Communicating Quantitative Information

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

What is the significance of Harding (1920)? Obama's victory: biggest by nonincumbent (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)

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 + 4 2 = d 2 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 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/ sierpinski.html Return to dimensionality Dimensions of space Positions on the globe Two dimensions: latitude and longitude Plus Height?

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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