"My computer tells me that $\\pi$ is *approximatively*"
...
...
@@ -18,7 +18,9 @@
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"metadata": {"hideCode": false,
"hidePrompt": false,
"scrolled": true},
"outputs": [
{
"name": "stdout",
...
...
@@ -35,7 +37,7 @@
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": {"hidePrompt": false},
"source": [
"## Buffon's needle\n",
"Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
...
...
@@ -44,12 +46,13 @@
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"metadata": {"hideCode": false,
"hidePrompt": false},
"outputs": [
{
"data": {
"text/plain": [
"3.128911138923655"
"3.1289111389236548"
]
},
"execution_count": 2,
...
...
@@ -68,7 +71,7 @@
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": { "hideCode": false},
"source": [
"## 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\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"