matematika.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Osnove\n",
    "Podane so točke $A(1, 2)$, $B(5, 2)$ in $C(7, 4)$. Zapiši vektorje $\\vec{AB}$, $\\vec{BC}$ in $\\vec{AC}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = (1, 2)\n",
    "B = (5, 2)\n",
    "C = (7, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "plt.plot((1, 5, 7), (2, 2, 4), 'ro')\n",
    "plt.annotate(xy=[1,1.5], text=\"A\", ha=\"center\")\n",
    "plt.annotate(xy=[5,1.5], text=\"B\", ha=\"center\")\n",
    "plt.annotate(xy=[7,3.5], text=\"C\", ha=\"center\")\n",
    "plt.axis([0, 8, 0, 5])\n",
    "\n",
    "plt.arrow(0, 0, *A, head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "plt.arrow(0, 0, *B, head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "plt.arrow(0, 0, *C, head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "\n",
    "plt.annotate(xy=[7/2, 4/2+0.3], text=\"rC\")\n",
    "plt.annotate(xy=[5/2, 2/2-0.3], text=\"rB\")\n",
    "plt.annotate(xy=[1/2-0.2, 2/2+0.25], text=\"rA\")\n",
    "\n",
    "\n",
    "# plt.arrow(*A, *AB, head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "# plt.arrow(*B, *BC, head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "# plt.arrow(*A, *AC, head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AB: [4 0], BC: [2 2], AC: [6 2]\n"
     ]
    }
   ],
   "source": [
    "def krajevni_vektor(tocka):\n",
    "    return numpy.array(tocka)\n",
    "\n",
    "rA = krajevni_vektor(A)\n",
    "rB = krajevni_vektor(B)\n",
    "rC = krajevni_vektor(C)\n",
    "\n",
    "AB = rB - rA\n",
    "BC = rC - rB\n",
    "AC = rC - rA\n",
    "\n",
    "print(f\"AB: {AB}, BC: {BC}, AC: {AC}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izračunaj vsoto $\\vec{AB} + 2\\vec{BC} - \\vec{AC}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AB + 2*BC - AC = [2 2]\n"
     ]
    }
   ],
   "source": [
    "print(f\"AB + 2*BC - AC = {AB + 2*BC - AC}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Določi točko $D$ tako, da bo štirikotnik $ABCD$ paralelogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D(3, 4)\n"
     ]
    }
   ],
   "source": [
    "rD = rA + BC\n",
    "D = tuple(rD)\n",
    "print(f\"D{D}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Določi dolžino vektorjev $\\vec{AB}$ in $\\vec{AC}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dolžina vektorja AB: 4.0\n",
      "Dolžina vektorja AC: 6.324555320336759\n"
     ]
    }
   ],
   "source": [
    "from numpy.linalg import norm\n",
    "print(f\"Dolžina vektorja AB: {norm(AB)}\")\n",
    "print(f\"Dolžina vektorja AC: {norm(AC)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Izražave"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "V pravokotniku $ABCD$ točki $U$ in $V$ delita stranico $DC$ na tri skladne dele. Označimo $\\vec{a} = \\vec{AB}$ in $\\vec{b} = \\vec{BC}$. Z njima izrazi vektorje \n",
    "$\\vec{AC}, \\vec{AU}, \\vec{VU}$ in $\\vec{VA}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "A = (1, 1)\n",
    "B = (5, 1)\n",
    "C = (5, 3)\n",
    "D = (1, 3)\n",
    "\n",
    "rA, rB, rC, rD = [krajevni_vektor(v) for v in [A, B, C, D]]\n",
    "\n",
    "DC = rC - rD\n",
    "rU = rD + 1/3 * DC\n",
    "rV = rD + 2/3 * DC\n",
    "\n",
    "U = tuple(rU)\n",
    "V = tuple(rV)\n",
    "\n",
    "plt.plot(*zip(A, B, C, D), 'ro')\n",
    "plt.plot(*zip(A, B, C, D, A))\n",
    "plt.plot(*zip(U, V), 'ro')\n",
    "\n",
    "offset_up = numpy.array((0, 0.3))\n",
    "offset_down = numpy.array((0, -0.3))\n",
    "offset_right = numpy.array((0.2, 0))\n",
    "\n",
    "annotations = [{\"xy\": rA + offset_down, \"text\": \"A\"},\n",
    "               {\"xy\": rB + offset_down, \"text\": \"B\"},\n",
    "               {\"xy\": rC + offset_up, \"text\": \"C\"},\n",
    "               {\"xy\": rD + offset_up, \"text\": \"D\"},\n",
    "               {\"xy\": rU + offset_up, \"text\": \"U\"},\n",
    "               {\"xy\": rV + offset_up, \"text\": \"V\"},\n",
    "               {\"xy\": (rB+rA)/2 + offset_down, \"text\": \"a\"},\n",
    "              {\"xy\": (rC+rB)/2 + offset_right, \"text\": \"b\"}]\n",
    "\n",
    "\n",
    "for annotation in annotations:\n",
    "    plt.annotate(**annotation, ha=\"center\")\n",
    "\n",
    "plt.arrow(*A, *(rB-rA), head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "plt.arrow(*B, *(rC-rB), head_width=0.2, head_length=0.3, length_includes_head=True)\n",
    "\n",
    "    \n",
    "plt.axis([0, 6, 0, 4])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AC = a + b\n",
      "AU = b + 1/3 a\n",
      "VU = -1/3 a\n",
      "VA = -2/3 a - b\n"
     ]
    }
   ],
   "source": [
    "print(\"AC = a + b\")\n",
    "print(\"AU = b + 1/3 a\")\n",
    "print(\"VU = -1/3 a\")\n",
