106 lines
2.2 KiB
Plaintext
106 lines
2.2 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Happy Pi Day!\n",
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"\n",
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"### Two Ways to Calculate Pi: \n",
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"Real pi = 3.14159265359\n",
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"\n",
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"### 1. percentage of unit square random points that lie in unit circle\n",
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"This method is only as good as our random number generator. And with number of iterations the accuracy improves, up to about 1 million."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"3.1419916\n"
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]
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}
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],
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"source": [
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"import random\n",
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"in_square = in_circle = pi = 0\n",
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"\n",
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"for i in range(10000000):\n",
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" x = random.random()\n",
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" y = random.random()\n",
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" dist = (x*x + y*y) ** 0.5\n",
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"\n",
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" in_square += 1\n",
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" if dist <= 1.0:\n",
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" in_circle += 1\n",
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" \n",
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"pi = 4 * in_circle / in_square\n",
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"print(pi)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 2. using series addition\n",
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"pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 ... \n",
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"This method is the more accurate of the two, and is faster. Its accuracy only depends on the size of n."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"3.1415924535897797\n"
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]
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}
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],
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"source": [
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"pi = 0.0\n",
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"for i in range(1, 10000000, 4):\n",
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" pi += 4/i\n",
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" pi -= 4/(i+2)\n",
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"print(pi)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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