oct. 2004math meets mapsslide 1 math meets maps a lesson in the “math + fun!” series

Oct. 2004 Math Meets Maps Slide 1

Math Meets MapsA Lesson in the “Math + Fun!” Series


About This Presentation

Edition Released Revised Revised

First Oct. 2004

This presentation is part of the “Math + Fun!” series devised by Behrooz Parhami, Professor of Computer Engineering at University of California, Santa Barbara. It was first prepared for special lessons in mathematics at Goleta Family School during the 2003-04 and 2004-05 school years. The slides can be used freely in teaching and in other educational settings. Unauthorized uses are strictly prohibited. © Behrooz Parhami


Globes and Flat MapsContinents and countries appear to scale on a globebut they get distorted when drawn on some flat maps

Africa same size on globe and map,but Greenland much wider on map


The Globe Can Be Flattened

Segment in a photographic map of Mercury, with gaps inserted to preserve scale


1. Cut out the two pieces on the left and attach them to form a strip

2. Make the strip into a circle

3. Bring the tips of opposing petals together so that the small circles at the tips overlap; glue or tape

Activity 1:Making a

Hemisphere


Activity 2: Flattening a Globe

1. Take the hemisphere you made or half an orange peel or ball and draw a map on it

3. Open up the hemisphere or cut the orange peel and flatten it (make sure you don’t cut to the edge)

4. Measure the distance between the same two cities and explain what happened

2. Mark two cities on the map and measure their distance

The hemisphere you made out of paperor half an orange peel or rubber ball


Another Way of Drawing Flat Maps


The Equator

The Equator

Verticallongitudinal

lines

Curvedlongitudinal

lines


0 100 200 300 400 500 1000 MilesMap Scale

Scale doesnot apply to HI & AL


ReliefMap ofCalifornia

Sea level

Hillsides

Hills

Mountains

Belowsea level


A Closer Look atthe Relief Map forSouthern California

0 50 100 mi


We sometimesdistort scaleon purpose

Mountains, withheights doubled


Other Examples of Distorted Images


Aerial Image Looking South from Goleta toward Santa Barbara


The Previous Image with Exaggerated

Mountain Heights


Satellite Image of theSanta Barbara Channel


Activity 3: From the lyrics of a 1950s song, “Twenty-six miles across the sea,Santa Catalina is awaitin’ for me” establish a scale for this map


Contour Map


Activity 4: Pick two points on this map andbuild a hiking trail between themso that it is as flat as possible.


Contour Map Under the Water


Distribution of news stories

during 1994-98

Cartograms CombineGeographic and Other Data

Standard US map, showing stateswon by Bush (red) and Kerry (blue)

Cartogram, with states distorted to haveareas proportional to electoral votes

Cartogram, with relative support levelfor candidates indicated by shading

Outcome ofthe 2004 USpresidential

election(S. Fabrikant,UCSB Geog Dept)


The Map Coloring ProblemWe want to color countries, oceans, lakes, and islands on a map so that no two adjacent areas have the same color.

Twocolors

Threecolors

Fourcolors


Map and Graph Coloring

Map to becolored

Equivalentgraph


Activity 5: Color These MapsUse as few colors as possible

Real map: One color already used Made-up map


Next LessonThursday, November 4, 2004

oct. 2004math meets mapsslide 1 math meets maps a lesson in the “math + fun!” series

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