Spatial mathematics: theory and practice through mapping
"Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics requ...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press, Taylor & Franics
2014
|
| Schlagworte: | |
| Online-Zugang: | Cover image Inhaltsverzeichnis |
| Zusammenfassung: | "Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces"-- Provided by publisher. -- "Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces. Written by a field leader in education involving mathematics and mapping software and a field leader in mathematical geography. Supplies robust material and exercises tested in workshop situations . Includes software to which exercises are geared. Explains and includes QR (quick response) codes that link text to downloads server. Focuses on detailed illustrations of mathematical backgrounds in GIS with an interdisciplinary interaction"-- Provided by publisher. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXVIII, 272 S. zahlr. Ill., graph. Darst., Kt. |
| ISBN: | 9781466505322 |
Internformat
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| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press, Taylor & Franics |c 2014 | |
| 300 | |a XXVIII, 272 S. |b zahlr. Ill., graph. Darst., Kt. | ||
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| 500 | |a Includes bibliographical references and index | ||
| 520 | |a "Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces"-- Provided by publisher. -- "Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces. Written by a field leader in education involving mathematics and mapping software and a field leader in mathematical geography. Supplies robust material and exercises tested in workshop situations . Includes software to which exercises are geared. Explains and includes QR (quick response) codes that link text to downloads server. Focuses on detailed illustrations of mathematical backgrounds in GIS with an interdisciplinary interaction"-- Provided by publisher. | ||
| 650 | 4 | |a Geografie | |
| 650 | 4 | |a Geowissenschaften | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Geography |x Mathematics | |
| 650 | 4 | |a Cartography |x Mathematics | |
| 650 | 4 | |a Geographic information systems |v Software | |
| 650 | 7 | |a MATHEMATICS / Applied |2 bisacsh | |
| 650 | 7 | |a SCIENCE / Earth Sciences / General |2 bisacsh | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems |2 bisacsh | |
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Datensatz im Suchindex
| _version_ | 1804150214959824896 |
|---|---|
| adam_text | Contents
Preface
................................xi
Acknowledgments
.......................xvii
Introduction
...........................xix
Authors
.............................xxvii
1
Geometry of the Sphere
................1
7. /
Introduction
.............................................................. 7
1.2
Theory: Earth coordinate systems
................................2
7.3
Theory: Earth s seasons—A visual display
................... 70
1.4
Theory: Precision of latitude and longitude values
....... 12
1.5
Other Earth models
................................................. 17
1.6
Practice using selected concepts from this chapter
....... 19
1.6.1
Antipodal points
.......................................... 19
1.6.2
Capturing points with a smartphone
...............20
1.6.3
Great circle routes
........................................24
1.6.4
Latitude and longitude, hemispheres, and
precision
.....................................................26
1.6.5
Final considerations
......................................28
1.7
Related theory and practice: Access through
QR codes
..............................................................28
2
Location, Trigonometry, and
Measurement of the Sphere
..............31
2.7
Introduction: Relative and absolute location
................32
2.2
Location and measurement: From antiquity to today
.... 33
v
2.3
Practice:
Measuring the circumference of the Earth
using GPS
..............................................................37
2.3.1
Measuring the Earth s polar circumference
using Table
2.1............................................37
2.3.2
Measuring the Earth s equatorial
circumference using Table
2.2.......................38
2.3.3
For further consideration: Polar circumference
and equatorial circumference
........................40
2.3.4
Determining the mass and volume of the
Earth using Table
2.3...................................41
2.4
Measuring positions on the Earth surface,
and fractions
..........................................................41
2.5
Other common coordinate systems
............................43
2.6
Practice: Coordinates using different systems
..............47
2.7
Theory: Visual trigonometry review
............................48
2.8
Practice: Find the length of one degree on the
Earth-sphere
...........................................................50
2.9
Practice: Determine Sun angles at different seasons
of the year
.............................................................51
2.10
Practice: Work with measurement, the graticule,
and map projections
...............................................52
2.1 1
Summary and looking ahead
...................................54
2.12
Related theory and practice: Access
through QR codes
...................................................54
3
Transformations: Analysis and
Raster/Vector Formats
.................57
3.1
Transformations
......................................................58
3.1.1
One-to-one, many-to-one, and one-to-many
transformations
............................................58
3.1.1.1
Postal transformation
........................61
3.1.1.2
Home ownership
.............................61
3.1.1.3
Composition of transformations
.........62
3.1.1.4
Other one-to-many situations
............63
3.1.2
Geoprocessing and transformations
................64
3.1.3
QRcodes
...................................................66
3.2
Partition: Point-line-area transformations
.....................66
3.2.1
Buffers
........................................................66
3.2.2
Buffers build bisectors
...................................67
3.2.3
Buffers build bisectors and proximity zones
.....68
3.2.4
Base maps: Know your data!
