1015.sagews

How thick is a single sheet of paper?

http://www.wolframalpha.com/input/?i=paper+thickness

OK, suppose you have a sheet of paper that thick.

Suppose you tear that sheet in half and stack the pieces.  How high will the stack be?

thickness = 4/1000

tears = 0

# initial height of stack in inches before tearing:
height = thickness
height

Evaluate and re-evaluate the following cell several times and verify the results.  Make sure you are clear about what is happening.

# height in inches after tearing and stacking:

tears = tears + 1
height = 2*height

print tears, 'tears:','height of stack --->', height, 'or',height.n(),'inches'

How high do you think the stack will be after 50 tears?

It might be annoying to evaluate the above cell 50 times, so following is some code that will do it all at once:

height = thickness
for tear in [0 .. 50]:
    height = 2*height
    print tear, 'tears:', height, '=',height.n()

Hmmm ... what do these numbers even mean?

Let's do this again and adjust for feet and miles as appropriate:

height = thickness
for tear in [0 .. 50]:
    feet = int(height/12)
    miles = int(feet/5280)
    inches = height - 12*feet
    feet = feet - 5280*miles
    print tear, 'tears:', miles, 'miles', feet, 'feet', inches.n(digits = 3), 'inches'
    height = 2*height

def height(thickness, tears): return thickness*2^tears

height(.005, 30)

\newcommand{\Bold}[1]{\mathbf{#1}}5.36870912000000 \times 10^{6}

def convert(height):
    feet = int(height/12)
    miles = int(feet/5280)
    inches = height - 12*feet
    feet = feet - 5280*miles
    return miles, feet, inches

convert(_)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(84, 3872, 5.12000000011176\right)