"evalue": "invalid syntax (<ipython-input-1-a53cacb01e8c>, line 1)",
"output_type": "error",
"traceback": [
"\u001b[0;36m File \u001b[0;32m\"<ipython-input-1-a53cacb01e8c>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m 1 On the computation of π\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
]
}
],
"source": [
"1 On the computation of π\n",
"1.1 Asking the maths library\n",
"My computer tells me that π is approximatively"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1 On the computation of π\n",
"## 1.1 Asking the maths library\n",
"My computer tells me that π is approximatively"
"# On the computation of $\\pi$\n",
"## Asking the maths library\n",
"My computer tells me that $\\pi$ is *approximatively*"
]
},
{
...
...
@@ -51,8 +31,8 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1.2 Buffon’s needle\n",
"Applying the method of Buffon’s needle, we get the approximation"
"## Buffon's needle\n",
"Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
]
},
{
...
...
@@ -84,9 +64,8 @@
"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\n",
"fact that if X ∼ U(0, 1) and Y ∼ U(0, 1), then P[X2 + Y2 ≤ 1] = π/4 (see \"Monte Carlo method\" on Wikipedia). The following code uses this approach:"
"## 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:"
]
},
{
...
...
@@ -126,8 +105,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"It is then straightforward to obtain a (not really good) approximation to π by counting how\n",
"many times, on average, X2 + Y2 is smaller than 1:"
"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:"