.........................69
3.3
Set theory
..............................................................69
3.4
Raster and vector mapping: Know your file formats
.....70
3.4.1
Representing the Earth using raster and
vector data
.................................................73
vi
Contents
3.4.2
Vector
data resolution: Considerations
............74
3.4.3
Raster data resolution: Considerations
............75
3.4.4
Determining if a data set is fit for use
..............76
3.5
Practice using selected concepts from this chapter
.......77
3.5.1
Drawing buffers from different
types of features
..........................................77
3.5.2
Geodesic versus Euclidean buffering
..............78
3.5.3
Siting an Internet
café
in Denver
....................79
3.5.4
Data management: Getting data sets and
getting them ready for analysis
......................80
3.5.5
Analyzing your data: Buffers
.........................82
3.6
Related theory and practice: Access through
QR codes
..............................................................84
4
Replication of Results: Color and Number.
. . 87
4.1
Introduction
............................................................87
4.2
Background— Color
................................................88
4.3
Color straws and color voxels
...................................90
4.4
Color ramps: Alternate metrics
..................................94
4.5
Algebraic aspects of ratios
.......................................96
4.6
Pixel algebra
..........................................................98
4.7
Preservation of the aspect ratio
.................................99
4.8
Image security
...................................................... 100
4.9
Theory finale
........................................................ 101
4.10
Practice using selected concepts from this chapter
..... 101
4.10.1
Changing symbol color and size to
enhance meaning on maps
......................... 101
4.10.2
Identifying and mapping trees for a stream
bank erosion control project
........................ 104
4.11
Related theory and practice: Access through
QR codes
............................................................ 109
5
Scale
..............................
Ill
5. /
Introduction
...........................................................112
5.2
Scale change
........................................................7 73
5.3
The dot density map: Theory and example
................115
5.3.1
Construction of a dot density map
.................115
5.3.2
Dot density map theory
................................//8
5.4
Practice using selected concepts from this chapter
..... 120
5.4.1
Scale change exercise
................................ 120
5.4.2
Dot density maps: Investigating population
change
..................................................... 123
5.4.3
Creating your own dot density maps: Exercise...
125
5.5
Related theory and practice: Access
through QR codes
................................................. 126
Contents
vii
6
Partitioning of Data: Classification
and Analysis
.....................· · · 129
6.1
Introduction
.......................................................... 130
6.2
The choice of data ranges
..................................... 130
6.2.1
Natural breaks
.......................................... 133
6.2.2
Quantile
................................................... 134
6.2.3
Geometrical interval
................................... 134
6.2.4
Equal interval
............................................ 134
6.2.5
Standard deviations
................................... 135
6.3
Normalizing data
................................................. 136
6.4
Inside, outside, wrong side around
.......................... 138
6.5
Making something from nothing?
.............................141
6.5.1 Isolines;
contours
........................................ 142
6.5.2
Mapplets
.................................................. 143
6.6
Practice using selected concepts from this chapter
..... 145
6.6.1
Investigate classification using ArcGIS online...
145
6.6.2
Digging deeper into classification using
ArcGIS for desktop
.................................... 147
6.6.3
Normalization activity
................................ 150
6.7
Related theory and practice: Access through
QR codes
............................................................ 152
7
Visualizing Hierarchies
................155
7.1
Introduction
.......................................................... 155
7.2
Hierarchies: Census data
....................................... 157
7.3
Thinking outside the pixel
....................................... 159
7.3.1
Hexagonal hierarchies and close packing
of the plane: Overview
............................... 160
7.3.2
Classical urban hexagonal hierarchies
.......... 160
7.3.3
Visualization of hexagonal hierarchies
using plane geometric figures
.......................161
7.3.3.1
Marketing principle
........................
7Ó
ľ
7.3.3.2
Transportation principle
.................. 163
7.3.4
Visualization of hexagonal hierarchies
using mapplets
.......................................... 166
7.4
Practice using selected concepts from this chapter
..... 167
7.4.1
An introduction to census tabulation
areas: Using ArcGIS online for
demographic analysis
................................. 167
7.4.2
Using ArcGIS desktop for
demographic analysis
..................................170
7.4.3
Denver Internet
café
analysis
........................172
7.5
Related theory and practice: Access
through QR codes
..................................................174
viii
Contents
8 Distribution
of Data: Selected Concepts
... .177
8.1
Introduction
.......................................................... 177
8.2
Ann Arbor, Michigan—Tornado siren infill project
......179
8.2.1
Filling gaps in tornado siren coverage: Ann
Arbor, Ml
...................................................179
8.2.2
Related research
.........................................181
8.3
Educational and marketing efforts to the public
........../8/
8.4
Examining the distribution of tornado data
............... 182
8.5
Activity: Examining the distribution of tornado data...
