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@ravy101
Last active February 3, 2020 09:13
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Probability Simulation
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{
"cells": [
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import matplotlib.patches as mpatches\n",
"import math"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The Question\n",
"\n",
"**Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle?**\n",
"\n",
"Lets start by creating a plot of the problem that we can re-use.\n"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f7117c21a90>"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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dcPiw7SQBI0XifCdOmF2MpCTbSYpl0qRJREdH06ZNG9tRim38+PH84x//YMeOHbaj+O7qq6FzZ1MoSgg5u3G+pCT49ltw4X7xzp07ue6668jIyODKK6+0Hccvw4YNIzMzk3fcOCLUjh1w/fVm7ImaNW2n+R85uxEIBw+aMQMcchGUrxISEnj22WddXyAABgwYwBdffMEXbrw2om5dM0CNCw96F0SKRH5JSeYy8MaNbSfx2Zdffsny5ctJSEiwHSUgKlSo4PzZv7xJSDAd8TIzbSfxmxSJPLt3w2uvmWHUXSY3N5eYmBiSkpKoWLGi7TgB8+ijj1KuXDlmzZplO4rvqlc3Y064pJ+KN1Ik8rzyihnUtlYt20l89tZbb1GqVCm6du1qO0pAKaVITU1lyJAhHD161HYc3/XpY0aw2rnTdhK/SJEA0y/i1VfN5L4u8+uvvzJ48OCgz8JlS3R0NO3bt2f06NG2o/iuYkXo2tX1g9OUvHdVccyfb45DXHON7SQ+GzNmDO3atePmm2+2HSVoxowZw2uvvUamG/fvn33WFInsbNtJik2KBJiLclzYitiyZQuvvvqqO+bY9MPll19O//796devn+0ovrvmGvMFNH++7STFJkViwwbYtAm6dLGdxGf9+vUjPj6eWi48juKr2NhY1q9fz9KlS21H8V2vXo6+OrQwUiSmTjUD2zpw1CZv0tPTWbNmDXFxcbajhETZsmWZNGkScXFx7pn9K0+XLuaLyG0jg3uEd5E4dgzefht69LCdxCdnz54lNjaWiRMnUs6FF6AVV+fOnalVqxbTpk2zHcU3F19svoimTrWdpFj8KhJKqSpKqfeVUpuUUhuVUq2UUtWUUv9WSmV67p17rfL8+dC6tZns10WmT59OZGQk97tsWH9/KaWYPHkyI0aM4IDbZtHq3t18IbnwAKa/LYlU4GOtdRRwHbARSADStdaNgHTPY2dKSzM9LF3k4MGDDB8+nJSUFJRStuOEXLNmzXj44YcZ5rZOb3XrmlnK//Mf20l8VuwLvJRSlYE1QAOdbyFKqc1AG631HqVUTWC51rqJt2VZucDr9GmoUQP++1+47LLQrtsPffr04ezZs7zs4gNh/jpw4ABXX3016enpXHvttbbjFN3IkXDoEFgac9TGBV4NgCzgdaXUd0qpGUqpCkANrfUeAM99gZ9ApVQPpVSGUiojKyvLjxjF9Nln0LSpqwrE+vXrmTNnDiNKyIVDxVW9enWGDh3qvtm/7r3XtF7dlBn/ikRpoDkwVWt9A3AcH3YttNbTtdbRWutoK7NKpaWZ6/5dQmtNXFwcQ4YMISIiwnYc6/72t7/xyy+/kJaWZjtK0V13HZw5Axs32k7iE3+KxE5gp9Z6pefx+5iisdezm4Hnfp9/EYNAa9cViYULF7Jjxw56ubDTVzCULl2alJQU+vbty+nTp23HKRqlzHvOTYUNP4qE1voXYIdSKu94Q1tgA5AGdPM81w1Y4FfCYFizxpyWuvpq20mK5PTp0/Tt25eUlBTKuGy6+2Bq164dzZo1IyUlxXaUonNhkSjt5+//HXhbKXUxsBV4ClN43lNKPQ1sBx7ycx2Bl5Zm9g9dcnZgypQpREVFcffdd9uO4jiTJk2iZcuWPPHEE9R00ChQF3TbbaZT1d695sC5C/h1ClRr/b3nuMIftNZdtNaHtNYHtNZttdaNPPcHAxU2YFasgLZtbacokr179zJu3DgmTZpkO4ojNWzYkKeffprBgwfbjlI0Zcuavjlffmk7SZGFX49LrWH1aoj2+UyQFYmJiTz55JM0duFoWaGSmJjIkiVLWLVqle0oRXPjjeY96BLhVyR++slMx3b55baTFGr16tUsXLiQ559/3nYUR6tcuTKjR492z+xfUiQcbvVq80dyuLxZuEaNGsWll15qO47jdevWjTNnzjBnzhzbUQqXVyTcUNAI1yLhgl2Nd999lxMnTvDUU0/ZjuIKF110EampqQwcOJDjx4/bjuNd7dpw0UWuGdYu/IpERobjWxInTpxgwIABrp2Fy5bWrVtz6623Mm7cONtRvFPKvAedMtdMIcKrSOQdtHR4kZgwYQKtWrXi1ltvtR3FdcaNG8fLL7/Mzz//bDuKdy46LhFeReLnnx1/0HL79u1MmTKF8SVomrhQqlu3Ln369GHAgAG2o3gnRcKhtmxx/MQ7AwcO5LnnnqNevXq2o7hWv379+Prrr/n8889tR7mwxo1h61bbKYokvIrEnj2OnldjxYoVfPHFF87/FnS48uXLM378eGJiYsjJybEdp2C1apn3owuEV5HYvdtRE7jml5ubS2xsLOPHj6dChQq247jeww8/TMWKFZk5c6btKAWrXBnOnjVDKDpceBWJPXscWyRmzZpFuXLleOSRR2xHKRHyZv8aOnQoR44csR3n95Qy70UXtCbCq0js3u3I3Y2jR4+SmJhIampqWA5JFyzNmzenU6dOjBw50naUgtWqZd6TDhdeRcKhLYlRo0bRoUMHol3QycttRo0axaxZs9i8ebPtKL/nkpaEv5eKu4sDWxKZmZnMnDmTdevW2Y5SItWoUYOEhATi4+NZuHCh7Ti/JS0Jh9HakS2J+Ph4BgwYwOUO7rvhdn369OG///0vH3/8se0ov1WzphQJR8nNhZMnoVIl20n+Z+nSpWzYsIGYmBjbUUq0iy++mOTkZOLi4sh20rwXl14Kv/5qO0WhwqdInD0LDhr6LTs7m7i4OCZNmkTZsmVtxynx7rnnHurVq+esqQjKlDHvS4cLnyKRnQ2lnXMIZtq0adSqVYvOLhqM182UUiQnJzNq1CisTOFQkNKlXTGjV/gUCQe1JPbv38/IkSOZPHmynPIMoaZNm9K1a1eGDh1qO4ohLQmHcdAAH8OGDePPf/4zzZo1sx0l7AwfPpx58+axZs0a21EMB70vL8Q57e9gc0jVXrt2LXPnzmWjyyZoKSmqVq3K8OHDiY2N5dNPP7XbknNQ69ab8GlJlC5tvUhorYmNjWXo0KFUr17dapZw1r17d/bv38+HH35oN8jZs446TnYh4VUkLB8kWrBgAXv37uVvf/ub1RzhLm/2r/j4eE6dOmUviMMOpl9I+BSJUqXMH+TECSurP3XqFPHx8aSkpFDaBW+Mkq5t27bccMMNJFua4RswV4CWL29v/UUUPkUi76q7X36xsvqUlBSuvfZa2rVrZ2X94vcmTpzIpEmT2LVrl50ADh/fJE/4FAmw1g12z549TJgwgYkTJ4Z83eLCGjRoQM+ePRk0aJCdAA4e3yS/8CoSlkYDGjx4MM888wwNGzYM+bqFd4MGDSI9PZ2VK1eGfuUuaUmE186xhUtzV61axZIlS9i0aVNI1yuKplKlSowZM4aYmBi+/PJLLroohN+bDrzgsCDh15II4e6G1po+ffowevRoKleuHLL1Ct88/vjj5Obm8vbbb4d2xQ4cuqAg4VUkQtySeOedd8jOzqZbt24hW6fwXd7sXwkJCRwL1ZiTx46ZU6AumMIxvIpECFsSx48fZ+DAgaSmpoa2CSuKpVWrVtxxxx2MHTs2NCvMOx7hgmt3wuvdW69eyOY6GDduHH/84x9p3bp1SNYn/JeUlMS0adPYtm1b8Fe2dat5P7qA30VCKVVKKfWdUmqh5/GVSqmVSqlMpdS7SqmL/Y8ZII0awb59cOhQUFfz008/8dJLLzl/TkrxG7Vr1yYuLo7+/fsHf2WrV0Pz5sFfTwAEoiURA+S/WmkcMFlr3Qg4BDwdgHUERqlScP318O23QV3NgAEDiImJoW7dukFdjwi8+Ph4MjIyWLZsWXBX5II5afP4VSSUUnWAe4AZnscKuAN43/OSN4Au/qwj4II8B+Nnn33GypUr6devX9DWIYLnkksuYeLEicTGxnI2mBcEhkuRAFKAAUCu53F14LDWOm/r7gRq+7mOwIqODlqRyMnJISYmhvHjx1PeBX3yRcH+9Kc/UbVqVWbMmBGcFezfb3Z5XdK5rthFQinVCdintc7/iSvoUG2Bo2oopXoopTKUUhkhHU7sxhshIyMoi545cyaVKlXi4YcfDsryRWgopUhJSWHYsGEcCsbxq7zjES456+VPytZAZ6XUT8A/MbsZKUAVpVReT846QIHnHLXW07XW0Vrr6MjISD9i+Khx46AcvDx8+DDPP/+8zMJVQlx//fV06dKFESNGBH7hLtrVAD+KhNZ6kNa6jta6PvAI8KnW+i/AMuBBz8u6AQv8ThlIQTp4OXLkSO69916au+SItSjcqFGjmD17duBHEQuXIuHFQKCvUupHzDGK14KwDv/83//B8uUBW9zmzZt54403GDVqVMCWKeyLjIxk8ODBxMXFoQM1FmVODqxYAa1aBWZ5IRCQIqG1Xq617uT5eavW+iatdUOt9UNa69OBWEdA3XsvfPRRwBbXt29fEhISqFGjRsCWKZyhd+/e/PTTTyxevDgwC1y5Ei6/HOrXD8zyQsAdR04CrVUr2LULfv7Z70X961//IjMzkz59+gQgmHCavNm/+vbty5kzZ/xfYFoauGyulfAsEqVKwT33+N2ayJuFKzk5mYsvdk7HUhFYHTt25KqrruLFF1/0f2FSJFwkALscL730EvXr1+eee+4JUCjhVMnJyYwdO5Z9+/YVfyE//mjOqkVHBy5YCIRvkbjrLvjqKzh6tFi/npWVxejRo2UWrjARFRXF448/zpAhQ4q/kI8+gk6dXNM/Io+70gZSpUrQujUsWVKsX3/++efp2rUrV199dYCDCacaOnQoaWlpfPfdd8VbgAt3NSCciwSYP9j8+T7/2po1a/jwww8ZPnx44DMJx6pSpQovvPACsbGxvp8SPXDA9I9o2zY44YIovIvEgw/C4sU+9b7Mm4Vr+PDhVK1aNYjhhBM988wzHD58mPfff7/wF+f35pvmOJgLr+kJ7yIRGWnOcsyaVeRfmTdvHgcOHKB79+7ByyUcq1SpUqSmptK/f39OnjxZtF/KzYWpU6F37+CGC5LwLhIAvXqZP2BubqEvPXnyJP369ZNZuMJcmzZtaNGiRdHnUUlPNy0IF/WyzE+KRKtW5g+Ynl7oS5OTk7nhhhu44447QhBMONmECRNISUlhx44dhb/45ZfNl5FLz4JJkVDK/AFfftnry3bt2kVycrLMwiUAqF+/Ps8++ywJCQneX7hjB3z+OXTtGppgQSBFAswf8PPPzR/0AgYNGkTPnj1p0KBBCIMJJ0tISOCzzz7jyy+/vPCLpk+Hv/wFKlYMXbAAkyIB5g/4l7+YP2gBvv76a9LT0+3NGSkcqWLFiiQlJRETE0NuQce0zpyBGTPg2WdDHy6ApEjk6d3bFIkjR37zdG5uLjExMYwdO5ZKlSpZCiecqmvXrpQuXZo333zz9//45pvQrBm4vMOdFIk8TZpAx45w3jGH2bNnA/DYY4/ZSCUcLm/2r8GDB3M0fxf/kyfhhRdg9Gh74QJEikR+w4ebA5i//ALAsWPHGDRokMzCJby66aabuPPOOxkzZsy5J//xD7jpJnNzORWwEXf8EB0drTOCNDitz/r2NfuSL75IYmIi27dv56233rKdSjjc7t27+cMf/sDKlSu5qlo1M5bqihUQFWU72v8opVZrrX2+BFWKxPn274eoKLbOnUuLBx/khx9+oHZtZ80KIJxp7NixfPPNN3wYFQVZWeagpYMUt0hIt8HzRURATAz9n3iCdu3asXXrVraGaP5Q4W7R0dGMHTOGT9LTabdhg+04ASNFoiBxcdRMSmJNZiaDBw+2nUa4yHUVK8Ktt0KdOrajBIwUiYJUrMiLEybAnDnw2WeuGyREWLJ6NXToANOm2U4SUPLuv5CePUFrc5RaiMKcPg1PPgnJyVCtmu00ASVF4kJKlYLXX4eRI83YhEJ4M2oUNGhgeu6WMFIkvGnUCIYMgb/+tUiXkoswtXo1vPKK2c1w6ZWe3kiRKMzf/24KhOx2iILk382oWdN2mqCQIlGY/LsdmZm20winGTmyxO5m5JEiURSNGkFiotntyMmxnUY4RUaGuSiwhO5m5JEiUVR9+kDZsiCXiwswPSofeghefLHE7mbkkSJRVKVKwbvvwgcfgFzLEd7OnDEjrT/6KDz8sO00QSedqXxRvTosWAD6JW1dAAAKeUlEQVS3324uLS8BV/iJYujTBy691Jz2DAPSkvBVs2bw2mvwwAOwe7ftNCLUpk41V3fOnh02PXGlJVEcnTvD2rXQpYvptn3JJbYTiVBYtsyMOfLll1C5su00IVPsUqiUqquUWqaU2qiUWq+UivE8X00p9W+lVKbnvmROczV4sDn11aOH6b4tSratW80xiHfegauusp0mpPxpL50F4rXWVwMtgd5KqaZAApCutW4EpHselzxKwcyZsHGjKRhSKEquX34xF24NGeLKuTz9VewiobXeo7X+1vPzr8BGoDZwH/CG52VvAF38DelY5cvDxx+bKeVHjrSdRgTD/v3Qrh089hg895ztNFYE5JiEUqo+cAOwEqihtd4DppAopS4LxDocKyLCzP51221QrhwMGGA7kQiUQ4fgzjvNMaghQ2ynscbvIqGUqgh8AMRqrY+qIvY8U0r1AHoAXHHFFf7GsKtGjXOFQmsYONB2IuGvAwdMgbj9djPidQnuUVkYv87hKKXKYArE21rreZ6n9yqlanr+vSawr6Df1VpP11pHa62jIyMj/YnhDLVrmzMdr79uhlKXYxTutXcvtGkDd90FkyaFdYEA/85uKOA1YKPWOjnfP6UB3Tw/dwMWFD+ey+QVivffN923pVC4z65dpkX4pz/B2LFhXyDAv5ZEa+Bx4A6l1PeeW0cgCbhTKZUJ3Ol5HD5q1DDn05ctM6fMTpywnUgU1cqVcPPN8PTTpj+EFAjAj2MSWusvgAttxfA7T5RfRAQsX276UNxyi+nKXbeu7VTCm7feMnOuzJgB991nO42jhEe/UhsuucTMBfnoo+bb6T//sZ1IFCQnB/r3Ny2HZcukQBRAikQwKWXegDNmwP33m85XwjkOH