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"\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"
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"source": [
"1 On the computation of π\n",
"1.1 Asking the maths library\n",
"My computer tells me that π is approximatively"
]
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"# 1 On the computation of π\n",
"# On the computation of $\\pi$\n",
"## 1.1 Asking the maths library\n",
"## Asking the maths library\n",
"My computer tells me that π is approximatively"
"My computer tells me that $\\pi$ is *approximatively*"
]
]
},
},
{
{
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@@ -51,8 +31,8 @@
...
@@ -51,8 +31,8 @@
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"## 1.2 Buffon’s needle\n",
"## Buffon's needle\n",
"Applying the method of Buffon’s needle, we get the approximation"
"Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
]
]
},
},
{
{
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@@ -84,9 +64,8 @@
...
@@ -84,9 +64,8 @@
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"## 1.3 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\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:"
"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:"
]
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{
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@@ -126,8 +105,7 @@
...
@@ -126,8 +105,7 @@
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"It is then straightforward to obtain a (not really good) approximation to π 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, X2 + Y2 is smaller than 1:"
