Communicating Quantitative Information

ElectionsCredit 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/weekinreview/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.html

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)

Can recreate triangle and calculate AC and BC

A

B

C

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.pdfmany, many on-line sources

Crow flies versus …

• What is the distance between A and B?A

B

4 m.

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/dymaxion_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_descriptions/robinson.html

Projections

• … term for generating map from globeprojecting the point

http://www.colorado.edu/geography/gcraft/notes/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/sierpinski.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.)