# Purchase as Is

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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
20attitude&st=cse

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
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

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
• Dimensions of space
• Positions on the globe
– Two dimensions: latitude and longitude
– Plus Height?
• When is this important?
– Directions
– Also, ways of incorporating into applications
– 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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