# Book:  Spatial Mathematics: Theory and Practice Through Mapping

Blog Post created by jkerski-esristaff on Apr 1, 2015

Dr Sandra Lach Arlinghaus and I have co-written a book entitled Spatial Mathematics—Theory and Practice Through Mapping, published by CRC Press/Taylor & Francis.  Spatial mathematics draws on the theoretical underpinnings of both mathematics and geography.  Spatial mathematics draws from geometry, topology, graph theory, trigonometry, modern algebra, symbolic logic, set theory, and more.  To build bridges between mathematics and geography, each of the book’s 10 chapters begins with theoretical discussions that form the bridge foundation, and activities that form the span between the two disciplines.  It can be used as a text in geography, GIS, or mathematics courses at the university or community college level, and by researchers interested in these intersections, and by GIS practitioners who seek deeper insight into the mathematics behind their spatial analysis.

1.  Geometry of the Sphere
2.  Location, Trigonometry, and Measurement of the Sphere
3.  Transformations: Analysis and Raster/Vector Formats
4.  Replication of Results: Color and Number
5.  Scale
6.  Partitioning of Data: Classification and Analysis
7.  Visualizing Hierarchies
8.  Distribution of Data: Selected Concepts
9.  Map Projections
10.  Integrating Past, Present, and Future Approaches
The book also includes a Glossary, References, Further Reading, and Related Materials.

Waldo Tobler of the University of California Santa Barbara, wrote, “Two ancient texts had a profound and lasting impact on the literate world—Euclid’s Elements, and the rediscovery in the 1400s of Ptolemy’s Geography from AD 150. […]  Now, in this book, additional insight for the mathematical solution of geographical tasks is provided. The pedagogical orientation is especially worthy of comment.”  Michael Batty, of the Centre for Advanced Spatial Analysis at University College London, wrote “Teaching mathematics can be tough but here is a book that is a gentle introduction to the mathematics of the spatial world through the medium of mapping.  The use of QR codes to access additional map-based material is clever and innovative, and provides a nice link to the very technologies that this mathematics supports.”

Michael Goodchild, of the University of California, Santa Barbara, wrote that “Mathematics underpins geography in many ways, especially in this new era of computerized mapping and geographic information systems. Geography can also be an exciting and relevant way of teaching many of the basic concepts of mathematics, from geometry and topology to statistics. So this book on spatial mathematics as applied to mapping is both timely and welcome. The wealth of practical examples and the enthusiasm of its authors will fill an important niche in a mapping literature that often underplays the importance and relevance of mathematics.”    Marc Schlossberg of the University of Oregon, wrote, “This book is both all about the map and all about the math behind the map, using what has become ubiquitous on our smart phones and in our vehicles as a vehicle itself to teach complex concepts accessible, meaningful, and useful for students.”