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    "\n",
    "### Our goal\n",
    "\n",
    "Let's renew our acquaintance with the Python programming language, and begin to get to know the NumPy library and Jupyter notebooks."
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    "### A parametric definition of a line\n",
    "\n",
    "Let's suppose that we have two distinct points in the plane:\n",
    "\n",
    "* Let $\\vec{p_0} = (x_0, y_0)$.\n",
    "* Let $\\vec{p_1} = (x_1, y_1)$.\n",
    "\n",
    "For all $t$ such that $0.0 \\leq t \\leq 1.0$ it is the case that the points returned by the function $\\vec{p}(t)$ lie on the line segment defined by $\\vec{p_0}$ and $\\vec{p_1}$:\n",
    "\n",
    "* $\\vec{p}(t) = \\vec{p_0} + t \\cdot (\\vec{p_1} - \\vec{p_0})$\n",
    "\n",
    "If $t < 0.0$ or $t > 1.0$, then $\\vec{p}(t)$ is a point on the line that passes through $\\vec{p_0}$ and $\\vec{p_1}$ but does not lie between those two points.\n"
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    "### Exercise\n",
    "\n",
    "Write code that creates $N$ points on a line segment bounded by two points $(x_0, y_0)$ and $(x_1, y_1)$ and stores this data in a NumPy array.\n",
    "\n",
    "* Create a variable $N$. Assign to it any positive integer value that you choose.\n",
    "* Create variables to represent the coordinates of the two points. Assign to these variables values in the interval $[-1.0, +1.0]$. Select any values in that range that you like, so long as they define distinct points.\n",
    "* Write a loop to generate the points. Inside the loop, generate random values of the parameter $t$. Draw the values of $t$ from a uniform distribution of random numbers in the range $0.0$ to $1.0$.\n",
    "* Define function and write comments as appropriate to make concise, easy to understand code.\n",
    "\n"
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    "# Here's how to get the numpy functions.\n",
    "import numpy as np\n",
    "\n",
    "# Learn what kinds of vector arithmetic you can do\n",
    "# with NumPy arrays.\n",
    "\n",
    "# Learn what kinds of functions NumPy provides for\n",
    "# generating random numbers."
   ]
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  {
   "cell_type": "code",
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    "# Here's how to define a function.\n",
    "\n",
    "def makePoints( n ):\n",
    "    # This function returns dummy data.\n",
    "    # This is just a placeholder. \n",
    "    \n",
    "    # Create a list of lists.\n",
    "    listOfPoints = [[0.0, 0.0], [1.0,1.0]]\n",
    "    \n",
    "    # From the list create a NumPy array.\n",
    "    return np.array( listOfPoints )"
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     "text": [
      "[0. 0.]\n",
      "[1. 1.]\n"
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   "source": [
    "if __name__ == '__main__':\n",
    "    N = 12\n",
    "    data = makePoints(N)\n",
    "    \n",
    "    for p in data:\n",
    "        print( p )\n",
    "        "
   ]
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