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    "* Vector transformations are functions that take vectors as inputs and return vectors as outputs. Vector transformations can operate on 2D or 3D vectors.\n",
    "\n",
    "* To effect a geometric transformation of the model, apply a vector transformation to every vertex of every polygon of a 3D model.\n",
    "\n",
    "* You can combine existing vector transformations by composition of functions to create new transformations, which are equivalent to applying the existing vector transformations sequentially.\n",
    "\n",
    "* Functional programming is a programming paradigm that emphasizes composing and, otherwise, manipulating functions.\n",
    "\n",
    "* The functional operation of currying turns a function that takes multiple arguments into a function that takes one argument and returns a new function. Currying lets you turn existing Python functions (like scale and add ) into vector transformations.\n",
    "\n",
    "* Linear transformations are vector transformations that preserve vector sums and scalar multiples. In particular, points lying on a line segment still lie on a line segment after a linear transformation is applied.\n",
    "\n",
    "* A linear combination is the most general combination of scalar multiplication and vector addition. Every 3D vector is a linear combination of the 3D standard basis vectors, which are denoted $e_1 = (1, 0, 0)$, $e_2 = (0, 1, 0)$, and $e_3 = (0, 0, 1)$. Likewise, every 2D vector is a linear combination of the 2D standard basis vec- tors, which are $e_1 = (1, 0)$ and $e_2 = (0, 1)$.\n",
    "\n"
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    "Once you know how a given linear transformation acts on the standard basis vectors, you can determine how it acts on any vector by writing the vector as a linear combination of the standard basis and using the fact that linear combinations are preserved.\n",
    "\n",
    "– In 3D, three vectors or nine total numbers specify a linear transformation.\n",
    "\n",
    "– In 2D, two vectors or four total numbers do the same.\n",
    "\n",
    "This last point is critical: linear transformations are both well-behaved and easy-to-compute with because they can be specified with so little data."
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