4ZOneDbb+Gbb8x1OeJ3pEiEQseO8PnnkJQEMTGQnW07kdi8GVq2NAMKffyxucJXFEiKRKhERZkDY5mZ0KoVrFtnO1F4ys2Fl16C1q0hPh6mTIEyZWyncjS5CjSUqlaFRYvM7sftt0NcnOmhWVr+DCGxdas5c3HqFHzxhaMm83UyaUmEmlLQvbsZhn35ctPklVZFcOW1Hm66Ce65RwqEj+QrzJYrroAlS6RVEWzSevCbtCRsKqhV8fnntlOVDCdOwLhx0noIACkSTpDXqoiLg27dzNmQNWtsp3Kns2fh1VehcWNYtcqMItWvnxnIWBSLFAmnUMpM8LJpkxng5O67zRgG27bZTuYOWptrZq65xswGP2+eedy4se1kridFwmnKljVTC2ZmmnP4LVqY0Zn37rWdzLk+/dT0ah0zxkzHmJ4uI5kHkBQJp6pUCYYNM8PjXXQRNG0KvXqZAXiFmfvin/+EW2+Fnj1Nn4eMDHN5t1yYFVBSJJwuMhJSUkxxqFED2rc3H4w5c8wHJdxs325GibriCnPsITYWNmyAP/85bIa4DzXZqm5Rq5ZpWfz0k/lgzJhhPiiJieaDU5Ll5sLSpWYKgxtugF9/NRdjpaebcR+kx2RQyUl5tylTxnww/vQnsysybZr54DRvbq5gvPdeqFfPdkr/nT1rzkykpcGHH5rdr9694e23oUIF2+nCitIOGD0pOjpaZ2Rk2I7hXsePm1OoaWmm23etWmbw1s6d4cYb3dMMP3r03P9j8WKoX98Uvc6dTSGUYw1+UUqt1lpH+/x7UiRKmJwc+Ppr80FLS4MjR8zl0LfcAtHRZg5Tp/QZOHoUvvvOHHBcutS0HG65xRSFTp1koJ4AkyIhCpaZCQsXmitQMzLMqdTrrjMtjOhocx+KwpG/IKxebW47d57Lctttpm9IpUrBzRHGpEiIojl82AyykvdBzcgwM1TVqQM1a5pbrVq//7l8eXNdSZky5j431xw3yM42t0OHzATKe/aY2/k/Hzx4riDk3a6+Wq5VCSEpEqL4jh41o0TnfbDPv9+zx1wglZ19rjBcdNG5glG6tLkMPn9ROf++dm0pCJYVt0jIX02YGbIrVzbf7EKcxyWHvYUQtkiREEJ4JUVCCOGVFAkhhFdSJIQQXkmREEJ4JUVCCOGVFAkhhFdSJIQQXkmREEJ4JUVCCOFVUIqEUqq9UmqzUupHpVRCMNYhhAiNgBcJpVQp4CWgA9AUeFQp1TTQ6xFChEYwWhI3AT9qrbdqrc8A/wTuC8J6hBAhEIwiURvYke/xTs9zQggXCkaRKGi00t+NbKOU6qGUylBKZWRlZQUhhhAiEIJRJHYC+UcwrQPsPv9FWuvpWutorXV0ZGRkEGIIIQIhGEViFdBIKXWlUupi4BEgLQjrEUKEQMCHr9Nan1VKPQcsAUoBM7XW6wO9HiFEaARljEut9WJgcTCWLYQILelxKYTwSoqEEMIrKRJCCK+kSAghvJIiIYTwyhHT/CmlsoCfi/DSCGB/kOP4SzIGjhtyuiljPa21zz0XHVEkikoplVGcuQxDSTIGjhtyhkNG2d0QQnglRUII4ZXbisR02wGKQDIGjhtylviMrjomIYQIPbe1JIQQIeaKIuHUgXWVUnWVUsuUUhuVUuuVUjGe56sppf6tlMr03Fd1QNZSSqnvlFILPY+vVEqt9GR813NZv818VZRS7yulNnm2ZyunbUelVJzn77xOKTVHKVXOCdtRKTVTKbVPKbUu33MFbjtlTPF8ln5QSjUvbPmOLxIOH1j3LBCvtb4aaAn09mRLANK11o2AdM9j22KAjfkejwMmezIeAp62kuqcVOBjrXUUcB0mq2O2o1KqNtAHiNZaN8MMg/AIztiOs4D25z13oW3XAWjkufUApha6dK21o29AK2BJvseDgEG2c10g6wLgTmAzUNPzXE1gs