The Earth by descending powers of 2

  Interactive eBooks, refereed.  New volumes are underway.


  Student Series--work primarily of students but also with instructor "models" and "comment" included.  Please feel free to nominate work to be included in this section (from any university).  Unless a special arrangement is made, links are to original sites; thus, if work is removed, links will not work.   Students retain all rights to their own work and all responsibility for it.

University of Michigan, Maps, Timelines and the Internet, RCSSCI 461; AAPTIS 491; MENAS 591
          Fall 2008      Fall 2007
University of Michigan, 3D Modeling of Campus Competition, Directed Study, School of Natural Resources and Environment.  See Solstice link for models in "Awards" section.  Spring half-term, 2007.
University of Michigan, College of Engineering, Virtual Reality Series of Group Projects, 1996-2006.
University of Michigan, Taubman College of Architecture and Urban Planning, Geographic Information Systems, prerequisite UP406 or equivalent
Winter, 2003     Winter, 2002     Winter, 2001
University of Michigan, Taubman College of Architecture and Urban Planning, Maps and Decisions
Fall, 2003    Fall, 2002    Fall, 2001
University of Michigan, School of Natural Resources and Environment, Spatial Analysis, Advanced Projects, Prerequisite NRE530 or equivalent
Winter, 1999   Winter, 1998
University of Michigan, School of Natural Resources and Environment, Spatial Analysis, Theory and Practice:  Experimental, 1996-97; regular, 1998-99.
Fall, 1999    Fall, 1998    Fall, 1997    Fall, 1996
University of Michigan, School of Natural Resources and Environment, Population-Environment Dynamics series, 1992-1998

 Monograph Series, Classic eBooks in pdf format, refereed.  Revised, interactive versions are underway.
  • All materials copyrighted; all rights reserved, worldwide.
  • Earlier Monographs were bound in the classic cover shown here and in earlier versions of the same.  Now all are available in eBook (paperless) form. 
  • Entire books are reproduced in signed Portable Document Files, with the "signature" from IMaGe certifying that the electronic copy is one made directly from the original document.
  • Use Adobe Acrobat Reader to read these eBooks; animation is not supported.   Thus, later issues of Solstice, contemporary eBooks, and other documents are available only in formats that do support animation, applets, virtual reality, and various other features.
  • The means of original production is noted next to the book title.  Early copies of Solstice were typeset using TeX; the pdfs of printouts from the TeX file are shown here; to see the original TeX file, go to the Solstice Archive.  Readers were sent, via electronic mail, the electronic TeX files, with instructions to print out their own typeset journal if they wished (using their own printing equipment).
  • Click on the monograph numeral below to go directly to the eBook.
  • Readers wishing to order CDs or DVDs with monographs on them should contact IMaGe:  image@imagenet.org



