613-Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dave is doing his homework on the balcony and, preparing a presentation about Pythagorean triangles, has just cut out a triangle with side lengths 30cm, 40cm and 50cm from some cardboard, when a gust of wind blows the triangle down into the garden.\n",
    "\n",
    "# Another gust blows a small ant straight onto this triangle. The poor ant is completely disoriented and starts to crawl straight ahead in random direction in order to get back into the grass.\n",
    "\n",
    "# Assuming that all possible positions of the ant within the triangle and all possible directions of moving on are equiprobable, what is the probability that the ant leaves the triangle along its longest side?\n",
    "\n",
    "# Give your answer rounded to 10 digits after the decimal point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_______\n",
    "\n",
    "# Since $50^{2} = 2500 = 900 + 1600 = 30^{2} + 40^{2}$, we know that this triangle is a right angle triangle\n",
    "\n",
    "# Let's see what the triangle looks like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = 10, 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x1605841a710>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 40.01, 0.01)\n",
    "y = 30 - x*(30/40.0)\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.fill_between(x,y,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now, let's assume an ant falls onto a random spot on the triangle\n",
    "\n",
    "### We can assume the random spot is 5, 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_x, random_y = 5, 10\n",
    "x = np.arange(0, 40.01, 0.01)\n",
    "y = 30 - x*(30/40.0)\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.fill_between(x,y,0)\n",
    "plt.scatter(random_x, random_y, s=50, facecolors='r', marker = 'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now, we visualize a circle surrounding the ant, and draw lines from the ant to each vertex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_x, random_y = 5, 10\n",
    "x = np.arange(0, 40.01, 0.01)\n",
    "y = 30 - x*(30/40.0)\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.fill_between(x,y,0)\n",
    "plt.scatter(random_x, random_y, s=10000, facecolors='y', marker = 'o')\n",
    "plt.scatter(random_x, random_y, s=9000, facecolors='b', marker = 'o')\n",
    "plt.scatter(random_x, random_y, s=50, facecolors='r', marker = 'o')\n",
    "\n",
    "x_left = np.arange(0,random_x+0.01, 0.01)\n",
    "y1 = 30 - 4*x_left\n",
    "plt.plot(x_left, y1, color = 'y', ls = 'dashed')\n",
    "y2 = 2*x_left\n",
    "plt.plot(x_left, y2, color = 'y', ls = 'dashed')\n",
    "\n",
    "x_right = np.arange(random_x, 40.01, 0.01)\n",
    "y3 = (80 - 2*x_right)/7.0\n",
    "plt.plot(x_right, y3, color = 'y', ls = 'dashed')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Since the ant walks in a random direction, the probability that it walks off the longest edge is equal to the proportion of the circumference of the circle in the top right section\n",
    "\n",
    "# Let's choose another random point to show how this ratio can change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_x, random_y = 27, 5\n",
    "x = np.arange(0, 40.01, 0.01)\n",
    "y = 30 - x*(30/40.0)\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.fill_between(x,y,0)\n",
    "plt.scatter(random_x, random_y, s=10000, facecolors='y', marker = 'o')\n",
    "plt.scatter(random_x, random_y, s=9000, facecolors='b', marker = 'o')\n",
    "plt.scatter(random_x, random_y, s=50, facecolors='r', marker = 'o')\n",
    "\n",
    "x_left = np.arange(0,random_x+0.01, 0.01)\n",
    "y1 = 30 - ((30-random_y)/(random_x))*x_left\n",
    "plt.plot(x_left, y1, color = 'y', ls = 'dashed')\n",
    "y2 = (random_y/random_x)*x_left\n",
    "plt.plot(x_left, y2, color = 'y', ls = 'dashed')\n",
    "\n",
    "x_right = np.arange(random_x, 40.01, 0.01)\n",
    "m = (-random_y)/(40-random_x)\n",
    "b = random_y-(m*random_x)\n",
    "y3 = b + m*x_right\n",
    "plt.plot(x_right, y3, color = 'y', ls = 'dashed')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We can solve for the proportion by calculating four angles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/613.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First of all, we notice that combining angles 2 and 3 forms a right angle, so we really only need to find 1 and 4\n",
    "\n",
    "# We can calculate these angles as\n",
    "\n",
    "## 1. $\\tan\\left ( \\text{Angle 1} \\right ) = \\frac{30 - y}{x}$\n",
    "\n",
    "## 4. $\\tan\\left ( \\text{Angle 4} \\right ) = \\frac{40 - x}{y}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# For any $x$ and $y$ pair on the surface of the triangle, the probability of walking off the long edge given by the function:\n",
    "\n",
    "# $f(x,y) = 1 - \\frac{\\arctan\\left( \\frac{30-y}{x} \\right) + \\arctan\\left( \\frac{40-x}{y} \\right) + \\frac{\\pi}{2}}{2\\pi}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# To solve for the total probability by integrating this function over all possible $x$ and $y$ values, and dividing by the area of the triangle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $P\\left ( \\text{Walking off long edge} \\right ) = \\frac{1}{40\\cdot30\\cdot\\frac{1}{2}}\\int_{x=0}^{x=40}\\int_{y=0}^{y=30-0.75x}f(x,y)dydx$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We'll use the scipy [`integrate.nquad`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.nquad.html#scipy.integrate.nquad) function to solve this integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def function(y,x):\n",
    "    angle1 = np.arctan((30-y)/x)\n",
    "    angle4 = np.arctan((40-x)/y)\n",
    "    total = np.pi/2 + angle1 + angle4\n",
    "    other_angle = 2*np.pi - total\n",
    "    return other_angle/(2*np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bounds_x():\n",
    "    return [0, 40]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bounds_y(x):\n",
    "    return [0, 30 - 0.75*x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "area = integrate.nquad(function, [bounds_y, bounds_x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob = area[0]/(30*40/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3916721504"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(prob, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Answer: 0.3916721504"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}