+VcdTxvlDuAhZghBvcDpQvaxhbyVQa24TlGlu95x2xHzo3dWg0zxMJC4G6nbEegPrCusG0HvAI8WtDrLnRzfEsClwysq5SqD9wArARqaK33AHjuL7OXDIAUYACQ63lcHTistT7reWx7mzYAsoDXPbtEM5RSFXDQdtRa7wImAtuBPcARYDXO2o75XWjb+fx5ckORKNLAujYppSoCHwCxWuujtvPkp5TqBOzTWq/O/3QBL7W5TUsDzYGpWusbgOM4Yxftfzz79PcBVwK1gAqYpvv5HPXeLIDPf3s3FIkiDaxri1KqDKZAvK21nud5eq9Sqqbn32sC+2zlA1oDnZVSP2HmQLkD07KoopTKG5nM9jbdCezUWq/0PH4fUzSctB3bAdu01lla62xgHvB/OGs75nehbefz58kNRcKxA+sqpRTwGrBRa52c75/SgG6en7thjlVYobUepLWuo7Wuj9l2n2qt/wIsAx70vMx2xl+AHUqpJp6n2gIbcNB2xOxmtFRKlff83fMyOmY7nudC2y4NeMJzlqMlcCRvt+SCbB0I8vGgTEfgv8AWINF2nny5bsE01X4AvvfcOmL2+dOBTM99NdtZPXnbAAs9PzcAvgF+BOYCZS1nux7I8GzL+UBVp21H4AVgE7AOeAso64TtCMzBHCfJxrQUnr7QtsPsbrzk+SytxZyt8bp86XEphPDKDbsbQgiLpEgIIbySIiGE8EqKhBDCKykSQgivpEgIIbySIiGE8EqKhBDCq/8HDOs7yLkvxVMAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"\n",
"def draw_question(cent, rad, poly_sides = 1):\n",
" fig=plt.figure()\n",
" ax=fig.add_subplot(1,1,1)\n",
" ax.set_aspect('equal')\n",
" top_point = (cent[0], cent[1] + rad)\n",
" plt.plot([0,2.4*rad],[2.4*rad,2.4*rad], color=\"white\", alpha=0)\n",
" plt.plot([2.4*rad,0],[0,0], color=\"white\", alpha=0)\n",
" centreCircle = mpatches.Circle(cent,rad,color=\"red\",fill=False)\n",
"\n",
" centreSpot = mpatches.Circle(top_point,0.8,color=\"blue\")\n",
" poly = mpatches.RegularPolygon(cent, poly_sides, radius=rad, fill=False)\n",
"#Draw the circles to our plot\n",
" ax.add_patch(centreCircle)\n",
" ax.add_patch(centreSpot)\n",
" ax.add_patch(poly)\n",
" return ax\n",
"radius = 40\n",
"centre = (1.2*radius,1.2*radius)\n",
"n = 3\n",
"draw_question(centre, radius, n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Interpretation\n",
"\n",
"We will consider for the sake of this experiment that the randomly selected chord is line connecting 2 randomly selected points lying on the circumference of the circle, point 1 and point 2 are independent, and all points on the circle are equally likely."
