Spatial mathematics : theory and practice through mapping

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Title:

Personal Author:

Arlinghaus, Sandra L. (Sandra Lach), author

Publication Information:

Boca Raton : CRC Press, Taylor & Francis Group, 2014

Physical Description:

xxviii, 272 pages : illustrations (chiefly color) ; 25 cm.

ISBN:

9781466505322

Abstract:

"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

Subject Term:

Geography -- Mathematics

Cartography -- Mathematics

Geographic information systems -- Software

Added Author:

Kerski, Joseph J.,

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010345589	G70.23 A75 2014	Open Access Book	Book	Searching... Unknown

On Order

Summary

In terms of statistics, GIS offers many connections. With GIS, data are gathered, displayed, summarized, examined, and interpreted to discover patterns. Spatial Mathematics: Theory and Practice through Mapping uses GIS as a platform to teach mathematical concepts and skills through visualization of numbers. It examines theory and practice from disparate academic disciplines such as geography, mathematics, physics, and general social science. This approach allows students to grapple with biodiversity, crime, natural hazards, climate, energy, water, and other relevant real-world issues of the twenty-first century.

Includes QR Codes Linked to Animated Maps, a Mapping Activity Site, or to an Interactive Webpage, Creating an Interactive Resource That Stays Relevant

The book integrates competing philosophical views of the world: synthesis and analysis. These two approaches yield different results and employ different tools. This book considers both approaches to looking at real-world issues that have mathematics as a critical, but often unseen, component. This approach shows readers how to use mathematics to consider the broad problem at hand and to explore diverse realms in the worlds of geography and mathematics and in their interface.

A truly interdisciplinary text, the book bridges the worlds of mathematics and geography and demonstrates how they are inextricably linked. It takes advantage of the convergence in citizen science, STEM education, and mapping that help readers become critical consumers of data--understanding its content, quality, limitations, and benefits. It provides thorough grounding in the analytical, statistical, and computational skills required for working in any field that uses geospatial technologies--not just surveyors and remote sensing analysts.

Author Notes

Sandra Lach Arlinghaus is an American educator who is Adjunct Professor in the School of Natural Resources and Environment at the University of Michigan.