 
Monograph One  78 pp.  (master document prepared using MTS by Gwen Nystuen) 
Sandra L. Arlinghaus and John D. Nystuen, 1986. 
Mathematical Geography and Global Art: the Mathematics of David Barr's `Four Corners Project'.
2009:  Link to Supplementary Materials.
  • Front Matter
  • Table of Contents
  • Chapter 1.  Introduction
  • Chapter 2.  Four Corner Sites for the Tetrahedron Sculpture
  • Chapter 3.  Extension of Barr's Problem to the Set of Platonic Solids
  • Chapter 4.  Uniqueness Questions
  • Appendix A.  Some Solid Geometry
  • Appendix B.  Some Linear Algebra
  • Appendix C.  Terrae Antipodum:  Antipodal Landmass Map
Monograph Two  79 pp.  (master document prepared using a typewriter)
Sandra L. Arlinghaus, 1986.
Down the Mail Tubes: the Pressured Postal Era, 1853-1984.
2009:  Link to Supplementary Materials.
  • Front Matter
  • Review by Sylvia L. Thrupp
  • Table of Contents
  • Introduction
  • Pneumatic Postal Networks in Western Europe
  • Pneumatic Postal Networks in the United States
  • Transfer of Technology
  • Appendix
  • Notes
  • Source of Maps and Figures
Monograph Three  167 pp.  (original document prepared by the author using a typewriter)
Sandra L. Arlinghaus, 1986.
Essays on Mathematical Geography.
2009:  Link to Supplementary Materials.
  • Front Matter
  • Table of Contents
  • The Well-tempered Map Projection
  • Antipodal Graphs
  • Measuring the Vertical City
  • Concavity and Human Settlement Patterns
  • Steiner Transformations
  • Analogue Clocks
  • Fad and Permanence in Human Systems
  • Topological Exploration in Geography
  • A Space for Thought
  • Chaos in Human Systems--The Heine-Borel Theorem
Monograph Four  118 pp. plus front matter.  (Original document prepared by the author using a typewriter)
Robert F. Austin, 1986.
A Historical Gazetteer of Southeast Asia.
2009:  Link to Supplementary Materials.
  • Cover
  • Front Matter
  • Introduction
  • Gazetteer
  • Notes and Abbreviations
  • Additional References
Monograph Five  101 pp. (original document prepared by the author using ChiWriter)
Sandra L. Arlinghaus, 1987.
Essays on Mathematical Geography-II.
  • Cover
  • Dedication
  • Frontispiece:  The Atlantic Drainage Tree
  • Acknowledgment
  • Table of Contents
  • Getting a Handel on Water-graphs
  • Terror in Transit:  A Graph Theoretic Approach to the Passive Defense of Urban Networks
  • Terrae Antipodum
  • Urban Inversion
  • Fractals:  Constructions, Speculations, and Concepts
  • Solar Woks
  • A Pneumatic Postal Plan:  The Chambered Interchange and ZIPPR Code
  • Endpiece
Monograph Six  162 pp.  (Original document prepared by the authors using word processing software.)
Pierre Hanjoul, Hubert Beguin, and Jean-Claude Thill, 1988.
Theoretical Market Areas Under Euclidean Distance.
  • Abstract -- Acknowledgments
  • Table of Contents
  • 1.  Introduction
  • 2.  Modelling consumers' behaviour
  • 3.  Delimitation of the problem and definitions
  • 4.  Elementary properties of market areas
  • 5.  Variation of the transportation cost difference along specific curves
  • 6.  Remarkable bounds and asymptotic behaviour:  spatial extension
  • 7.  Variation of y with x along the indifference line
  • 8.  The standpoint of mathematical topology:  spatial structure
  • 9.  Properties of the measures of Zk and of the extra territory of centre j
