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DataAnalysis.nb
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(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
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Cell["\<\
Generating or Importing Data in Mathematica (with a Halloween twist)\
\>", "Chapter",
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To learn how to analyse data, let\[CloseCurlyQuote]s first generate our own \
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Imagine you have a circular dart disk hanging on a wall in a square frame \
whose side length is exactly the diameter of your circle.\
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Visualization of the dart disk and square frame. The corners of the Rectangle \
are at {-1,-1} and {1,1} and the Disk is centered at {0,0} with a radius of 1.\
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"Next, you also have created a robot that throws darts at your dart disk, \
however, you must have made a mistake, because it always hits within the \
square, but where in the square is totally random.\nSo how can this help us \
estimate pi? We know that the Area of the circle is",
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So let\[CloseCurlyQuote]s throw some darts."
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Generate Random pairs of coordinates between -1 and 1 in an array of \
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What we are actually interested in is not the coordinates themselves, but \
whether they lie inside of the circle or not. For this we can use the \
construct of a \[OpenCurlyDoubleQuote]pure function\[CloseCurlyDoubleQuote], \
check out the tutorial to learn more about them, for now you need to know \
that you are using &/@ to apply the function to every element in a list (like \
a For loop in python) and # to represent where in your function that list \
element should go.\
\>", "Text",
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See if the coordinates are members of the region described by the list.\
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Now we need to count how many of the darts landed inside of the circle (aka. \
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Multiplying this by 4 should give us an estimate of pi. To get a numeric \
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