Preface	p. xi
Acknowledgments	p. xvii
Introduction	p. xix
Authors	p. xxvii
1 Geometry of the Sphere	p. 1
1.1 Introduction	p. 1
1.2 Theory: Earth coordinate systems	p. 2
1.3 Theory: Earth's seasons-A visual display	p. 10
1.4 Theory: Precision of latitude and longitude values	p. 12
1.5 Other Earth models	p. 17
1.6 Practice using selected concepts from this chapter	p. 19
1.6.1 Antipodal points	p. 19
1.6.2 Capturing points with a smartphone	p. 20
1.6.3 Great circle routes	p. 24
1.6.4 Latitude and longitude, hemispheres, and precision	p. 26
1.6.5 Final considerations	p. 28
1.7 Related theory and practice: Access through QR codes	p. 28
2 Location, Trigonometry, and Measurement of the Sphere	p. 31
2.1 Introduction: Relative and absolute location	p. 32
2.2 Location and measurement: From antiquity to today	p. 33
2.3 Practice: Measuring the circumference of the Earth using GPS	p. 37
2.3.1 Measuring the Earth's polar circumference using Table 2.1	p. 37
2.3.2 Measuring the Earth's equatorial circumference using Table 2.2	p. 38
2.3.3 For further consideration: Polar circumference and equatorial circumference	p. 40
2.3.4 Determining the mass and volume of the Earth using Table 2.3	p. 41
2.4 Measuring positions on the Earth surface, and fractions	p. 41
2.5 Other common coordinate systems	p. 43
2.6 Practice: Coordinates using different systems	p. 47
2.7 Theory: Visual trigonometry review	p. 48
2.8 Practice: Find the length of one degree on the Earth-sphere	p. 50
2.9 Practice: Determine Sun angles at different seasons of the year	p. 51
2.10 Practice: Work with measurement, the graticule, and map projections	p. 52
2.11 Summary and looking ahead	p. 54
2.12 Related theory and practice: Access through QR codes	p. 54
3 Transformations: Analysis and Raster/Vector Formats	p. 57
3.1 Transformations	p. 58
3.1.1 One-to-one, many-to-one, and one-to-many transformations	p. 58
3.1.1.1 Postal transformation	p. 61
3.1.1.2 Home ownership	p. 61
3.1.1.3 Composition of transformations	p. 62
3.1.1.4 Other one-to-many situations	p. 63
3.1.2 Geoprocessing and transformations	p. 64
3.1.3 QR codes	p. 66
3.2 Partition: Point-line-area transformations	p. 66
3.2.1 Buffers	p. 66
3.2.2 Buffers build bisectors	p. 67
3.2.3 Buffers build bisectors and proximity zones	p. 68
3.2.4 Base maps: Know your data!	p. 69
3.3 Set theory	p. 69
3.4 Raster and vector mapping: Know your file formats	p. 70
3.4.1 Representing the Earth using raster and vector data	p. 73
3.4.2 Vector data resolution: Considerations	p. 74
3.4.3 Raster data resolution: Considerations	p. 75
3.4.4 Determining if a data set is fit for use	p. 76
3.5 Practice using selected concepts from this chapter	p. 77
3.5.1 Drawing buffers from different types of features	p. 77
3.5.2 Geodesic versus Euclidean buffering	p. 78
3.5.3 Siting an Internet café in Denver	p. 79
3.5.4 Data management: Getting data sets and getting them ready for analysis	p. 80
3.5.5 Analyzing your data: Buffers	p. 82
3.6 Related theory and practice: Access through QR codes	p. 84
4 Replication of Results: Color and Number	p. 87
4.1 Introduction	p. 87
4.2 Background-Color	p. 88
4.3 Color straws and color voxels	p. 90
4.4 Color ramps: Alternate metrics	p. 94
4.5 Algebraic aspects of ratios	p. 96
4.6 Pixel algebra	p. 98
4.7 Preservation of the aspect ratio	p. 99
4.8 Image security	p. 100
4.9 Theory finale	p. 101
4.10 Practice using selected concepts from this chapter	p. 101
4.10.1 Changing symbol color and size to enhance meaning on maps	p. 101
4.10.2 Identifying and mapping trees for a stream bank erosion control project	p. 104
4.11 Related theory and practice: Access through QR codes	p. 109
5 Scale	p. 111
5.1 Introduction	p. 112
5.2 Scale change	p. 113
5.3 The dot density map: Theory and example	p. 115
5.3.1 Construction of a dot density map	p. 115
5.3.2 Dot density map theory	p. 118
5.4 Practice using selected concepts from this chapter	p. 120
5.4.7 Scale change exercise	p. 120
5.4.2 Dot density maps: Investigating population change	p. 123
5.4.3 Creating your own dot density maps: Exercise	p. 125
5.5 Related theory and practice: Access through QR codes	p. 126
6 Partitioning of Data: Classification and Analysis	p. 129
6.1 Introduction	p. 130
6.2 The choice of data ranges	p. 130
6.2.1 Natural breaks	p. 133
6.2.2 Quantile	p. 134
