{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "67be90b62e46455bb0d9ac794c3d44b4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def Rotx(l,rot):\n",
    "    xr = [0*np.cos(rot)-0*np.sin(rot),(l[0])*np.cos(rot)-0*np.sin(rot),(x)*np.cos(rot)-y*np.sin(rot)]\n",
    "    return xr\n",
    "\n",
    "def Roty(l,rot):\n",
    "    yr=[0*np.sin(rot)+0*np.cos(rot),(l[0])*np.sin(rot)+0*np.cos(rot),(x)*np.sin(rot)+y*np.cos(rot)]\n",
    "    return yr\n",
    "\n",
    "fig = plt1.figure(figsize=(9,9), constrained_layout=True)\n",
    "widths = [2,7]\n",
    "heights = [2,7]\n",
    "gs=fig.add_gridspec(2,2,width_ratios=widths, height_ratios=heights, wspace=0.05)\n",
    "\n",
    "ax1=fig.add_subplot(gs[0:,0:])\n",
    "ax2=fig.add_subplot(gs[0,0])\n",
    "\n",
    "p= np.loadtxt(\"Primetable.txt\", delimiter=\",\", unpack=False)\n",
    "counter=np.arange(1,len(p)+1)\n",
    "\n",
    "ax1.clear()\n",
    "ax2.clear()\n",
    "\n",
    "#Set the number of fibonacci triangles to display\n",
    "q=56\n",
    "t=56\n",
    "\n",
    "q=56\n",
    "t=106\n",
    "\n",
    "colori=1\n",
    "\n",
    "while q <= t:\n",
    "    \n",
    "    #n=q**2\n",
    "    n=q\n",
    "    tempcount=np.arange(1,n)\n",
    "    total=len(tempcount)+1\n",
    "    ax1.clear()\n",
    "    ax2.clear()\n",
    "    \n",
    "    plt1.gca().set_prop_cycle(None)\n",
    "\n",
    "    rot=0\n",
    "    rot0=np.pi\n",
    "\n",
    "    x0=[0,0,0]\n",
    "    y0=[0,0,0]  \n",
    "    \n",
    "    #Counter for mean graph scaling\n",
    "    m=0\n",
    "    \n",
    "    for i in tempcount:\n",
    "\n",
    "        #Select 3 following primes, check if hypothenusa is smaller sum sides\n",
    "        l=[p[i-1],p[i],p[i+1]]\n",
    "        if (p[i+1]>(p[i-1]+p[i])):\n",
    "            continue\n",
    "            \n",
    "        l=[p[i-1],p[i-1+26],p[i-1+67]]\n",
    "        if ((p[i-1+67])>(p[i-1]+p[i-1+26])):\n",
    "            continue\n",
    "            \n",
    "        #Determine triangle charesteristics (cosine rule)\n",
    "        alpha=np.arccos((l[1]**2+l[2]**2-l[0]**2)/(2*l[1]*l[2]))\n",
    "        beta=np.arccos((l[0]**2+l[2]**2-l[1]**2)/(2*l[0]*l[2]))\n",
    "        gamma=np.arccos((l[0]**2+l[1]**2-l[2]**2)/(2*l[0]*l[1]))\n",
    "\n",
    "        #Height Fibonacci Prime Triangle\n",
    "        x=l[0]+l[1]*np.cos(np.pi-gamma)\n",
    "        y=l[2]*np.cos(np.pi/2-beta)\n",
    "\n",
    "        #Apply Rotation\n",
    "        rot=rot+np.pi-rot0\n",
    "        rot0=gamma\n",
    "        xr=Rotx(l,rot)\n",
    "        yr=Roty(l,rot)\n",
    "\n",
    "        #Triangle not translation\n",
    "        xr =xr+x0\n",
    "        yr =yr+y0\n",
    "        x0=x*np.cos(rot)-y*np.sin(rot)+x0\n",
    "        y0=x*np.sin(rot)+y*np.cos(rot)+y0\n",
    "        \n",
    "        #Plot triangles and color\n",
    "        color=str(i/(n+55))\n",
    "        ax1.fill(xr,yr,zorder=(-i),c=color)\n",
    "\n",
    "        r=np.sqrt(((xr[0]+xr[1]+xr[2])/3)**2+((yr[0]+yr[1]+yr[2])/3)**2)\n",
    "        m=m+r\n",
    "        \n",
    "    q=q+1    \n",
    "    \n",
    "    \n",
    "    \n",
    "#Plot last triangle and scale the plot    \n",
    "ax1.axis([-5*m/total,5*m/total, -5*m/total,5*m/total])  \n",
    "ax1.plot([xr[0],xr[1],xr[2],xr[0]],[yr[0],yr[1],yr[2],yr[0]],zorder=(0),c='blue',linewidth='0.6') \n",
    "ax1.axes.get_xaxis().set_visible(False)\n",
    "ax1.axes.get_yaxis().set_visible(False)\n",
    "\n",
    "#Draw reference triangle\n",
    "c=l[0]+l[1]+l[2]\n",
    "ax2.fill([0,l[0]/c,x/c],[0,0,y/c],c='0.75')\n",
