"My computer tells me that $\\pi$ is *approximately*"
"My computer tells me that $\\pi$ is *approximatively*"
]
]
},
},
{
{
"cell_type": "code",
"cell_type": "code",
"execution_count": 1,
"execution_count": 7,
"metadata": {},
"metadata": {},
"outputs": [
"outputs": [
{
{
...
@@ -43,7 +43,7 @@
...
@@ -43,7 +43,7 @@
},
},
{
{
"cell_type": "code",
"cell_type": "code",
"execution_count": 4,
"execution_count": 8,
"metadata": {},
"metadata": {},
"outputs": [
"outputs": [
{
{
...
@@ -52,7 +52,7 @@
...
@@ -52,7 +52,7 @@
"3.128911138923655"
"3.128911138923655"
]
]
},
},
"execution_count": 4,
"execution_count": 8,
"metadata": {},
"metadata": {},
"output_type": "execute_result"
"output_type": "execute_result"
}
}
...
@@ -71,12 +71,12 @@
...
@@ -71,12 +71,12 @@
"metadata": {},
"metadata": {},
"source": [
"source": [
"## Using a surface fraction argument\n",
"## 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 $X\\sim\\mathcal{U}(0,1)$ and $Y\\sim\\mathcal{U}(0,1)$, then $P[X^2+Y^2 \\le 1]=pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
"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 $P[X^2+Y^2 \\le 1]=\\pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"