  • 10. Dependence of the market areas on the exponent a when h = .^a
  • 11. Some limiting properties of market areas
  • 12. Relaxation of the assumptions about the transportation cost function h
  • 13. Descartes' ovals
  • Conclusion
  • References
  • Appendices
  • List of main symbols
Monograph Seven  115 pp.  (Origiinal document prepared by the editor using word processing software.)
Keith J. Tinkler, Editor, 1988.  With contributions by Keith J. Tinkler, John D. Nystuen, and Michael F. Dacey.
Nystuen--Dacey Nodal Analysis.
  • Acknowledgments
  • "Foreward" (Nystuen)
  • Table of Contents
  • Preface  (Tinkler)
  • Statistics for Nystuen Dacey Nodal Analysis  (Tinkler)
  • Appendix A  (Tinkler)
  • Appendix B  (Tinkler)
  • Appendix C  (Nystuen and Dacey)
  • Appendix D  (Nystuen and Dacey)
  • Appendix E  (Nystuen and Dacey)
  • Appendix F  (Tinkler)
Monograph Eight  85 pp. (Original document prepared by the author using word processing software.)
James W. Fonseca, 1989.
The Urban Rank-size Hierarchy: A Mathematical Interpretation.
  • Introduction
  • The Spiral Constant
  • Other Derivations of the Ratio of the Spiral Constant
  • Generating Rank-Size by the Spiral Constant
  • The Slope of the Rank-Size Distribution
  • The Spiral Constant and Concavity of Rank-Size Distributions
  • The Spiral Constant and the Primate City
  • Traditional Rank-Size Relationships
  • Rank-Size Central Place Theory
  • Directions for Further Research
  • Bibliography
  • About the Author
Monograph Nine  84 pp. (original document prepared by the author using Plain TeX)
Sandra L. Arlinghaus, 1989.
An Atlas of Steiner Networks.
  • Front Matter
  • Introduction
  • Networks of Minimal Total Length in the Triangle
  • Networks of Minimal Total Length, in General
  • Geometric Constructions: the Six Point Case
  • Enumeration of Candidate Steiner Networks
Monograph Ten  103 pp. (original document prepared by the author using word processing software)
Daniel A. Griffith, 1989.
Simulating K=3 Christaller Central Place Structures: An Algorithm Using A Constant Elasticity of Substitution Consumption Function.
  • Front Matter
  • Preface
  • Table of Contents
  • Chapter 1.0.  Introduction
  • Chapter 2.0.  Background
  • Chapter 3.0. Mathematical and numerical solutions to components of the K = 3 central place structure problem
  • Chapter 4.0.  A multinomial logit classification model for determining hierarchical levels for commodities
  • Chapter 5.0.  Results for contrived test data sets
  • Chapter 6.0.  About the algorithm
  • Chapter 7.0.  Conclusing comments
  • Chapter 8.0.  Bibliography
  • Appendix A:  BASIC computer code for IBM-Compatible PCs
Monograph Eleven  104 pp. (original document prepared by the authors using Plain TeX)
Sandra L. Arlinghaus and John D. Nystuen, 1990.
Environmental Effects on Bus Durability.
  • Front Matter
  • Chapter 1:  Climatic Effects
  • Chapter 2:  Terrain Effects
  • Chapter 3:  Congestion Effects
  • Chapter 4:  Combined Effects
Monograph Twelve  398 pp. (Original document prepared by IMaGe using TeX.)
Daniel A. Griffith, Editor, 1990.
Spatial Statistics: Past, Present, and Future 
(because the file for the entire book is large, over 147MB, pdfs for individual chapters are also given)
 
