An Electronic Journal of
Geography and Mathematics


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Founded in 1990.

Cite articles as:  Author names(s), Year.  Title of article, Solstice:  An Electronic Journal of Geography and Mathematics,
Vol. XX, No. YY.  Ann Arbor:  Institute of Mathematical Geography

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Final version of IMaGe logo created by Allen K. Philbrick from original artwork from the Founder.

June, 2017

28 is a perfect number--the sum of its proper divisors.
28 = 1 + 2 + 4 + 7 + 14.


Guest Creators: 
Sandra L. Arlinghaus, William E. Arlinghaus, Adrienne Coley Dison, Richard 'Clay' Hamilton


The word clouds (formed in, online) serve as a visual "abstract" of the adjacent article!

Introduction to the Special Issue

Sidewalk Carousel Horses

Sandra Lach Arlinghaus
William E. Arlinghaus, Adrienne Coley Dison, Richard 'Clay' Hamilton

Mathematics Workout:  Arithmetic, Addition and Multiplication through Fractions

Sandra L. Arlinghaus and William C. Arlinghaus
 with input from Danny Rushing

In the In
Letter from Ruth Favro

Geometry Links from George Mokray....a hat tip to George from IMaGe!

Business card Level 3 Menger Sponge at MIT and around the world
Jeannine Moseley did a folding session on the Menger Sponge with the Philomorphs once upon a time

John Coltrane and Geometry
hat tip to Steve Provizer

Camboo - bamboo pavilion for Phnom Penh

Constructive Interference - static-kinetic sculpture

Ornitographies by Xavi Bou

NASA’s space fabric - 4D printing, they say

Collatz Conjecture visualizations

Nick Cave’s Until at MOCA

Casey Curran’s kinetic sculptures

Seeing Theory - a visual introduction to probability and statistics

Buddy James visualizes the Dougherty Set
Hat tip to John Higli

The graphical language for the aliens in the film “Arrival”
Painting by Martine Bertrand upon which the language is based
Editorial Comment:  The film is well worth seeing and the team designed about 100 symbols and a methodology to create more.  Might be interesting to imagine such a language not only graphically but also sculpturally as well, a material speech.

Carbon fiber pavilion woven by robots and drones

Abdelaziz Nait Merzouk tiles and honeycombs

John Baez geometry

Collective Paper Aesthetics - cardboard and paper modular building systems

Josie Lewis geometric art

Myoshka really likes Greek meander patterns

Image of magnetic “bridge” between galaxies
hat tip Leela Corman

Frederik Vanhoutte's generative graphics

Nanoscale cell image - the research is on lipids but the figures show a detailed look at cell structure

Organic geometry by José Bernabé

Birdland by George Hart

World’s largest kaleidoscope - a rebuilt grain silo

John Edmark - spiraling patterns
hat tip John Belt

Lyman Whitaker - wind sculptures

2.  Editorial Board, Advice to Authors, Mission Statement
3.  Awards



  Selected News...
  1. Work progressing on forthcoming book, Spatial Thinking in Environmental Contexts:  Maps, Archives, and Timelines.  Editors and co-authors:  Sandra L. Arlinghaus, Joseph Kerski, Ann Evans Larimore, Matthew Naud.  Due at CRC Press in the summer of 2018.
  2. Quaestiones Geographicae, Special Issue.
  3. Chene Street History Project.
  4. Spatial Mathematics:  Theory and Practice Through Mapping. Sandra L. Arlinghaus and Joseph Kerski, (2013), CRC PressLinked video.  Published July 2013, 
  5. The work above is the first volume in a series of books to be published by CRC Press in its series "Cartography, GIS, and Spatial Science:  Theory and Practice."  If you have an idea for a book to include, or wish to participate in some other way, please contact the series Editor, Sandra L. Arlinghaus.
  6. Virtual Cemetery with William E. Arlinghaus; an ongoing project that continues in development run in the virtual world in parallel with the trust-funded model of a real-world cemetery.


Solstice:  An Electronic Journal of Geography and Mathematics
Institute of Mathematical Geography (IMaGe).
All rights reserved worldwide, by IMaGe and by the authors.
Please contact an appropriate party concerning citation of this article:

Solstice was a Pirelli INTERNETional Award Semi-Finalist, 2001 (top 80 out of over 1000 entries worldwide)

One article in Solstice was a Pirelli INTERNETional Award Semi-Finalist, 2003 (Spatial Synthesis Sampler).

Solstice is listed in the Directory of Open Access Journals maintained by the University of Lund where it is maintained as a "searchable" journal.

Solstice is listed on the journals section of the website of the American Mathematical Society,
Solstice is listed in Geoscience e-Journals
IMaGe is listed on the website of the Numerical Cartography Lab of The Ohio State University:
Ulrich's lists online journal availability for full text sources:
  • Colorado Alliance of Research Libraries
    • Open Access Digital Library, 01/01/1990-
  • Directory of Open Access Journals
    • Directory of Open Access Journals, 1990-
  • EBSCOhost
    • Academic Search Complete, 12/01/2006-
    • Academic Search R&D, 06/01/2006-
  • Geoscience e-Journals
    • Geoscience e-Journals, 1990-
  • HEAL Link
    • Hellenic Academic Libraries Link, 1990-
  • Multiple Vendors
    • Freely Accessible Science Journals, 1990-
  • National Institute of Standards and Technology
    • National Institute of Standards and Technology Virtual Library, 1990-
  • Universitätsbibliothek Regensburg
    • Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals, 1990-
  • 中国教育图书进出口公司 (China Educational Publications Import & Export Corporation)
    • Socolar, 2004-2010

Abstracting and Indexing Databases:
Review posted on Ulrich's site:

An interesting example of a privately issued electronic journal. As described in the mission statement of the journal, "The purpose of Solstice is to promote interaction between geography and mathematics." Articles are scholarly in presentation, with clear illustrations and charts. A number of the articles are written by the editor; the editorial advisory board lists individuals from throughout the country. Libraries should review and consider adding this to their collection of electronic journals. 
ML 11-15-1997

Library of Congress Number:  G70.23
Dewey Decimal System Numbers:  526, 510.

Congratulations to all Solstice contributors.
Remembering those who are gone now but who contributed in various ways to Solstice or to IMaGe projects, directly or indirectly, during the first 28 years of IMaGe:

Allen K. Philbrick  Alma S. Lach   Donald F. Lach | Frank Harary | William D. DrakeH. S. M. Coxeter | Saunders Mac Lane | Chauncy D. Harris | Norton S. Ginsburg | Sylvia L. Thrupp | Arthur L. Loeb | George Kish
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