"My computer tells me that $\\pi$ is _approximately_"
"## Asking the maths library\n",
"My computer tells me that $\\pi$ is *approximately*"
]
},
{
...
...
@@ -37,7 +37,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1.2 Buffon’s needle\n",
"## Buffon’s needle\n",
"Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
]
},
...
...
@@ -70,8 +70,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1.3 Using a surface fraction argument\n",
"\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\n",
"fact that if $X$ $\\sim$ $U(0, 1)$ and $Y$ $\\sim$ $U(0,1)$, then $P[X^2 + Y^2 ≤ 1]$ = $\\pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
]
...
...
@@ -115,7 +114,7 @@
"metadata": {},
"source": [
"It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how\n",
"many times, on average, $X^2 + Y^2$ is smaller than 1:"
"many times, on average, $X^2 + Y^2$ is smaller than 1:\n"
