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					Communicating Quantitative
     Information
                       Elections
                      Credit card
                   Survey of India.
   How big is Greenland? How long is the coast line?
          Map projections. Fractal dimension.
  Homework: Postings! Make proposal to moodle forum.
                  Work on Project II.
         (Study guide for final will be posted).
      Next class: Special lecture: artists and data
       A's for good behavior
• Author's construction: knowledge versus
  attitude:

 http://www.nytimes.com/2010/11/28/weeki
 nreview/28tyre.html?scp=1&sq=grading%
 20attitude&st=cse

• Comments?
From www.fivethirtyeight.com (data
     incomplete for Obama)
             Denominators
• What is the significance of Harding
  (1920)?

• Obama's victory: biggest by non-
  incumbent (and still counting). Is this a
  mandate?
  – apparently expectations too high!
          Election turnout
• Midterm results:
• http://elections.gmu.edu/Turnout_2010G.h
  tml
               Census year
• Re-districting at all levels
  – remember the gerrymander exercise and the
    districts don't have to look funny!
• Electoral college votes based on
  congressional counts plus 2 for senators
  – All but Maine and Nebraska winner take all.
    Maine and Nebraska do by congressional
    district. Note: Nebraska split in 2008.
                  Black Friday
• Original idea: this is when stores began being
  ahead ('in the black' versus 'in the red' = still in
  debt) for the year.
• Now: big sales day. Start of holiday buying.
• Confidence builder?

• What is current assessment? Posting (project)
  possibility!
   – May take time.
   – sales versus profits
Reprise (during times of shopping)
• Credit card balances will generate/are
  subject to interest!!!
  – Rules vary, but generally compounded daily.

  – Work out example
                  Move
• statistics to geometry
   Great Trigonometric Survey of
               India
• Measure
  – diameter of the earth
  – shape of earth: Earth is an oblate spheroid (more
    curved at equator than at poles)
    Goal: measure arc of meridian = length of 1 or some
    specified number of degrees of latitude along fixed
    longitude (meridian) to determine its length.

  – prepare information for maps
• Method: system of triangles
• http://www.positionmag.com.au/MM/content/200
  2/MM21/feature_2/MM21_feature_2.html
  – Started by William Lambton in 1799 and joined by
    George Everest in 1818
                  Trigonometry
• http://www-spof.gsfc.nasa.gov/stargaze/Strig1.htm
• Two-dimensional example: measure line A to B and
  angles BAC and ABC (name for angle measuring tool
  was theodolite)



        A


                            C




         B
   Can recreate triangle and calculate AC and BC
          Possible method
• Use jointed ruler.
• Create smaller (proportional) triangle by
  setting middle joint to represent side AB
• Rotate two other sides until the angles
  match CAB and CBA. Where sides cross
  represents point C.
                     Survey
• Many triangles were laid out this way.
   – towers, chains, and other actual physical marks:
     viewed by some/many as intrusian. Humans doing
     the calculations were called computers.
• Also, work in the 3rd dimension
   – measured the highest mountain using several
     different points
   – named Everest after the surveyor (Tibetan name
     Chomolungma: goddess mother of the world)
• Made measurements to calculate 'arc of longitude'
• Detected anomalies (errors/deviations) caused by the
  mass of the Himalayans

http://www.pupress.princeton.edu/books/maor/chapter_5.p
   df
many, many on-line sources
         Crow flies versus …
• What is the distance between A and B?
         A


  4 m.



                    B

             3 m.
        Pythagorean Theorem
• 32 + 42 = d2

• 9 + 16 = 25

• d = square root of 25
• d=5

• On tests, triangles tend to be 3-4-5, 5-12-13,
  with occasionally 1-1-sqrt(2)
         Crow flies versus …
• So if you needed to drive on roads laid out
  on a grid, and the blocks were 4miles and
  3 miles, to get from A to B,
  – you would go 4 + 3 miles = 7


• "Crow flies" (direct route) in this case
  would be 5 miles.
                 Exercise
• Sides of triangle are 6 and 8, what is
  hypotenuse?
• Sides of triangle are 6 and 10?
• Sides of triangle are 30 and 40?
• Sides of triangle are 10 and 10?
                  Note
• The blue & red paths are the same length
             At speed limit
• Speed limit 65 miles/hour
• Trip is 40 miles
• Traveling at the speed limit, trip takes
  40 miles / 65 miles/hour = .615 hours
     = (rounding) .615*60 minutes
     = 37 minutes
                Speeding
• 75 miles/hour
• 40 miles
• Takes 40 miles/75 m/hr = .5333 hours
  = .533 hours * 60 minutes/hour
  = 32 minutes


Time "saved": 5 minutes
Is it worth it?
            Route decision
• factors other than time: enjoy travel,
  chance to make stops, difficulty of driving
  (may be on highways or twisty side roads),
  chances of getting lost
• Time
  – Distance
  – Speed allowed/taken
                  Maps
• How to represent the globe (3-dimensional
  object) in a flat (2-dimensional) drawing?
• Imagine peeling an orange?
• half a circumference to a line is pi*r
     Map projection properties
Seek to minimize distortions
• shape (a point of the projection is conformal if
  scale is preserved in all directions, longitude and
  latitude are perpendicular)
• distance: from center to any point
• scale: one distance to another distance in
  proportion
• direction
• area (size)
CAN'T HAVE EVERYTHING
            Map projections
• vary as to the distortion of the properties
• Mercator: 1569. Conformal: preserved
  shapes. Great for navigation. Straight
  lines corresponded to constant compass
  bearing BUT areas distorted.
  – often cut off Antarctica, features Northern
    hemisphere ('Eurocentric')
  – Greenland is actually .8million sq. miles
    versus Africa is 11.6million sq. miles
Peters map (www.petersmap.com)
preserves size of areas, distorts shapes.
Gall-Peters (note: Gall was original
             designer)
             Fuller's Dymaxion:
 http://www.westnet.com/~crywalt/unfold.html

• http://friday.westnet.com/~crywalt/dym
  axion_2003/dymaxion_2003.swf
• 20 sided polyhedron (icosohedron)
• minimal distortion of shapes, areas,
  distances on major land masses
         Robinson projection
• Hand-crafted to look good!
• http://www.geography.wisc.edu/maplib/
• http://welcome.warnercnr.colostate.edu/
  class_info/nr502/lg2/projection_descript
  ions/robinson.html
              Projections
• … term for generating map from globe
  projecting the point

http://www.colorado.edu/geography/gcraft/n
  otes/mapproj/mapproj_f.html

Note: some maps are not exact projections,
 but use other techniques
          Projections, cont.
• Interactive program

http://www.btinternet.com/~se16/js/mapproj.
  htm
     Good summary of issues &
            techniques
• http://www.mapthematics.com/Essentials/
  Essentials.html
          Measuring Coasts
• depends on size/accuracy of ruler
• Coast line is twists, inlets, etc.
• related to Fractal: curve that repeats itself.
  Much work done by Benoit Mandelbrot
  (1924-2010)

  – http://faculty.purchase.edu/jeanine.meyer/sier
    pinski.html
     Return to dimensionality
• Dimensions of space
• Positions on the globe
  – Two dimensions: latitude and longitude
  – Plus Height?
     • When is this important?
   Google Maps/Google Earth
• Google maps
  – Directions
  – Also, ways of incorporating into applications
• Google Earth: free download
  – Create your own markings on earth!
  – See other layers
                Homework
• Posting possibility: alternative map
  projections
• Post proposal for Project II. The proposal
  is part of the assignment!
  – Prepare written report OR formal presentation
    for next week.
• (Study guide for final.)

				
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