    "ax2.plot([0,1/3,0.5/3,0],[0,0,0.5*np.sqrt(3)/3,0],zorder=(5),c='red',linewidth='0.6')  \n",
    "\n",
    "area=0.5*l[2]*l[0]*np.sin(beta)/c**2\n",
    "areaequi=0.5*1/3*np.sqrt(3)/6\n",
    "ratio=area/areaequi\n",
    "\n",
    "ax2.axis([-0.05,0.45,-0.05,0.45])\n",
    "ax2.axis([-0.05,0.45,-0.05,0.45])\n",
    "ax2.text(0.05,0.95, 'Prime Triangle: [' +str(l[0]) +', '+ str(l[1]) +', '+  str(l[2]) + '] \\nEquilateral Triangle Fit: ' + str(round(ratio,8)) +'.', transform=ax2.transAxes, fontsize=10,\n",
    "    verticalalignment='top')\n",
    "ax2.axes.get_xaxis().set_visible(False)\n",
    "ax2.axes.get_yaxis().set_visible(False)   \n",
    "ax2.axis('off')\n",
    "\n",
    "plt1.show()\n",
    "plt1.savefig('Fibonacci Prime Triangle n=' + str(n), dpi=500, bbox_inches='tight')\n",
    "\n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "0578bbeed4af451aa662c46ca4d9ca51": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "164e70139bbd47179d4e5fb49d052014": {
      "model_module": "jupyter-matplotlib",
      "model_module_version": "^0.7.3",
      "model_name": "ToolbarModel",
      "state": {
       "layout": "IPY_MODEL_d197860480724fa5b4f83e17cb85e630",
       "toolitems": [
        [
         "Home",
         "Reset original view",
         "home",
         "home"
        ],
        [
         "Back",
         "Back to previous view",
         "arrow-left",
         "back"
        ],
        [
         "Forward",
         "Forward to next view",
         "arrow-right",
         "forward"
        ],
        [
         "Pan",
         "Pan axes with left mouse, zoom with right",
         "arrows",
         "pan"
        ],
        [
         "Zoom",
         "Zoom to rectangle",
         "square-o",
         "zoom"
        ],
        [
         "Download",
         "Download plot",
         "floppy-o",
         "save_figure"
        ]
       ]
      }
     },
     "5a1281f5846249828f31da175a7cfaa4": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "67be90b62e46455bb0d9ac794c3d44b4": {
      "model_module": "jupyter-matplotlib",
      "model_module_version": "^0.7.3",
      "model_name": "MPLCanvasModel",
      "state": {
       "_figure_label": "Figure 1",
       "_height": 900,
       "_image_mode": "diff",
       "_message": "x=4570.84      y=-1043.36    ",
       "_width": 900,
       "layout": "IPY_MODEL_5a1281f5846249828f31da175a7cfaa4",
       "toolbar": "IPY_MODEL_6d9c4167cfb04e30ae7906e3f5396ac2",
       "toolbar_position": "left"
      }
     },
     "6d9c4167cfb04e30ae7906e3f5396ac2": {
      "model_module": "jupyter-matplotlib",
      "model_module_version": "^0.7.3",
      "model_name": "ToolbarModel",
      "state": {
       "layout": "IPY_MODEL_0578bbeed4af451aa662c46ca4d9ca51",
       "toolitems": [
        [
         "Home",
         "Reset original view",
         "home",
         "home"
        ],
        [
         "Back",
         "Back to previous view",
         "arrow-left",
         "back"
        ],
        [
         "Forward",
         "Forward to next view",
         "arrow-right",
         "forward"
        ],
        [
         "Pan",
         "Pan axes with left mouse, zoom with right",
         "arrows",
         "pan"
        ],
        [
         "Zoom",
         "Zoom to rectangle",
         "square-o",
         "zoom"
        ],
        [
         "Download",
         "Download plot",
         "floppy-o",
         "save_figure"
        ]
       ]
      }
     },
     "d197860480724fa5b4f83e17cb85e630": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "ffb9033ec01f4fcaab4f92d58f42d695": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}