Spatial mathematics :
xxviii, 272 p. : illustrations (chiefly color) ; 25 cm. Content notes : 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. The 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. The 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. An 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. A 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--
Glossary--
References, further reading, and related materials. Cartography - Mathematics. Geographic information systems - Software. MATHEMATICS / Applied. SCIENCE / Earth Sciences / General. TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems.