6.2.3 Geometrical interval	p. 134
6.2.4 Equal interval	p. 134
6.2.5 Standard deviations	p. 135
6.3 Normalizing data	p. 136
6.4 Inside, outside, wrong side around	p. 138
6.5 Making something from nothing?	p. 141
6.5.1 Isolines; contours	p. 142
6.5.2 Mapplets	p. 143
6.6 Practice using selected concepts from this chapter	p. 145
6.6.1 Investigate classification using ArcGIS online	p. 145
6.6.2 Digging deeper into classification using ArcGIS for desktop	p. 147
6.6.3 Normalization activity	p. 150
6.7 Related theory and practice: Access through QR codes	p. 152
7 Visualizing Hierarchies	p. 155
7.1 Introduction	p. 155
7.2 Hierarchies: Census data	p. 157
7.3 Thinking outside the pixel	p. 159
7.3.1 Hexagonal hierarchies and close packing of the plane: Overview	p. 160
7.3.2 Classical urban hexagonal hierarchies	p. 160
7.3.3 Visualization of hexagonal hierarchies using plane geometric figures	p. 161
7.3.3.1 Marketing principle	p. 161
7.3.3.2 Transportation principle	p. 163
7.3.4 Visualization of hexagonal hierarchies using mapplets	p. 166
7.4 Practice using selected concepts from this chapter	p. 167
7.4.1 An introduction to census tabulation areas: Using ArcGIS online for demographic analysis	p. 167
7.4.2 Using ArcGIS desktop for demographic analysis	p. 170
7.4.3 Denver Internet café analysis	p. 172
7.5 Related theory and practice: Access through QR codes	p. 174
8 Distribution of Data: Selected Concepts	p. 177
8.1 Introduction	p. 177
8.2 Ann Arbor, Michigan-Tornado siren infill project	p. 779
8.2.1 Filling gaps in tornado siren coverage: Ann Arbor, MI	p. 179
8.2.2 Related research	p. 181
8.3 Educational and marketing efforts to the public	p. 181
8.4 Examining the distribution of tornado data	p. 181
8.5 Activity: Examining the distribution of tornado data	p. 186
8.6 Mean center and standard deviational ellipse	p. 187
8.7 Activities using mean center and standard deviational ellipse	p. 189
8.7.1 Computing and analyzing mean center and standard deviational ellipse using historical population data	p. 189
8.7.2 Standard deviational ellipse	p. 191
8.7.3 Applying measures of distribution to tornado data	p. 192
8.8 Related theory and practice: Access through QR codes	p. 193
8.9 Appendix of media commentary	p. 195
9 Map Projections	p. 197
9.1 Introduction	p. 197
9.2 In the news	p. 198
9.3 Looking at maps and their underlying projections	p. 199
9.4 Sampling projection distortion	p. 203
9.5 Some projection characteristics	p. 206
9.6 Pseudo or miscellaneous projections	p. 206
9.7 Contemporary approach: Web Mercator Auxiliary Sphere projection	p. 208
9.8 Sampling the environment: The degree confluence project	p. 209
9.9 Practice using selected concepts from this chapter	p. 210
9.9.1 Overview	p. 210
9.9.2 Comparing projected data using ArcGIS online	p. 210
9.10 Around the theoretical corner?	p. 213
9.11 Exercises	p. 216
9.11.1 Overview	p. 276
9.11.2 Comparing projections with ArcGIS for desktop	p. 216
9.11.3 Internet cafe in Denver activity	p. 218
9.12 Related theory and practice: Access through QR codes	p. 218
10 Integrating Past, Present, and Future Approaches	p. 221
10.1 Introduction	p. 222
10.2 From the classics to the modern: Past and present	p. 222
10.3 A non-Euclidean future?	p. 227
10.3.1 Projective geometry	p. 227
10.3.2 Perspective projections	p. 228
10.3.3 Harmonic conjugates	p. 228
10.3.4 Harmonic map projection theorem?	p. 229
10.4 Practice using selected concepts from the chapter	p. 232
10.4.1 Examining population change using the gridded population data set	p. 232
10.4.2 Network analysis: Offline and online	p. 234
10.4.2.1 Offline	p. 234
10.4.2.2 Online	p. 235
10.4.3 Routing exercise: Determining best route for a tour bus in Manhattan	p. 236
10.4.4 Routing exercise: Determining best route for trucking goods across the USA	p. 237
10.4.5 Find the busy streets-Denver	p. 240
10.4.6 Putting it all together: Practice-Denver Internet cafe activity	p. 241
10.5 Graph theory and topology: Discrete and continuous spatial mathematics	p. 243
10.6 Putting it all together: Theory	p. 245
10.7 Related theory and practice: Access through QR codes	p. 246
Glossary	p. 247
References, Further Reading, and Related Materials	p. 255
Index	p. 263

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Author Notes

Table of Contents