{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"pi can be approximated by throwing darts at a circle in a square, and calculating the ratio of darts landing on the circle vs the square."
]
},
{
"cell_type": "code",
"execution_count": 200,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import math\n",
"import random"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## simple way\n",
"\n",
"First, we generate a bunch of throws by using random.random()\n",
"\n",
"We are throwing darts in only the top right quadrant of the square, so the origin is the center of the square, and the diameter of the circle is 2.\n",
"\n",
"We figure out if the points are in the circle by using the pythogeras theorem to calculate the distance of each point from the origin `(0,0)`. If the distance is greater than the radius of the circle, it's outside."
]
},
{
"cell_type": "code",
"execution_count": 209,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"estimate: 3.146\n",
"actual: 3.141592653589793\n",
"difference is 0.004407346410206792\n"
]
}
],
"source": [
"darths_thrown = 10000\n",
"throws = [[random.random(), random.random()] for i in range(darths_thrown)]\n",
"\n",
"in_circle=0\n",
"out_circle=0\n",
"\n",
"for throw in throws:\n",
" if math.sqrt(throw[0]**2 + throw[1]**2) <= 1:\n",
" in_circle +=1\n",
" else:\n",
" out_circle += 1\n",
"\n",
"pi_estimate = in_circle/len(throws) * 4\n",
"\n",
"print(f'estimate: {pi_estimate}')\n",
"print(f'actual: {math.pi}')\n",
"print(f'difference is {abs(pi_estimate-math.pi)}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# now to jazz this up visually"
]
},
{
"cell_type": "code",
"execution_count": 210,
"metadata": {},
"outputs": [
{
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