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    Spatial mathematics : theory and practice through mapping / Sandra Lach Arlinghaus, Joseph J. Kerski.

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    • Title:Spatial mathematics : theory and practice through mapping / Sandra Lach Arlinghaus, Joseph J. Kerski.
    •    
    • Author/Creator:Arlinghaus, Sandra L. (Sandra Lach), author.
    • Other Contributors/Collections:Kerski, Joseph J., author.
    • Published/Created:Boca Raton, FL : CRC Press, [2014]

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    • Library of Congress Subjects:Geography--Mathematics.
      Cartography--Mathematics.
      Geographic information systems--Software.
    • Description:xxviii, 272 pages : illustrations (chiefly color) ; 25 cm
    • Summary:"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.
    • Notes:Includes bibliographical references and index.
    • ISBN:9781466505322 (hardback)
      146650532X (hardback)
    • Contents:Machine generated contents note: 1. Geometry of the Sphere
      1.1. Introduction
      1.2. Theory: Earth coordinate systems
      1.3. Theory: Earth's seasons
      -A visual display
      1.4. Theory: Precision of latitude and longitude values
      1.5. Other Earth models
      1.6. Practice using selected concepts from this chapter
      1.6.1. Antipodal points
      1.6.2. Capturing points with a smartphone
      1.6.3. Great circle routes
      1.6.4. Latitude and longitude, hemispheres, and precision
      1.6.5. Final considerations
      1.7. Related theory and practice: Access through QR codes
      2. Location, Trigonometry, and Measurement of the Sphere
      2.1. Introduction: Relative and absolute location
      2.2. Location and measurement: From antiquity to today
      2.3. Practice: Measuring the circumference of the Earth using GPS
      2.3.1. Measuring the Earth's polar circumference using Table 2.1
      2.3.2. Measuring the Earth's equatorial circumference using Table 2.2
      2.3.3. For further consideration: Polar circumference and equatorial circumference
      2.3.4. Determining the mass and volume of the Earth using Table 2.3
      2.4. Measuring positions on the Earth surface, and fractions
      2.5. Other common coordinate systems
      2.6. Practice: Coordinates using different systems
      2.7. Theory: Visual trigonometry review
      2.8. Practice: Find the length of one degree on the Earth-sphere
      2.9. Practice: Determine Sun angles at different seasons of the year
      2.10. Practice: Work with measurement, the graticule, and map projections
      2.11. Summary and looking ahead
      2.12. Related theory and practice: Access through QR codes
      3. Transformations: Analysis and Raster/Vector Formats
      3.1. Transformations
      3.1.1. One-to-one, many-to-one, and one-to-many transformations
      3.1.1.1. Postal transformation
      3.1.1.2. Home ownership
      3.1.1.3. Composition of transformations
      3.1.1.4. Other one-to-many situations
      3.1.2. Geoprocessing and transformations
      3.1.3. QR codes
      3.2. Partition: Point-line-area transformations
      3.2.1. Buffers
      3.2.2. Buffers build bisectors
      3.2.3. Buffers build bisectors and proximity zones
      3.2.4. Base maps: Know your data!
      3.3. Set theory
      3.4. Raster and vector mapping: Know your file formats
      3.4.1. Representing the Earth using raster and vector data
      3.4.2. Vector data resolution: Considerations
      3.4.3. Raster data resolution: Considerations
      3.4.4. Determining if a data set is fit for use
      3.5. Practice using selected concepts from this chapter
      3.5.1. Drawing buffers from different types of features
      3.5.2. Geodesic versus Euclidean buffering
      3.5.3. Siting an Internet cafe in Denver
      3.5.4. Data management: Getting data sets and getting them ready for analysis
      3.5.5. Analyzing your data: Buffers
      3.6. Related theory and practice: Access through QR codes
      4. Replication of Results: Color and Number
      4.1. Introduction
      4.2. Background
      -Color
      4.3. Color straws and color voxels
      4.4. Color ramps: Alternate metrics
      4.5. Algebraic aspects of ratios
      4.6. Pixel algebra
      4.7. Preservation of the aspect ratio
      4.8. Image security
      4.9. Theory finale
      4.10. Practice using selected concepts from this chapter
      4.10.1. Changing symbol color and size to enhance meaning on maps
      4.10.2. Identifying and mapping trees for a stream bank erosion control project
      4.11. Related theory and practice: Access through QR codes
      5. Scale
      5.1. Introduction
      5.2. Scale change