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.patches.Circle at 0x7f7117926588>"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"ax = draw_question(centre, radius)\n",
"plt.plot([centre[0]+radius, centre[1]], [centre[0], centre[1] + radius], color=\"blue\")\n",
"ax.add_patch(mpatches.Circle((centre[0]+radius, centre[1]),0.8,color=\"blue\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## By Intuition\n",
"We can see that our triangle divides the circumference of the circle into 3 even arcs. If for the sake of visualization we assume that our first point lies at one of the vertex of the triangle, we can see that if the second point lands in either of the 2 adjacent arcs, a line connecting the points will be shorter than the nearby triangle side. If the point lands in the arc opposite our first point, the line will be longer than the sides of the triangle. Meaning that a line connecting the first point to the second will be longer than the sides of the triangle if the second point lies in 1 out of 3 equal arcs. If all points are equally likely, then the probability of this is 1/3.\n",
"\n",
"Since we are working with a circle, the selection of the first point is arbitrary and the probability of the distance between point one and point two is 1/3 regardless of the selection of point 1.\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f7117d54828>]"
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"ax = draw_question(centre, radius, n)\n",
"plt.plot([centre[0], centre[1] + radius], [centre[0] + radius, centre[1]], color=\"red\")\n",
"plt.plot([centre[0], centre[1] - radius], [centre[0] + radius, centre[1]], color=\"red\")\n",
"plt.plot([centre[0], centre[1]], [centre[0] - radius, centre[1]+radius], color=\"green\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualizing\n",
"\n",
"We have our circle and triangle, we know that the circumradius of the triangle is equal to the radius of the circle, we will call this r.\n",
"\n",
"We can calculate the length of a side of a regular polygon by 2r * sin(pi/n) where n is the number of sides of the polygon.\n"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [],
"source": [
"#with a triangle we have 3 sides\n",
"n = 3\n",
"def calc_crit_len(rad, poly_sides):\n",
" return 2* rad * math.sin(math.pi/poly_sides)\n",
"critical_length = calc_crit_len(radius, n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So we have the length of our triangle sides, that is our critical distance. Lets visualise our circle as before, and overlay a circle with radius equal to the length of the triangle sides indicating every point that is closer to point 1 than our critical distance."
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.patches.Circle at 0x7f711c9e8ef0>"
]
},
"execution_count": 77,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"ax = draw_question(centre, radius, n)\n",
"critical_circle = mpatches.Circle((centre[0], centre[1] + radius),critical_length,color=\"yellow\",fill=True, alpha=.5)\n",
"ax.add_patch(critical_circle)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we can see that 2/3 of the circumference is within the critical distance to the first point (the area covered by the yellow circle) and 1/3 of the circumference is outside of the critical distance (not covered by the yellow circle). This confirms our intuition."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Experiment\n",
"Now we will randomly generate pairs of point and compare the chord they form to our calculated critical length. To do this we will randomly generate pairs continuous variable between 0 and 2 * pi, then map these to points on our circle's circumference.\n"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [],
"source": [
"import random\n",
"def RandPoints(r,n=100):\n",
" points = [(random.uniform(0, 2*math.pi), random.uniform(0, 2*math.pi)) for x in range(0,n)] \n",
" return [[(math.cos(p[0])*r,math.sin(p[0])*r),(math.cos(p[1])*r,math.sin(p[1])*r)] for p in points]\n",
"\n",
"#generate pairs of points\n",
"sample_size = 200\n",
"points = RandPoints(radius,sample_size)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets sanity check our data by plotting the points to make sure they are on a circle."
