Goode's 80th!
Sandra Lach Arlinghaus

In 1925, Professor J. P. Goode of the University of Chicago Geography Department superimposed a sinusoidal and a Mollweide (homolographic) projection and noted similarities in the maps on either side of the equator [3].  Eureka!  The "homolographic" projection was born (Figure 1).  Anderson and Tobler note that the "kinks" in the edge of the Goode homolosine, at about 40 degrees north and south latitude, show where the Mollweide is joined to the sinusoidal:  sinusoidal is central and Mollweide is polar [1].  This familiar equal area interrupted projection is often used to display global distributions of terrestrial phenomena.

Figure 1.  Goode's homolosine projection used to portray global land use patterns (source: [4] Lethcoe, Kent J. and Klaver, Robert W.  Simulating the Interrupted Goode Homolosine Projection with ArcInfo. Used with permission of the authors and the USGS/EROS Data Center).

Goode documented his observations using the technology of the time; it was not possible to offer a visual display, in a bound journal, of the act of overlaying one map on another.  Thus, Goode's actual, direct observation could not be recorded.  In an electronic journal, it is possible to offer such displays.  The maps in Figure 2 show a Mollweide (Figure 2a) and a sinusoidal projection (Figure 2b) in adjacent rows of a table.  These maps were made using ArcView 3.2 GIS (ESRI) and scaled so that the equator and prime meridian have identical length in both projections.  In both, small circles are line segments parallel to the equator.  In the Mollweide, meridians are halves of ellipses; in the sinusoidal, meridians are formed from arcs of the sine curve.  The two projections are similar in geometric construction but differ in the formulae used to make calculations within that general structure.  The reader interested in the detail of construction might wish to read the clear and thorough explanantion offered by Snyder [5].

Figure 2a.  Mollweide projection.  Meridians are halves of ellipses of increasingly sharp curvature as one moves away from the central meridian.

Figure 2b.  Sinusoidal projection.  Meridians are arcs of a sine wave of increasingly sharp curvature as one moves away from the central meridian.

When one looks at Figure 2a, and then at Figure 2b, it may not be clear how Figure 1 arises from the images in Figure 2.  A simple solution is to overlay the images and see if we might imagine today what it was that captured the imagination of Professor Goode in 1925.  Figure 3 shows an overlay of the Mollweide and the sinusoidal in a QuickTime (trademark, Apple) movie format.  The movie should play once in the browser, automatically.  The reader has complete control over the movie and can scroll it back and forth using the "controller" bar below the animation.  Animated maps are useful because they combine elements of a presentation that cannot be captured in the static form of the printed page.  Often, they merge space with time [2].  Here, they offer a means to capture a thought process and give the reader interactive control of it:  to enter a process from 80 years ago and imagine what might Goode have seen!

Figure 3.  Overlay of Mollweide and sinusoidal projections captured as an animation (in .mov format).  Drag the handle on the controller bar to see elements of  the overlay.  If the animation is not running automatically, and you wish to have it do so, pressing the reload button on the browser is one alternative that should work independent of other issues (presuming that QuickTime (Apple) is loaded on your computer (independent of brand)).

In the animation, watch the tip of South America.  As the animation progresses, the southern part of South America seems to fly off the globe in the sinusoidal while the northern part of South America remains relatively clear in both projections but perhaps closer to globe-form in the sinusoidal.  Thus, one might imagine that a scholar, such as Professor Goode, would wish to capture the closer-to-globe form of the sinusoidal on either side of the equator and couple it with the closer-to-globe form of the Mollweide closer to the poles.  Notice, however, that exaggeration in the sinusoidal increases as one moves away from the central meridian.  Focus attention on the meridians in the animation of Figure 3.  Clearly the Mollweide and the sinusoidal are closer together near the central meridian than they are toward the edges of the map where the rate of increase in curvature of the sine wave greatly exceeds the rate of increase in curvature of the ellipse.  Thus, one might consider introducing multiple central meridians so that no land mass is ever too far from some central meridian:  hence, the need to interrupt the map to achieve this goal.

Animation has long been present as an entertainment device.  It offers, however, a largely untapped source of power in academic endeavors of all sorts.  Here, the simple idea of actually looking at the overlay, as Goode might have 80 years earlier, offers insight into research process and blends past effort with future technology.


1.  Anderson, Paul B. and Tobler, W.  2004.  Blended Map Projections are Splendid Projections. [forthcoming]

2.  Arlinghaus, Sandra L.; Drake, William D.; Nystuen, John D.; with Audra Laug, Kris Oswalt, and Diana Sammataro.  1998.  Animaps.  Solstice: An Electronic Journal of Geography and Mathematics.  Ann Arbor:  Institute of Mathematical Geography.  Other articles on animated maps appear in later issues of Solstice.

3.  Goode, J. P. 1925.   "The Homolosine Projection:  A New Device for Displaying the Earth's Surface Entire,"  Annals, Association of American Geographers, 15, 3: 119-125

4.  Lethcoe, Kent J. and Klaver, Robert W.  Simulating the Interrupted Goode Homolosine Projection with ArcInfo.  Archived at (downloaded Dec. 1, 2004)

5.  Snyder, John P. 1993. Flattening the Earth:  Two Thousand Years of Map Projections. Chicago and London:  The University of Chicago Press.

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