f38 math meets maps

Math Meets Maps: 

Math Meets Maps A Lesson in the 'Math + Fun!' Series

About This Presentation: 

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

Globes and Flat Maps: 

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

The Globe Can Be Flattened: 

  The Globe Can Be Flattened Segment in a photographic map of Mercury, with gaps inserted to preserve scale

Slide5: 

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: 

  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 paper or half an orange peel or rubber ball

Another Way of Drawing Flat Maps: 

Another Way of Drawing Flat Maps

Slide8: 

Vertical longitudinal lines Curved longitudinal lines

Slide9: 

Map Scale Scale does not apply to HI andamp; AL

Slide10: 

Relief Map of California Sea level Hillsides Hills Mountains Below sea level

Slide11: 

A Closer Look at the Relief Map for Southern California 0 50 100 mi

Slide12: 

Mountains, with heights doubled

Other Examples of Distorted Images: 

Other Examples of Distorted Images

Slide14: 

Aerial Image Looking South from Goleta toward Santa Barbara

Slide15: 

The Previous Image with Exaggerated Mountain Heights

Slide16: 

Satellite Image of the Santa Barbara Channel

Slide17: 

Slide18: 

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

Slide19: 

Contour Map

Slide20: 

Activity 4: Pick two points on this map and build a hiking trail between them so that it is as flat as possible.

Slide21: 

Contour Map Under the Water

Slide22: 

Distribution of news stories during 1994-98 Cartograms Combine Geographic and Other Data

The Map Coloring Problem: 

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

Map and Graph Coloring: 

Map and Graph Coloring Map to be colored Equivalent graph

Activity 5: Color These MapsUse as few colors as possible: 

  Activity 5: Color These Maps Use as few colors as possible Real map: One color already used Made-up map

Next Lesson: 

Next Lesson Thursday, November 4, 2004