186
8.6
Mean center and standard deviational ellipse
.......... 187
8.7
Activities using mean center and standard
deviational ellipse
................................................. 189
8.7.1
Computing and analyzing mean center and
standard deviational ellipse using historical
population data
......................................... 189
8.7.2
Standard deviational ellipse
.........................191
8.7.3
Applying measures of distribution to
tornado data
............................................. 192
8.8
Related theory and practice: Access
through QR codes
................................................. 193
8.9
Appendix of media commentary
............................. /95
9
Map Projections
.....................197
9.
í
Introduction
.......................................................... 197
9.2
In the news
......................................................... 198
9.3
Looking at maps and their underlying projections
......
J
99
9.4
Sampling projection distortion
................................203
9.5
Some projection characteristics
...............................206
9.6
Pseudo
or miscellaneous projections
........................206
9.7
Contemporary approach: Web Mercator Auxiliary
Sphere projection
.................................................208
9.8
Sampling the environment: The degree
confluence project
................................................209
9.9
Practice using selected concepts from this chapter
......210
9.9.1
Overview
...................................................210
9.9.2
Comparing projected data using
ArcCIS online
.............................................210
9.10
Around the theoretical corner?
.................................213
9.1 1
Exercises
..............................................................216
9.11.1
Overview
...................................................216
9.11.2
Comparing projections with ArcGIS
for desktop
.................................................216
9.11.3
Internet
café
in Denver activity
......................218
9.12
Related theory and practice: Access
through QR codes
..................................................218
Contents
ix
10
Integrating Past Present, and
Future Approaches
...................221
JO.
1
Introduction
..........................................................222
10.2
From the classics to the modern: Past and present
.....222
10.3
A non-Euclidean future?
.........................................227
10.3.1
Projective
geometry
....................................227
10.3.2
Perspective projections
................................228
10.3.3
Harmonic conjugates
..................................228
10.3.4
Harmonic map projection theorem
...............229
10.4
Practice using selected concepts from the chapter
.......232
10.4.1
Examining population change using the
gridded population data set
........................232
10.4.2
Network analysis: Offline and online
............234
10.4.2.1
Offline
.......................................234
10.4.2.2
Online
.......................................235
10.4.3
Routing exercise: Determining best route for
a tour bus in Manhattan
.............................236
10.4.4
Routing exercise: Determining best route for
trucking goods across the USA
....................237
10.4.5
Find the busy streets—Denver
......................240
10.4.6
Putting it all together: Practice—Denver
Internet
café
activity
...................................241
10.5
Graph theory and topology: Discrete and
continuous spatial mathematics
...............................243
10.6
Putting it all together: Theory
..................................245
10.7
Related theory and practice: Access
through QR codes
.................................................246
Glossary
.............................247
References, Further Reading, and Related
Materials
............................255
Update Bank!
http://www-personаl.umich.edu/~sаrhаus/
SpatialMathematics/index.html
Index
...............................263
χ
Contents
|
| any_adam_object | 1 |
| author | Arlinghaus, Sandra L. Kerski, Joseph J. |
| author_GND | (DE-588)1045234966 |
| author_facet | Arlinghaus, Sandra L. Kerski, Joseph J. |
| author_role | aut aut |
| author_sort | Arlinghaus, Sandra L. |
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| building | Verbundindex |
| bvnumber | BV040920366 |
| callnumber-first | G - Geography, Anthropology, Recreation |
| callnumber-label | G70 |
| callnumber-raw | G70.23 |
| callnumber-search | G70.23 |
| callnumber-sort | G 270.23 |
| callnumber-subject | G - General Geography |
| classification_rvk | RB 10103 |
| ctrlnum | (OCoLC)859368046 (DE-599)BVBBV040920366 |
| dewey-full | 910.01/51 |
| dewey-hundreds | 900 - History & geography |
| dewey-ones | 910 - Geography and travel |
| dewey-raw | 910.01/51 |
| dewey-search | 910.01/51 |
| dewey-sort | 3910.01 251 |
| dewey-tens | 910 - Geography and travel |
| discipline | Geographie |
| format | Book |
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Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces"-- Provided by publisher. -- "Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces. Written by a field leader in education involving mathematics and mapping software and a field leader in mathematical geography. Supplies robust material and exercises tested in workshop situations . Includes software to which exercises are geared. Explains and includes QR (quick response) codes that link text to downloads server. 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| id | DE-604.BV040920366 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:35:22Z |