]
},
{
"cell_type": "code",
"execution_count": 79,
"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": [
"fig=plt.figure()\n",
"ax=fig.add_subplot(1,1,1)\n",
"ax.set_aspect('equal')\n",
"for p in points:\n",
" plt.scatter(p[0][0], p[0][1])\n",
" plt.scatter(p[1][0], p[1][1])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our points look good, lets create a function to calculate the straight line distance between 2 points, ie the length of the chord."
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [],
"source": [
"def chord_len(p1, p2):\n",
" return math.sqrt((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets now use our points and our distance function to see how many of our pairs of points form a chord longer than the critical value for this triangle. We will save this function to re-use later."
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Radius: 40, Sides of polygon: 3, Critical Length: 69.28203230275508\n",
"Total chords: 200, Number of Chords Longer than critical length: 57\n",
"Experimental probability estimate: 0.285\n",
"Expected probability: 0.3333333333333333\n"
]
},
{
"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": [
"def chord_experiment(rad, n, ex_points):\n",
" crit = calc_crit_len(rad, n)\n",
" green_count = 0\n",
" red_count = 0\n",
" fig=plt.figure()\n",
" ax=fig.add_subplot(1,1,1)\n",
" ax.set_aspect('equal')\n",
" for p in ex_points:\n",
" chord = chord_len(p[0], p[1])\n",
" if chord > crit:\n",
" col = \"green\"\n",
" green_count += 1\n",
" else:\n",
" col = \"red\"\n",
" red_count += 1\n",
" \n",
" plt.scatter(p[0][0], p[0][1], color = col)\n",
" plt.scatter(p[1][0], p[1][1], color = col)\n",
" plt.plot([p[0][0], p[1][0]], [p[0][1],p[1][1]], color = col)\n",
"\n",
" print(\"Radius: {}, Sides of polygon: {}, Critical Length: {}\".format(rad, n, crit))\n",
" print(\"Total chords: {}, Number of Chords Longer than critical length: {}\".format(len(points), green_count))\n",
" print(\"Experimental probability estimate: {}\".format(green_count/len(points)))\n",
" print(\"Expected probability: {}\".format((n-2)/n))\n",
"\n",
"chord_experiment(radius, n, points)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Summing Up for Triangles\n",
"\n",
"Now we can run our experiment and find that the frequency of having a chord longer than our triangle side. We find that it is close to our predicted value of 1/3."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generalizing Our Solution\n",
"\n",
"We can also extend this principal to other regular polygons. If a polygon divides a circle into n even arcs, the probability that a random chord is longer than the length of the side of the polygon will be the number of arcs, minus the 2 adjacent arcs divided by the total number of arcs.\n",
"\n",
"P(Chord>Side) = (n-2)/n\n",
"\n",
"Lets try a pentagon. If our reasoning is correct, the probability should be 3/5."
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.patches.Circle at 0x7f7117d61160>"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"new_n = 5\n",
"crit = calc_crit_len(radius, new_n)\n",
"ax = draw_question(centre, radius, new_n)\n",
"crit_circle = mpatches.Circle((centre[0], centre[1] + radius), crit, color=\"yellow\",fill=True, alpha=.5)\n",
"ax.add_patch(crit_circle)"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Radius: 40, Sides of polygon: 5, Critical Length: 47.022820183397855\n",
"Total chords: 200, Number of Chords Longer than critical length: 117\n",
"Experimental probability estimate: 0.585\n",
"Expected probability: 0.6\n"
]
},
{
"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": [
"sample_size = 200\n",
"points = RandPoints(radius,sample_size)\n",
"chord_experiment(radius, new_n, points)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our experimental probability appears close to our prediction! \n",
"\n",
"Our generalized solution appears to be plausible!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.6.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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