Some changes

parent c731b818
...@@ -4,8 +4,13 @@ ...@@ -4,8 +4,13 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# On the computation of $\\pi$\n", "# On the computation of $\\pi$"
"\n", ]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Asking the maths library\n", "## Asking the maths library\n",
"\n", "\n",
"My computer tells me that $\\pi$ is *approximatively*" "My computer tells me that $\\pi$ is *approximatively*"
...@@ -34,8 +39,7 @@ ...@@ -34,8 +39,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Buffon’s needle\n", "## Buffon’s needle\n",
"\n", "Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
"Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the **approximation**"
] ]
}, },
{ {
...@@ -68,9 +72,7 @@ ...@@ -68,9 +72,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Using a surface fraction argument\n", "## Using a surface fraction argument\n",
"\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 $P[X^2 + Y^2 \\le 1] = \\pi/4$ (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\"\n",
"on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
] ]
}, },
{ {
...@@ -113,8 +115,7 @@ ...@@ -113,8 +115,7 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how\n", "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller than 1:"
"many times, on average, $X^2 + Y^2$ is smaller than 1:"
] ]
}, },
{ {
......
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