| institution | BVB |
| isbn | 9781466505322 |
| language | English |
| lccn | 2012049508 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025899540 |
| oclc_num | 859368046 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-824 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-824 |
| physical | XXVIII, 272 S. zahlr. Ill., graph. Darst., Kt. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | CRC Press, Taylor & Franics |
| record_format | marc |
| spelling | Arlinghaus, Sandra L. Verfasser aut Spatial mathematics theory and practice through mapping Sandra Lach Arlinghaus ; Joseph J. Kerski Boca Raton, Fla. [u.a.] CRC Press, Taylor & Franics 2014 XXVIII, 272 S. zahlr. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces"-- Provided by publisher. -- "Spatial mathematics and analysis, two different approaches to scholarship, yield different results and employ different tools. This book explores both approaches to looking at real world issues that have mathematics as a critical, but often unseen, component. Readers learn the mathematics required to consider the broad problem at hand, rather than learning mathematics according to the determination of a (perhaps) artificial curriculum. This format motivates readers to explore diverse realms in the worlds for geography and mathematics and in their interfaces. Written by a field leader in education involving mathematics and mapping software and a field leader in mathematical geography. Supplies robust material and exercises tested in workshop situations . Includes software to which exercises are geared. Explains and includes QR (quick response) codes that link text to downloads server. Focuses on detailed illustrations of mathematical backgrounds in GIS with an interdisciplinary interaction"-- Provided by publisher. Geografie Geowissenschaften Mathematik Geography Mathematics Cartography Mathematics Geographic information systems Software MATHEMATICS / Applied bisacsh SCIENCE / Earth Sciences / General bisacsh TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems bisacsh Räumliche Statistik (DE-588)4386767-4 gnd rswk-swf Geoinformationssystem (DE-588)4261642-6 gnd rswk-swf ArcGIS (DE-588)4740955-1 gnd rswk-swf Mathematische Geografie (DE-588)4169101-5 gnd rswk-swf Geoinformationssystem (DE-588)4261642-6 s Räumliche Statistik (DE-588)4386767-4 s DE-604 Mathematische Geografie (DE-588)4169101-5 s ArcGIS (DE-588)4740955-1 s Kerski, Joseph J. Verfasser (DE-588)1045234966 aut http://jacketsearch.tandf.co.uk/common/jackets/covers/websmall/978146650/9781466505322.jpg Cover image Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025899540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arlinghaus, Sandra L. Kerski, Joseph J. Spatial mathematics theory and practice through mapping Geografie Geowissenschaften Mathematik Geography Mathematics Cartography Mathematics Geographic information systems Software MATHEMATICS / Applied bisacsh SCIENCE / Earth Sciences / General bisacsh TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems bisacsh Räumliche Statistik (DE-588)4386767-4 gnd Geoinformationssystem (DE-588)4261642-6 gnd ArcGIS (DE-588)4740955-1 gnd Mathematische Geografie (DE-588)4169101-5 gnd |
| subject_GND | (DE-588)4386767-4 (DE-588)4261642-6 (DE-588)4740955-1 (DE-588)4169101-5 |
| title | Spatial mathematics theory and practice through mapping |
| title_auth | Spatial mathematics theory and practice through mapping |
| title_exact_search | Spatial mathematics theory and practice through mapping |
| title_full | Spatial mathematics theory and practice through mapping Sandra Lach Arlinghaus ; Joseph J. Kerski |
| title_fullStr | Spatial mathematics theory and practice through mapping Sandra Lach Arlinghaus ; Joseph J. Kerski |
| title_full_unstemmed | Spatial mathematics theory and practice through mapping Sandra Lach Arlinghaus ; Joseph J. Kerski |
| title_short | Spatial mathematics |
| title_sort | spatial mathematics theory and practice through mapping |
| title_sub | theory and practice through mapping |
| topic | Geografie Geowissenschaften Mathematik Geography Mathematics Cartography Mathematics Geographic information systems Software MATHEMATICS / Applied bisacsh SCIENCE / Earth Sciences / General bisacsh TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems bisacsh Räumliche Statistik (DE-588)4386767-4 gnd Geoinformationssystem (DE-588)4261642-6 gnd ArcGIS (DE-588)4740955-1 gnd Mathematische Geografie (DE-588)4169101-5 gnd |
| topic_facet | Geografie Geowissenschaften Mathematik Geography Mathematics Cartography Mathematics Geographic information systems Software MATHEMATICS / Applied SCIENCE / Earth Sciences / General TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems Räumliche Statistik Geoinformationssystem ArcGIS Mathematische Geografie |
| url | http://jacketsearch.tandf.co.uk/common/jackets/covers/websmall/978146650/9781466505322.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025899540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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