Math Plus Fun, Math Meets Maps - University of California ...

Math Plus Fun, Math Meets Maps - University of California ...

Math Meets Maps A Lesson in the Math + Fun! Series Oct. 2004 Math Meets Maps Slide 1 About This Presentation 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 Oct. 2004 Edition Released First Oct. 2004

Revised Math Meets Maps Revised Slide 2 Globes and Flat Maps Continents and countries appear to scale on a globe but they get distorted when drawn on some flat maps Africa same size on globe and map,

but Greenland much wider on map Oct. 2004 Math Meets Maps Slide 3 The Globe Can Be Flattened Segment in a photographic map of Mercury, with gaps inserted to preserve scale Oct. 2004 Math Meets Maps

Slide 4 Activity 1: Making a Hemisphere 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

Oct. 2004 Math Meets Maps Slide 5 Activity 2: Flattening a Globe 1. Take the hemisphere you made or half an orange peel or ball and draw a map on it 2. Mark two cities on the map and measure their distance 3. Open up the hemisphere or cut the orange peel

and flatten it (make sure you dont cut to the edge) 4. Measure the distance between the same two cities The hemisphere you made out of paper and explain what happened or half an orange peel or rubber ball Oct. 2004 Math Meets Maps Slide 6

Another Way of Drawing Flat Maps Oct. 2004 Math Meets Maps Slide 7 Vertical longitudinal lines The Equator

Curved longitudinal lines The Equator Oct. 2004 Math Meets Maps Slide 8 Map Scale

0 100 200 300 400 500 1000 Miles Scale does not apply to HI & AL Oct. 2004 Math Meets Maps Slide 9 Relief

Map of California Mountains Hills Hillsides Sea level Below sea level Oct. 2004 Math Meets Maps Slide 10

A Closer Look at the Relief Map for Southern California 0 50 Oct. 2004 100 mi Math Meets Maps Slide 11

We sometimes distort scale on purpose Mountains, with heights doubled Oct. 2004 Math Meets Maps Slide 12

Other Examples of Distorted Images Oct. 2004 Math Meets Maps Slide 13 Aerial Image Looking South from Goleta toward Santa Barbara Oct. 2004

Math Meets Maps Slide 14 The Previous Image with Exaggerated Mountain Heights Oct. 2004 Math Meets Maps Slide 15

Satellite Image of the Santa Barbara Channel Oct. 2004 Math Meets Maps Slide 16 Oct. 2004 Math Meets Maps Slide 17

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 Oct. 2004 Math Meets Maps Slide 18 Contour Map

Oct. 2004 Math Meets Maps Slide 19 Activity 4: ck two points on this map and uild a hiking trail between them o that it is as flat as possible. Oct. 2004

Math Meets Maps Slide 20 Contour Map Under the Water Oct. 2004 Math Meets Maps Slide 21 Cartograms Combine

Geographic and Other Data Outcome of the 2004 US presidential election Standard US map, showing states won by Bush (red) and Kerry (blue) (S. Fabrikant, UCSB Geog Dept) Cartogram, with states distorted to have areas proportional to electoral votes

Distribution of news stories during 1994-98 Oct. 2004 Math Meets Maps Cartogram, with relative support level for candidates indicated by shading Slide 22 The Map Coloring Problem We want to color countries, oceans, lakes, and islands on

a map so that no two adjacent areas have the same color. Two colors Three colors Four colors Oct. 2004 Math Meets Maps Slide 23

Map and Graph Coloring Map to be colored Equivalent graph Oct. 2004 Math Meets Maps Slide 24

Activity 5: Color These Maps Use as few colors as possible Real map: One color already used Oct. 2004 Math Meets Maps Made-up map Slide 25 Next Lesson Thursday, November 4, 2004

Oct. 2004 Math Meets Maps Slide 26

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