    "print(\"VA = -2/3 a - b\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Izražave\n",
    "\n",
    "Podane so točke $A(0, 1)$, $B(4, 1)$, $C(6, 3)$ in $D(2, 3)$.\n",
    "\n",
    "Določi presečišče $S$ diagonal $AC$ in $BD$ v štirikotniku $ABCD$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S: (3, 2)\n",
      "k: 1/2, l: 1/2\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "A = (0, 1)\n",
    "B = (4, 1)\n",
    "C = (6, 3)\n",
    "D = (2, 3)\n",
    "\n",
    "rA, rB, rC, rD = [krajevni_vektor(v) for v in [A, B, C, D]]\n",
    "\n",
    "AC = rC - rA\n",
    "BD = rD - rB\n",
    "\n",
    "plt.plot(*zip(A, B, C, D), 'ro')\n",
    "plt.plot(*zip(A, B, C, D, A))\n",
    "\n",
    "offset_up = numpy.array((0, 0.3))\n",
    "offset_down = numpy.array((0, -0.3))\n",
    "offset_right = numpy.array((0.2, 0))\n",
    "\n",
    "plt.arrow(*A, *AC, head_width=0.0, head_length=0.3, length_includes_head=True)\n",
    "plt.arrow(*B, *BD, head_width=0.0, head_length=0.3, length_includes_head=True)\n",
    "    \n",
    "import sympy\n",
    "from sympy import Matrix as M\n",
    "\n",
    "k, l = sympy.symbols(['k', 'l'])\n",
    "equation = sympy.Eq(M(rA) + k*M(AC), M(rB) + l*M(BD))\n",
    "solution = sympy.solve(equation, k, l)\n",
    "\n",
    "rS = rA + solution[k]*AC\n",
    "S = tuple(rS)\n",
    "\n",
    "plt.plot(*S, 'ro')\n",
    "\n",
    "annotations = [{\"xy\": rA + offset_down, \"text\": \"A\"},\n",
    "               {\"xy\": rB + offset_down, \"text\": \"B\"},\n",
    "               {\"xy\": rC + offset_up, \"text\": \"C\"},\n",
    "               {\"xy\": rD + offset_up, \"text\": \"D\"},\n",
    "               {\"xy\": rS + offset_up, \"text\": \"S\"},]\n",
    "\n",
    "for annotation in annotations:\n",
    "    plt.annotate(**annotation, ha=\"center\")\n",
    "\n",
    "plt.axis([-1, 7, 0, 4])\n",
    "plt.show()\n",
    "\n",
    "print(f\"S: {S}\")\n",
    "print(f\"k: {solution[k]}, l: {solution[l]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Določi razmerje med $BS$ in $DS$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l : (1-l) = 1\n"
     ]
    }
   ],
   "source": [
    "print(f\"l : (1-l) = {solution[l]/(1-solution[l])}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kot med vektorjema\n",
    "Dana sta vektorja $\\vec{a} = (3, 1)$ in $\\vec{b} = (2, −1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "\n",
    "def vektor(koordinate):\n",
    "    return numpy.array(koordinate)\n",
    "\n",
    "a = vektor((3, 1))\n",
    "b = vektor((2, -1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izračunaj dolžini obeh vektorjev."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dolžina vektorja a: 3.1622776601683795.\n",
      "Dolžina vektorja b: 2.23606797749979.\n"
     ]
    }
   ],
   "source": [
    "from numpy.linalg import norm\n",
    "\n",
    "print(f\"Dolžina vektorja a: {norm(a)}.\")\n",
    "print(f\"Dolžina vektorja b: {norm(b)}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izračunaj skalarni produkt $\\vec{a}\\cdot\\vec{b}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Skalarni product a in b: 5.\n"
     ]
    }
   ],
   "source": [
    "print(f\"Skalarni product a in b: {numpy.dot(a, b)}.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izračunaj kot med vektorjema $\\vec{a}$ in $\\vec{b}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kot med vektorjema a in b je 0.7853981633974484 radianov.\n",
      "To je 45.00000000000001 stopinj.\n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "\n",
    "angle = numpy.arccos(numpy.dot(a, b) / (norm(a)*norm(b)))\n",
    "print(f\"Kot med vektorjema a in b je {angle} radianov.\")\n",
    "print(f\"To je {360*angle/(2*pi)} stopinj.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vektorji v prostoru\n",
    "\n",
    "Podan je trikotnik z oglišči $A(0, 10, 5)$, $B(10, −2, 7)$ in $C(11, 7, 0)$.\n",
    "\n",
    "Izračunaj dolžino težiščnice na $c$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dolžina težiščnice na c je 9.0.\n"
     ]
    }
   ],
   "source": [
    "A = (0, 10, 5)\n",
    "B = (10, -2, 7)\n",
    "C = (11, 7, 0)\n",
    "rA = krajevni_vektor(A)\n",
    "rB = krajevni_vektor(B)\n",
    "rC = krajevni_vektor(C)\n",
    "\n",
    "rSC = ((rA + rB)/2) \n",
    "CSC = rSC-C\n",
    "print(f\"Dolžina težiščnice na c je {norm(CSC)}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izračunaj koordinate težišča trikotnika."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Koordinate težišča trikotnika so: [7. 5. 4.].\n"
     ]
    }
   ],
   "source": [
    "rT = 1/3 * (rA + rB + rC)\n",
    "print(f\"Koordinate težišča trikotnika so: {rT}.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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