Euler_sinAndcos_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_sinAndcos_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>$e^{jn\\theta}=\\cos(n\\theta)+j\\sin(n\\theta)$</h1></b>\n",
        "\n",
        "Dr. Bingsen Wang\n",
        "\n",
        "2/9/2025\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hv0YxDrWU4h8"
      },
      "source": [
        "#Python Code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "XeGsHYTt8IXU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "dba42589-c77a-4473-a239-fa36b8d80886"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1200 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "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 = 8,2000,2.8,[0,4,4],[0,0,-8]\n",
        "n,theta = np.linspace(1,Nl,Nl),np.linspace(0,np.pi*2,Nf)\n",
        "clst = list(cm.tab10.colors) #colors of lines\n",
        "fig = pyplot.figure(figsize=([12,12]))\n",
        "ax = fig.add_axes([0,0,1,1],xlim=[-4,12],ylim=[-12,4])\n",
        "ax.axis('off')\n",
        "ax.plot(r*np.cos(theta),r*np.sin(theta),[3.2,-3.2],[y0[2]+3.2,y0[2]-3.2],lw=2,c='0.3',alpha=.6)\n",
        "[ax.annotate('',[(x0[i]+[3.5,7,7][i],y0[i]),(x0[i],y0[i]+3.5)][k],\n",
        "              [(x0[i]+[-3.5,-.2,-.2][i],y0[i]),(x0[i],y0[i]-3.5)][k],\n",
        "             arrowprops={'arrowstyle':'->','lw':1.5}) for i in range(3) for k in range(2)]\n",
        "[ax.text([x0[i]+[3.5,7,7][i],x0[i]][k],[y0[i],y0[i]+3.5][k],\n",
        "         ['$Re$',r'$\\theta$',r'$\\theta$','$Im$',r'$\\sin(n\\theta)$',r'$\\cos(n\\theta)$'][i+k*3],\n",
        "         size=25,va='top') for i in range(3) for k in range(2)]\n",
        "sc=[ax.scatter(n*0,n*0,marker='o',c=clst[:len(n)],s=[150,80,80][k]) for k in range(3)]\n",
        "lines=[[ax.plot([],[],ls=['--','--','-','-'][k],lw=[1,1,4-2.5*i/(Nl-1),4-2.5*i/(Nl-1)][k],\n",
        "                c=clst[i])[0] for i in range(Nl)] for k in range(4)]\n",
        "lines.append(ax.plot([],[],lw=2,c='k')[0])\n",
        "txt = [[ax.text(0,0,'',c=clst[i],size=[30,25,25][k],ha=['center','left','left'][k],\n",
        "                va='center') for i in range(Nl)] for k in range(3)]\n",
        "txt.append(ax.text(0,0,'',c='k',size=25))\n",
        "def animate(k):\n",
        "  ejnt = np.array([r*np.exp(1j*theta[:k+1]*n[i]) for i in range(Nl)])\n",
        "  ejnt1=ejnt[:,-1]\n",
        "  [sc[i].set_offsets(np.c_[x0[i]+[ejnt1.real,theta[k]+np.zeros(Nl),theta[k]+np.zeros(Nl)][i],\n",
        "                           y0[i]+[ejnt1.imag,ejnt1.imag,ejnt1.real][i]]) for i in range(3)]\n",
        "  [lines[0][i].set_data([0,ejnt1[i].real,theta[k]+x0[1]], [0,ejnt1[i].imag,ejnt1[i].imag]) for i in range(Nl)]\n",
        "  [lines[1][i].set_data([ejnt1[i].real,ejnt1[i].real,theta[k]+x0[2]],\n",
        "   [ejnt1[i].imag,y0[2]+ejnt1[i].real,y0[2]+ejnt1[i].real]) for i in range(Nl)]\n",
        "  [lines[2+m][i].set_data(x0[1+m]+theta[:k+1],y0[1+m]+[ejnt.imag[i],ejnt.real[i]][m])\n",
        "     for i in range(Nl) for m in range(2)]\n",
        "  lines[4].set_data(.25*ejnt[0].real,.25*ejnt[0].imag)\n",
        "  [txt[m][i].set_text([rf'$e^{{j',rf' $\\sin{{',rf' $\\cos{{'][m]+rf'{n[i]:.0f}\\theta}}$')\n",
        "     for i in range(Nl) for m in range(3)]\n",
        "  [txt[m][i].set_position((x0[m]+[1.15*ejnt[i,-1].real,theta[k],theta[k]][m],\n",
        "   y0[m]+[1.15*ejnt[i,-1].imag,ejnt[i,-1].imag,ejnt[i,-1].real][m])) for i in range(Nl) for m in range(3)]\n",
        "  txt[3].set_position((.4*(ejnt1[0]**.5).real,.4*(ejnt1[0]**.5).imag))\n",
        "  txt[3].set_text(fr'$\\theta={theta[k]:.3f}$')\n",
        "  return\n",
        "anim = animation.FuncAnimation(fig, animate, frames=Nf, interval=50)\n",
        "anim.save(\"Euler_sincos_ntheta.mp4\",writer=animation.FFMpegWriter(fps=50),dpi=200)"
      ]
    }
  ]
}