      5.3. dot density map: Theory and example
      5.3.1. Construction of a dot density map
      5.3.2. Dot density map theory
      5.4. Practice using selected concepts from this chapter
      5.4.1. Scale change exercise
      5.4.2. Dot density maps: Investigating population change
      5.4.3. Creating your own dot density maps: Exercise
      5.5. Related theory and practice: Access through QR codes
      6. Partitioning of Data: Classification and Analysis
      6.1. Introduction
      6.2. choice of data ranges
      6.2.1. Natural breaks
      6.2.2. Quantile
      6.2.3. Geometrical interval
      6.2.4. Equal interval
      6.2.5. Standard deviations
      6.3. Normalizing data
      6.4. Inside, outside, wrong side around
      6.5. Making something from nothing?
      6.5.1. Isolines; contours
      6.5.2. Mapplets
      6.6. Practice using selected concepts from this chapter
      6.6.1. Investigate classification using ArcGIS online
      6.6.2. Digging deeper into classification using ArcGIS for desktop
      6.6.3. Normalization activity
      6.7. Related theory and practice: Access through QR codes
      7. Visualizing Hierarchies
      7.1. Introduction
      7.2. Hierarchies: Census data
      7.3. Thinking outside the pixel
      7.3.1. Hexagonal hierarchies and close packing of the plane: Overview
      7.3.2. Classical urban hexagonal hierarchies
      7.3.3. Visualization of hexagonal hierarchies using plane geometric figures
      7.3.3.1. Marketing principle
      7.3.3.2. Transportation principle
      7.3.4. Visualization of hexagonal hierarchies using mapplets
      7.4. Practice using selected concepts from this chapter
      7.4.1. introduction to census tabulation areas: Using ArcGIS online for demographic analysis
      7.4.2. Using ArcGIS desktop for demographic analysis
      7.4.3. Denver Internet cafe analysis
      7.5. Related theory and practice: Access through QR codes
      8. Distribution of Data: Selected Concepts
      8.1. Introduction
      8.2. Ann Arbor, Michigan
      -Tornado siren infill project
      8.2.1. Filling gaps in tornado siren coverage: Ann Arbor, MI
      8.2.2. Related research
      8.3. Educational and marketing efforts to the public
      8.4. Examining the distribution of tornado data
      8.5. Activity: Examining the distribution of tornado data
      8.6. Mean center and standard deviational ellipse
      8.7. Activities using mean center and standard deviational ellipse
      8.7.1. Computing and analyzing mean center and standard deviational ellipse using historical population data
      8.7.2. Standard deviational ellipse
      8.7.3. Applying measures of distribution to tornado data
      8.8. Related theory and practice: Access through QR codes
      8.9. Appendix of media commentary
      9. Map Projections
      9.1. Introduction
      9.2. In the news
      9.3. Looking at maps and their underlying projections
      9.4. Sampling projection distortion
      9.5. Some projection characteristics
      9.6. Pseudo or miscellaneous projections
      9.7. Contemporary approach: Web Mercator Auxiliary Sphere projection
      9.8. Sampling the environment: The degree confluence project
      9.9. Practice using selected concepts from this chapter
      9.9.1. Overview
      9.9.2. Comparing projected data using ArcGIS online
      9.10. Around the theoretical corner?
      9.11. Exercises
      9.11.1. Overview
      9.11.2. Comparing projections with ArcGIS for desktop
      9.11.3. Internet cafe in Denver activity
      9.12. Related theory and practice: Access through QR codes
      10. Integrating Past, Present, and Future Approaches
      10.1. Introduction
      10.2. From the classics to the modern: Past and present
      10.3. non-Euclidean future?
      10.3.1. Projective geometry
      10.3.2. Perspective projections
      10.3.3. Harmonic conjugates
      10.3.4. Harmonic map projection theorem
      10.4. Practice using selected concepts from the chapter
      10.4.1. Examining population change using the gridded population data set
      10.4.2. Network analysis: Offline and online
      10.4.2.1. Offline
      10.4.2.2. Online
      10.4.3. Routing exercise: Determining best route for a tour bus in Manhattan
      10.4.4. Routing exercise: Determining best route for trucking goods across the USA
      10.4.5. Find the busy streets
      -Denver
      10.4.6. Putting it all together: Practice
      -Denver Internet cafe activity
      10.5. Graph theory and topology: Discrete and continuous spatial mathematics
      10.6. Putting it all together: Theory
      10.7. Related theory and practice: Access through QR codes.
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