Prime Triangles Growth+Error.ipynb

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    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt1\n",
    "import matplotlib.pyplot as plt2"
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      "100008\n",
      "Count:100009\n",
      "Between, -50<Error<50: 99107\n",
      "Percentage: 99.09808117269446\n"
     ]
    }
   ],
   "source": [
    "from ipywidgets import IntProgress\n",
    "from datetime import datetime\n",
    "from matplotlib import gridspec\n",
    "\n",
    "#Create Plot grid\n",
    "fig= plt1.figure(figsize=(9, 6), constrained_layout=True)\n",
    "widths = [2.25,2.25,2.25,2.25]\n",
    "heights = [3,3,0.5]\n",
    "gs=fig.add_gridspec(3,4,width_ratios=widths, height_ratios=heights, wspace=0.05)\n",
    "\n",
    "ax1a=fig.add_subplot(gs[0,:2])\n",
    "ax1b=fig.add_subplot(gs[0,2:])\n",
    "ax2a=fig.add_subplot(gs[1,:2])\n",
    "ax2b=fig.add_subplot(gs[1,2:])\n",
    "\n",
    "ax1a.clear()\n",
    "ax1b.clear()\n",
    "ax2a.clear()\n",
    "ax2b.clear()\n",
    "\n",
    "\n",
    "#Disable axis textfield plot\n",
    "#ax1b.axis('off')\n",
    "#ax1d.axis('off')\n",
    "#ax1e.axis('off')\n",
    "\n",
    "\n",
    "p2= np.loadtxt(\"Primetable.txt\", delimiter=\",\", unpack=False)\n",
    "counter=np.arange(1,len(p2)+1)\n",
    "\n",
    "print(len(p2))\n",
    "p0=np.roll(p2, 2)\n",
    "p0[0]=1\n",
    "p0[1]=1\n",
    "\n",
    "\n",
    "\n",
    "p1=np.roll(p2, 1)\n",
    "p1[0]=1\n",
    "p1[1]=1\n",
    "\n",
    "p2[0]=1.9\n",
    "p2[1]=1.9\n",
    "\n",
    "alpha=np.arccos((p1**2+p2**2-p0**2)/(2*p1*p2))\n",
    "beta=np.arccos((p0**2+p2**2-p1**2)/(2*p0*p2))\n",
    "gamma=np.arccos((p0**2+p1**2-p2**2)/(2*p0*p1))\n",
    "\n",
    "\n",
    "#Height Fibonacci Prime Triangle\n",
    "x=p0+p1*np.cos(np.pi-gamma)\n",
    "y=p2*np.cos(np.pi/2-beta)\n",
    "\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)\n",
    "label=\"slope: %.15f \" % slope\n",
    "\n",
    "ax1a.plot(x, y, marker='.',markersize=(2), color='black', linestyle='', label=label)\n",
    "ax1a.legend(loc='upper left',fontsize=8)\n",
    "ax1a.set_title('Height Fibonacci Prime Triangle')\n",
    "ax1a.set_xlabel('$x$')\n",
    "ax1a.set_ylabel('y')\n",
    "ax1a.grid(b=True, which='major', color='#666666', linestyle='-')\n",
    "ax1a.ticklabel_format(axis=\"x\", style=\"sci\", scilimits=(0,0))\n",
    "ax1a.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(0,0))\n",
    "\n",
    "#Slope Triangles\n",
    "\n",
    "slope=y/x\n",
    "\n",
    "ax1b.plot(counter, slope, marker='', color='black', linestyle='-', linewidth=1, label=\"Slope\")\n",
    "ax1b.plot([0,len(p2)], [np.sqrt(3),np.sqrt(3)], marker='', color='red', linestyle='-', linewidth=1, label=\"$\\sqrt{3}=1,73205080756$\")\n",
    "ax1b.legend(loc='lower right',fontsize=8)\n",
    "ax1b.set_title('Slope Individual Fibonacci Prime Triangles')\n",
    "ax1b.set_xlabel('Prime p(n)')\n",
    "ax1b.set_ylabel('Slope')\n",
    "ax1b.grid(b=True, which='major', color='#666666', linestyle='-')\n",
    "ax1b.ticklabel_format(axis=\"x\", style=\"sci\", scilimits=(0,0))\n",
    "ax1b.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(0,0))\n",
    "ax1b.set_xscale('log')\n",
    "\n",
    "#Plot error from prediction\n",
    "\n",
    "p2predicted=0.5*p0+np.sqrt(-0.75*p0**2+p1**2)\n",
    "error=p2predicted-p2\n",
    "\n",
    "histo_arr = error[error <= 50]\n",
    "histo_arr = histo_arr[histo_arr >= -50]\n",
    "\n",
    "\n",
    "print(\"Count:\" + str(len(counter)+1))\n",
    "print(\"Between, -50<Error<50: \" + str(len(histo_arr)+1))\n",
    "print(\"Percentage: \" + str(100*(len(histo_arr)+1)/(len(counter)+1)))\n",
    "\n",
    "#newarr = arr[filter_arr]\n",
    "\n",
    "ax2a.hist(histo_arr, density=True, bins=np.arange(-51,51)+0.5, rwidth=1, color='black', edgecolor='white', linewidth=0, zorder=1)\n",
    "#ax2a.set(xlim=(-0.8*lim,0.8*lim))\n",
    "ax2a.set_xlabel('$Bin$')\n",
    "ax2a.set_ylabel('$Density$')\n",
    "ax2a.set_title('Histogram Error')\n",
    "ax2a.grid(b=True, which='major', color='#666666', linestyle='-', zorder=0)\n",
    "\n",
    "ax2b.plot(p2,error , marker='.',markersize=(0.25), color='black', linestyle='')\n",
    "#ax2b.legend(loc='upper left',fontsize=8)\n",
    "ax2b.set_title('Error p(n+2)')\n",
    "ax2b.set_xlabel('Primenumber p(n+2)')\n",
    "ax2b.set_ylabel('Error')\n",
    "ax2b.grid(b=True, which='major', color='#666666', linestyle='-')\n",
    "ax2b.ticklabel_format(axis=\"x\", style=\"sci\", scilimits=(0,0))\n",
    "\n",
    "\n",
    "plt1.show()\n",
    "plt1.savefig('Fibonacci Prime Traingle', dpi=300, bbox_inches='tight')\n",
    "\n",
    "#ax2b.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(0,0))\n",
    "\n",
    "#print(p1[2])\n",
    "#print(p2[2])\n",
    "#print(p3[2])\n",
    "#print (len(Counter))\n",
    "\n",
    "\n",
    "\n",
    "\n"
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