Transcript Math Meets Maps

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
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Math Meets Maps
Slide 3
The Globe Can Be Flattened
Segment in a photographic map of Mercury,
with gaps inserted to preserve scale
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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
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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 don’t cut to the edge)
The hemisphere you made out of paper
or half an orange peel or rubber ball
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Math Meets Maps
4. Measure the distance
between the same two cities
and explain what happened
Slide 6
Another Way of Drawing Flat Maps
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Math Meets Maps
Slide 7
Vertical
longitudinal
lines
The Equator
Curved
longitudinal
lines
The Equator
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Slide 8
Map Scale
0 100 200 300 400 500
1000 Miles
Scale does
not apply
to HI & AL
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Slide 9
Relief
Map of
California
Mountains
Hills
Hillsides
Sea level
Below
sea level
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Math Meets Maps
Slide 10
A Closer Look at
the Relief Map for
Southern California
0
50
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100 mi
Math Meets Maps
Slide 11
We sometimes
distort scale
on purpose
Mountains, with
heights doubled
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Math Meets Maps
Slide 12
Other Examples of Distorted Images
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Math Meets Maps
Slide 13
Aerial Image Looking South
from Goleta toward Santa Barbara
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Math Meets Maps
Slide 14
The Previous Image with Exaggerated
Mountain Heights
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Math Meets Maps
Slide 15
Satellite Image of the
Santa Barbara Channel
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Slide 16
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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
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Math Meets Maps
Slide 18
Contour Map
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Slide 19
Activity 4:
Pick two points on this map and
build a hiking trail between them
so that it is as flat as possible.
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Slide 20
Contour Map Under the Water
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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
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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
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Math Meets Maps
Slide 23
Map and Graph Coloring
Map to be
colored
Equivalent
graph
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Slide 24
Activity 5: Color These Maps
Use as few colors as possible
Real map: One color already used
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Math Meets Maps
Made-up map
Slide 25
Next Lesson
Thursday, November 4, 2004
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Math Meets Maps
Slide 26