Front Matter 4.  Robert P. Haining 8.  Daniel A. Griffith 12. Graham J. G. Upton
1,  Brian Ripley 5.  R. J. Martin 9.  Kanti V. Mardia 13. Patrick Doreian
2.  J. Keith Ord 6.  Daniel Wartenberg 10. Ashish Sen Index
3.  Luc Anselin 7  J. H. P. Paelinck 11. Sylvia Richardson
Monograph Thirteen  (original document prepared by the editor using Plain TeX)
Sandra L. Arlinghaus, Editor, 1990.
Solstice:  An Electronic Journal of Geography and Mathematics, Volume I.
  • Front matter for entire volume
  • Front matter for Volume I, Number 1, Summer, 1990
  • Postulates of the Science of Space (reprint), W. K. Clifford
  • Beyond the fractal, S. L. Arlinghaus
  • Groups, graphs, and God, W. C. Arlinghaus
  • Regular features
  • Front matter for Volume I, Number 2, Winter, 1990
  • A city of strangers:  spatial aspects of alienation in the Detroit metropolitan area (reprint), J. D. Nystuen
  • Scale and dimension:  their logical harmony, S. L. Arlinghaus.
  • Parallels between parallels, S. L. Arlinghaus
  • The Hedetniemi matrix sum:  a real-world application, S. L. Arlinghaus, W. C. Arlinghaus, J. D. Nystuen
  • Fractal geometry of infinite pixel sequences:  "Super-definition" resolution?  S. L. Arlinghaus
  • Regular Features
Monograph Fourteen 52 pp. (original document prepared by the author using Plain TeX)
Sandra L. Arlinghaus, 1991.
Essays on Mathematical Geography--III.
  • Cover
  • Dedication
  • Copyright statement
  • Preface
  • Table of Contents
  • Table for Central Place Fractals
  • Tiling According to the "Administrative" Principle
  • Moire Maps
  • Triangle Partitioning
  • An Enumeration of Candidate Steiner Networks
  • A Topological Generation Gap
  • Synthetic Centers of Gravity:  Conjecture
Monograph Fifteen  (original document prepared by the editor using Plain TeX)
Sandra L. Arlinghaus, Editor, 1991.
Solstice:  An Electronic Journal of Geography and Mathematics, Volume II.
  • Front Matter, Number 1, Volume II.
  • The Spatial Shadow:  Light and Dark---Whole and Part.  S. Arlinghaus, D. Barr, J. Nystuen.
  • Construction Zone:  Logistic Curve.  S. Arlinghaus.
  • Construction Zone:  Spatial Theory lectures.  S. Arlinghaus.
  • End Matter, Number 1, Volume II.
  • Front Matter, Number 2, Volume II.
  • Reprint:  Proof, Truth, and Confusion.  S. Mac Lane.
  • Digital Maps and Data Bases:  Aesthetics versus Accuracy.  R. F. Austin
  • End Matter, Number 2, Volume II.
Monograph Sixteen  (original document prepared by the editor  using Plain TeX)
Sandra L. Arlinghaus, Editor, 1992.
Solstice:  An Electronic Journal of Geography and Mathematics,. Volume III.
  • Front Matter, Number 1, Volume III.
  • Computing Areas of Regions with Discretely Defined Boundaries.  H. L. Stern
  • The Quadratic World of Kinematic Waves.  S. Arlinghaus, J. Nystuen, M. Woldenberg.
  • End Matter, Number 1, Volume III.
  • Front Matter, Number 2, Volume III.
  • Reprint:  What Are Mathematical Models and What Should They Be?  Frank Harary
  • Reprint:  Where Are We?  Comments on the Concept of the "Center of Population".  Frank Barmore.
  • The Pelt of the Earth:  An Essay on Reactive Diffusion.  S. Arlinghaus, J. Nystuen.
  • End Matter, Number 2, Volume III.
Monograph Seventeen  (original document prepared by the editor using Plain TeX)
Sandra L. Arlinghaus, Editor, 1993.
Solstice:  An Electronic Journal of Geography and Mathematics,. Volume IV.
  • Front Matter, Number 1, Volume IV.
  • Electronic Journals:  Observations Based on Actual Trials, 1987-Present.  S. Arlinghaus and R. Zander
  • Wilderness As Place.  J. Nystuen
  • Reprint:  The Earth Isn't Flat.  And It Isn't Round Either:  Some Significant and Little Known Effects of the Earth's Ellipsoidal Shape.  F. Barmore.
  • Microcell Hexnets?  S. Arlinghaus
  • Sum Graphs and Geographic Information.  S. Arlinghaus, W. Arlinghaus, F. Harary.
  • End Matter, Number 1, Volume IV.
  • Front Matter, Number 2, Volume IV.
  • Villages in Transition:  Elevated Risk of Micronutrient deficiency.  W. Drake, S. Pak, I. Tarwotjo, Muhilal, J. Gorstein, R. Tilden
  • End Matter, Number 2, Volume IV.
Monograph Eighteen 109 pp.  (Original document prepared by the author using word processing software.)
David J. Gordon. 1995.
The Cause of Location of Roads in Maryland: A Study in Cartographic Logic.
  • Chapter 1:  Introduction to the Cause of Location of Roads
  • Chapter 2:  Developing the Hypothesis of Ridge Roads
  • Chapter 3:  Constructing a Model of Ridge Roads
  • Chapter 4:  Central Maryland:  a Case Study
