CS 1025 01 - Week #7 (Oct 06 - Oct 10)

Monday, October 6th

1. Monte Carlo estimating area example.

                              b
   Do you understand the a = --- (d) formula and concepts.
                              c
    
   Can you look at a Monte Carlo problem 
       and find the a, 
                the b,                         b
                the c,                   The -----
                the d?                         c
   
       and figure out which of the four parts is the goal, the unknown?
   
   It is all in the above study guide PDF.   See page CCC.  See CCC.
    
   BICTION = if the INK don' flow, the understanding don't grow.
     
   Take some notes, use some lead or ink, consume some scratch paper.
   Practice.  Don't just read over and look at.  DO!  Nike.  Just DO it.
   

2. Monte Carlo with NetLOGO cows and houses.

3. Throwing darts. Old Monte Carlo quiz: Estimate the area of the circle. To keep the calculations simple, only 20 darts were thrown.

4. Drawing an OVAL and estimating the area of the OVAL with NetLOGO and Monte Carlo.

Wednesday, October 8th

1. What is a? What is b? What is c? What is d?

                b
       a   =  ----- * d
                c
   
       1.  Understand the problem:  Dr. Peter Venkman
   
           i. What is given?  What do you know?   What is the input?
   
          ii. What is the goal?  Or what is the unknown?
              What is it we need to find?
   
           Let's not rush things.  We don't even know WHAT you have here yet.
   
              (What Dr. Peter Venkman says as the Ghostbusters arrive at 
               the NYC Public Library in scene III of the movie).
   
       When you finish with Phase I of the problem solving process, you
       will have answers to the WHAT questions.
   
       For Monte Carlo problems, this will generally be:
   
           I am given 3 of the 4 or can derive 3 of the 4 numbers.
   
           I am given                    I need to find, the goal is:
                      a and b and c,               FIND d
             or       b and c and d,               FIND a
             or       a and c and d,               FIND b
             or       a and b and d.               FIND c
                                         
        Or you might be given a proportion, which is the 
        value of 
                   b
                 -----   or be asked to find the proportion.
                   c
   
        Suppose you are told that the proportion of darts or turtles
        that landed inside the circle was exactly 0.4 or 40%.
   
        And you were given that the entire area of the turtles grid
        was 625 (25 rows of patches and 25 columns of patches).
   
        And your goal is to estimate the area of the circle in patches.
   
              b                        ---
        a =  --- * d   =  0.40 * 625 = 250 patches is estimated circle area.
              c                        ---
   
        What is radius of the circle, by this area estimate?
                                                                           2
        area = pi * radius squared       area = PI r squared or area = PI r
        250 = 3.14159 * radius * radius
   
        250
      ------- = radius squared   so radius = squareRootOf( 250 / 3.14159 )
      3.14159
                                    radius = squareRootOf( 79.578 )
                                    radius = 8.92
   
          64 < 79.578 < 81 so the answer should be 8.something,
                           and since 79.578 is close to 81 or 9 squared,
                           it should be 8.8 or 8.9.
   
          So 8.92 makes sense as the answer.
   

Friday, October 10th

1. SOH, CAH, TOA - Sine, Cosine, Tangent. Opposite, Adjacent, Hypotenuse. Tri to get an angle on SOH, CAH, TOA.

2. VIP: Turtle Trigonometry problem with 12 turtles. Where is turtle with WHO number 2?