        "  ejt,ejt1 = .5*np.exp(1j*theta[:k+1]),.7*np.exp(1j*theta[k]/2)\n",
        "  sinnt = [y0+r*np.sin(n[i]*theta[:k+1]) for i in range(Nl)]\n",
        "  sc[0].set_offsets(np.c_[ejnt.real+x0[0],ejnt.imag+y0])\n",
        "  sc[1].set_offsets(np.c_[theta[k]+x0[1]+ejnt.real*0,ejnt.imag+y0])\n",
        "  [lines[0][i].set_data([x0[0],ejnt[i].real+x0[0],theta[k]+x0[1]],\n",
        "   [y0,ejnt[i].imag+y0,ejnt[i].imag+y0]) for i in range(Nl)]\n",
        "  [lines[1][i].set_data(x0[1]+theta[:k+1],sinnt[i]) for i in range(Nl)]\n",
        "  lines[2].set_data(x0[0]+ejt.real,y0+ejt.imag)\n",
        "  [txt[i].set_text(fr'$e^{{j{n[i]:.0f}\\theta}}$') for i in range(Nl)]\n",
        "  [txt[i].set_position((x0[0]+1.1*ejnt[i].real,y0+1.1*ejnt[i].imag)) for i in range(Nl)]\n",
        "  txt[Nl].set_position((x0[0]+ejt1.real,y0+ejt1.imag))\n",
        "  txt[Nl].set_text(fr'$\\theta={theta[k]:.3f}$')\n",
        "  return\n",
        "anim = animation.FuncAnimation(fig, animate, frames=Nf, interval=50)\n",
        "anim.save(\"Euler_sin_ntheta.mp4\",writer=animation.FFMpegWriter(fps=50),dpi=200)"
      ]
    }
  ]
}