  • Chapter 5:  Generalizing the Results
  • References Cited
  • Appendix A  Glossary
  • Appendix B  Constructing the Contour Map of Travel Cost
Added link to folder containing figures.
Monograph Nineteen  (original document prepared by the editor using Plain TeX)
Sandra L. Arlinghaus, Editor, 1994.
Solstice:  An Electronic Journal of Geography and Mathematics,. Volume V.
  • Front Matter, Number 1, Volume V.
  • Reprint:  Getting Infrastructure Built, Virginia Ainslie and Jack Licate.
  • Reprint:  Center Here; Center There; Center, Center Everywhere, Frank Barmore.
  • Equal-Area Venn Diagrams of Two Circles:  Their Use with Real-World Data, B. Burkhalter
  • Los Angeles, 1994--A Spatial Scientific Study
  • End Matter, Number 1, Volume V.
  • Front Matter, Number 2, Volume V.
  • The Paris Metro:  Is its Graph Planar?  S. Arlinghaus, W. Arlinghaus, F. Harary.
  • Interruption!  S. Arlinghaus
  • Reprint:  Imperfections in the Uniform Plane, M. Dacey.
  • Construction Zone:  The Braikenridge-MacLaurin Construction
  • End Matter, Number 2, Volume V.
Monograph Twenty
Sandra L. Arlinghaus, Editor, 1995.
Solstice:  An Electronic Journal of Geography and Mathematics, Volume VI.
  • Chapter 0:  Front Matter
  • Chapter 1:  Fifth Anniversary of Solstice
  • Chapter 2:  New Format for Solstice
  • Chapter 3:  "Motor Vehicle Transport and Global Climate Change:  Policy Scenarios," R. Wallace
  • Chapter 4:  "Discrete Mathematics and Counting Derangements in Blind Wine Tastings,"  J. Nystuen, S. Arlinghaus, W. Arlinghaus
  • Chapter 5:  Index
Monograph Twenty One
Sandra L. Arlinghaus, Editor, 1996.
Solstice:  An Electronic Journal of Geography and Mathematics, Volume VII.
  • Chapter 0:  Front Matter
  • Chapter 1:  "The Greening of Detroit, 1975-1992:  Physical Effects of Decline," J. Nystuen, R. Ryznar, T. Wagner
  • Chapter 2:  "Algebraic Aspects of Ratios," S. Arlinghaus
  • Chapter 3:  "U.S. Route 12 Buffer,"  D. Jacobs
  • Chapter 4:  "Web Fractals,"  S. Arlinghaus
  • Chapter 5:  "Part II.  Elements of Spatial Planning:  Theory.  Merging Maps:  Node Labeling Strategies,"  S. Arlinghaus
  • Chapter 6:  Index
Monograph Twenty Two
Sandra L. Arlinghaus, Editor, 1997
Solstice:  An Electronic Journal of Geography and Mathematics,  Volume VIII.
  • Front Matter
  • "Why Whales Don't Freeze or Kidney-Shaped Airports:  Spatial Analysis and Spatial Design."  John D. Nystuen
  • "To the Memory of Clyde Tombaugh, 1906-1997."  Frank Harary
  • "The Photographic Record.  SunSweep:  A Visit on the Summer Solstice."  John D. Nystuen
  • "Buffers and Duality."  Sandra L. Arlinghaus, Frederick L. Goodman, Daniel A. Jacobs
  • "A Graph Theoretic View of the Join-Count Statistic."  Sandra L. Arlinghaus and William C. Arlinghaus
  • "Differences in Feature Representation in Digital Map Bases."  John D. Nystuen and Andrea I. Frank
Monograph Twenty Three
Sandra L. Arlinghaus, Editor, 1998
Solstice:  An Electronic Journal of Geography and Mathematics,  Volume IX.  
SEE ASSOCIATED ARTICLES IN SOLSTICE TO VIEW ANIMATION...
  • Front Matter
  • "Animaps."  Sandra L. Arlinghaus, William D. Drake, and John D. Nystuen with Audra Laug, Kris S. Oswalt, and Diana Sammataro
  • "Spatial Analysis, the Wisconsin Idea and the UW-System:  The Use and Abuse of Dispersion Statistics."  Frank E. Barmore
  • "Revitalizing Maps or Images?"  Sandra L. Arlinghaus and Ruben De la Sierra
  • Book Review by John D. Nystuen:  The Universe Below by William J. Broad.
  • "Animated Four Color Theorem:  Sample Map."  Sandra Lach Arlinghaus
  • "Animaps, II."  Sandra Lach Arlinghaus
  • Book Review by Daniel Albert: Rising Tide:  The Great Mississippi Flood of 1927 and How it Changed America by John M. Barry


Institute of Mathematical Geography
1964 Boulder Drive
Ann Arbor, MI 48104

734.975.0246
sarhaus@umich.edu
 


Founding Director and Creator of IMaGe:
Sandra Lach Arlinghaus
1964 Boulder Drive
Ann Arbor, MI 48104
U.S.A.
e-mail:  image@imagenet.org
phone:  734.975.0246


All material is copyrighted and copyrights for IMaGe materials are filed, along with original copy, in the Library of Congress. Please employ standards for fair use and citation practice similar to those for conventional printed matter. From the original IMaGe logo, Allen K. Philbrick created, for IMaGe, this graphic variation (in 1986) used as the background for this site.
Source of original (single) Earth animation, downloaded from: http://www.dsu.edu/~crosse/animation/earth.gif

This site was created, first, on December 19, 1995.