COP 3223H meeting -*- Outline -*-

* Friday Problems with Python Numeric Types and Expressions

** A few left over points

*** floating point numbers are approximations
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    FLOATING POINT 'e' (or 'E') NOTATION

>>> 0.2718e1

>>> 3.0e-4

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    ... 2.718 == 2.718e0
    ... 0.0003
    Q: What does that e mean following the number?
      The exponent (following e) is a power of 10
      i.e., eX means "times 10**X"

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 FLOATING POINT NUMBERS ARE APPROXIMATIONS
       NOT EXACT!

They are not exact!

>>> 1/9.232 * 9.232

>>> 1e-5 + 1e5

>>> 1e-9 + 1e9

>>> 1e-27 + 1e27

>>> 1 - 3*(4/3 - 1)

>>> 0.1 + 0.1 + 0.1

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    Q: For each of these, what should the mathematical answer be?
    
    Note that while mathematically 1/9.232 * 9.232 should be 1.0, it is not

    Note the loss of precision in representing even 1e-9 + 1e9

    Q: How many real numbers are there between 0 and 10**(308.25)?
    an uncountably infinite number
    Q: How many floats are there in that range?
         (2**2045)*(2**51) (plus a few more), which is big, but not infinite
         So each float represents a range of reals, not exactly.

    The approximate nature of floating point numbers means that some
    mathematical identities don't hold!

    Moral: if you need exact results (e.g., finance, proofs) use ints!

    The advantage of floats is that they are fast to compute with
      and for many problems we can live with the approximations
** Problems
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       SOME PROBLEMS FOR YOU

Define functions to solve these problems:

1. How long would it take for you to drive
   a distance of D miles at a speed of
   V miles/hour?






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     It may help to think about the units!


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           MORE PROBLEMS

2. What is the energy (in Joules) needed
   to heat a given volume of water a
   given number of degrees Celsius?





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        Note: the heat-capacity of Water is 4.186 Joules/(grams * degC)
              and note that 1ml of water weighs 1 gram

        It is best to define the heat capacity of water in a variable:
            HEAT_CAPACITY = 4.186  # Joules/(grams * degC)


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3. Given the dimensions of a TV screen
   in inches, what is the diagonal measure
   of that screen?





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      Can use the Pythagorean theorem (a**2 + b**2 = c**2) to solve
      for c (the diagonal)


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4. Given an age, in years, return the
   number of miles that a person that age
   has traveled around the sun.






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     Note that 1 AU = distance from earth to the sun is 9.2955807e7 miles
     Assume the earth's orbit is roughly circular


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            MORE PROBLEMS

5. If you could stand on the surface of
   Pluto, what would a scale you brought
   with you say you weighed?





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     Pluto's mass is about 1.303e22 kg
     Pluto's radius is about 1187 km
     Netwon's grav. constant is 6.674e-11 N*m/kg**2
     1 N = 0.224809 foot-pound
     Newton's law: F = G*(m1*m2/r**2)