Created
January 13, 2018 02:10
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 93, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"import matplotlib.ticker as tick" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 84, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"%%capture\n", | |
"!pip install shapely" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 85, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from shapely.geometry import Point\n", | |
"from shapely.geometry.polygon import Polygon" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 86, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def rand_point_on_circle():\n", | |
" angle = np.random.uniform(0.0, 2 * np.pi)\n", | |
" x, y = np.cos(angle), np.sin(angle)\n", | |
" return (x, y), angle" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 89, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"trials = 5000\n", | |
"arr = np.empty((trials, 3))\n", | |
"\n", | |
"origin = Point(0.0, 0.0)\n", | |
"\n", | |
"A = (1.0, 0.0)\n", | |
"\n", | |
"for i in range(trials):\n", | |
" B, arr[i][0] = rand_point_on_circle()\n", | |
" C, arr[i][1] = rand_point_on_circle()\n", | |
" triangle = Polygon([A, B, C])\n", | |
" arr[i][2] = triangle.contains(origin)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 90, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"0.2498\n" | |
] | |
} | |
], | |
"source": [ | |
"print(np.sum(arr[:, 2]) / trials)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 98, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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RM4ehiMt87rp+WeQDJAuyAxu6o0oUHnnbC1vQ9PyGzHjzB47uy47syaV3FX6qV9rJ9Lmr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\n0YlDTk+4HwAAAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1058a3d30>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig, ax = plt.subplots()\n", | |
"ax.scatter(arr[:, 0] / np.pi, arr[:, 1] / np.pi, c=arr[:, 2])\n", | |
"\n", | |
"ax.set_xlabel('Angle of Point B')\n", | |
"ax.xaxis.set_major_formatter(tick.FormatStrFormatter('%g $\\pi$'))\n", | |
"ax.xaxis.set_major_locator(tick.MultipleLocator(base=1.0))\n", | |
"\n", | |
"ax.set_ylabel('Angle of Point C')\n", | |
"ax.yaxis.set_major_formatter(tick.FormatStrFormatter('%g $\\pi$'))\n", | |
"ax.yaxis.set_major_locator(tick.MultipleLocator(base=1.0))\n", | |
"\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"* if both B and C in (0, pi) doesn't contain origin\n", | |
"* if both B and C in (pi, 2pi) doesn't contain origin\n", | |
"* if B in (0, pi) then if C in (pi, pi + B) to contain origin (and vice versa)\n", | |
"\n", | |
"=> P = 1 / 4" | |
] | |
} | |
], | |
"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": "3.6.1" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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