list of numbers

parent c48af447
......@@ -4,16 +4,15 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"March 28, 2019"
"# 1 On the computation of π\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1 On the computation of π\n",
"\n",
"### 1.1 Asking the maths library"
"## 1.1 Asking the maths library"
]
},
{
......@@ -38,8 +37,8 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1.2 Buffon’s needle\n",
"Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the **approximation**"
"## 1.2 Buffon’s needle\n",
"Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
]
},
{
......@@ -71,8 +70,8 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1.3 Using a surface fraction argument \n",
"A method that is easier to understand and does not make use of the sin function is based on the fact that if X ∼ U(0, 1) and Y ∼ U(0, 1), then $P[X^2 + Y^2 ≤ 1]$ = π/4 (see \"[Monte Carlo method\"\n",
"## 1.3 Using a surface fraction argument \n",
"A method that is easier to understand and does not make use of the sin function is based on the fact that if $X\\sim U(0,1)$ and $Y\\sim U(0,1)$, then $P[X^2+Y^2\\leq 1] = \\pi/4$ (see \"[Monte Carlo method\"\n",
"on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
]
},
......@@ -136,13 +135,6 @@
"source": [
"4*np.mean(accept)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
......
{
"cells": [],
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"a = np.array([14.0, 7.6, 11.2, 12.8, 12.5, 9.9, 14.9, 9.4, 16.9, 10.2, 14.9, 18.1, 7.3, 9.8, 10.9,12.2, 9.9, 2.9, 2.8, 15.4, 15.7, 9.7, 13.1, 13.2, 12.3, 11.7, 16.0, 12.4, 17.9, 12.2, 16.2, 18.7, 8.9, 11.9, 12.1, 14.6, 12.1, 4.7, 3.9, 16.9, 16.8, 11.3, 14.4, 15.7, 14.0, 13.6, 18.0, 13.6, 19.9, 13.7, 17.0, 20.5, 9.9, 12.5, 13.2, 16.1, 13.5, 6.3, 6.4, 17.6, 19.1, 12.8, 15.5, 16.3, 15.2, 14.6, 19.1, 14.4, 21.4, 15.1, 19.6, 21.7, 11.3, 15.0, 14.3, 16.8, 14.0, 6.8, 8.2, 19.9, 20.4, 14.6, 16.4, 18.7, 16.8, 15.8, 20.4, 15.8, 22.4, 16.2, 20.3, 23.4, 12.1, 15.5, 15.4, 18.4, 15.7, 10.2, 8.9, 21.0])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(14.113000000000001, 4.312369534258399, 23.4, 2.8, 14.113000000000001, 14.5)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(a), np.std(a), max(a), min(a), np.average(a), np.median(a)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
......@@ -16,10 +62,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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