## Gallery of Map Cards

I had long been interested in map projections, so when digital geographic data became available in the 1970s, I wrote a program for producing them. A playful use of the program has been to make the map-themed annual greeting cards that are gathered here.

Most of the maps cover the whole world or a large part of it, because that's where map projections get interesting. Some demonstrate geographic facts. Some are novelties.

I am particularly intrigued by the mathematics of projections called conformal. To lay the globe out flat, it must be stretched. In conformal projections the stretching at each point is uniform in all directions, although the scale necessarily varies from point to point. In all other projections squashing prevails, so that at almost all poinst the scale varies with direction.

``Wallpaper maps'' are a special class of conformal projection. Repeating copies of a wallpaper map seamlessly cover the plane with equal-sided tiles. The collection of wallpaper maps here is complete; no others are possible.

The capabilities of both my map-projection program and the retail printing industry grew with time. You can see technique progress from pasted-up monochrome copy to fully electronic color composition and printing. However, I never developed graphic capability much beyond linear features, for that entails more art than math.

Only a few of the cards are shown in their entirety. Family news, free-standing greetings, and large blank areas have been elided. Card backs or parts thereof are shown only to the extent that they contain auxiliary maps or explanatory legends.

### Image index

Click on a thumbnail for a larger image, other content of the card, and explanation of the projection.
 Key (C) Conformal projection (C*) Conformally resurfaced globe (G) Special geographic fact (H) Historical interest (N) Novelty (P) Map on polyhedron (W) Wallpaper map
 1983 (CPW) 1984 (CHW) 1985 (CW) 1986 (CW) 1987 (N) 1988 (N) 1989 (N) 1990 (H) 1991 (H) 1992 (G) 1993 (NP) 1994 (NG) 1995 (CHN) 1996 (C*N) 1997 (NG) 1998 (CG) 1999 (CH) 2000 (CN) 2001 (G) 2002 (N) 2003 (P) 2004 (CP) 2005 (C) 2006 (CP) 2007 (NG) 2008 (G) 2010 (C*) 2011 (CN) 2012 (C*G) 2013 (CG) 2014 (CP) 2016 (CW) 2020 (CW)

### Conformal projections

More than half the images, marked (C) in the index, involve conformal projections. You can't make a flat map without stretching various parts of the map unequally. At every interior point of a conformal projection, the stretching is simple magnification, although the degree of magnification varies from point to point. In non-conformal projections the amount of stretch varies with direction, causing shapes to be squashed or sheared.

I'm partial to conformal maps for several reasons. They are kind to shape. They have lovely mathematics (analytic functions in the complex plane). And the possibilities are boundless: The globe can be mapped conformally onto any outlined shape. This collection boasts fifteen identifiable shapes plus a movie in which the shape varies continuously from frame to frame.

I have dubbed a special family of conformal projections wallpaper maps. Repeated copies of these maps fit together smoothly to cover a flat surface, over which a journey can extend forever, with crossings of tile boundaries being as imperceptible as crossings of the the Date Line are on a journey round and round the world. There are exactly five kinds of wallpaper map; all are represented here (1983/2016, 1984, 1985, 1986, 2020). A technical report, “Wallpaper maps”, tells the mathematics of the family.

Another family consists of conformal projections onto unfolded regular solids, represented here by tetrahedron (1983/2016), cube (2014), octahedron (2006) and dodecahedron (2004). There is no icosahedron in the collection; twenty faces seemed too busy for a card. One regular solid, the tetrahedron, serves also as a wallpaper map.

Maps marked C* illustrate various projections, none of them conformal. The designation signifies that, before being projected onto the plane, the surface of the globe was smoothly rearranged by conformally squeezing some areas and stretching others, as explained in the map descriptions.

### Projection index

 Anamorphic 1996 Geographic 1997 Azimuthal equidistant 1992 Globular (Apian) 1987 Bonne 1991 Gnomonic 1993, 2003 Conformal Hammer equal-area 2007 Cube 2014 Lagrange 1998, 2011 Dodecahedron 2004 Mercator 1990, 2002, 2011, 2013 Hexagon (Adams) 1986 Orange peel 1988 Lens 1995 Orthographic 2001, 2010, 2012 Octahedron 2006 Perspective 1993 Pentagonal star 2005 Quincuncial (Peirce) 1984 Square I (Adams) 1985 Retroazimuthal (Hammer) 1994, 2000 Square II (Adams) 2020 Sinusoidal 1991, 2008 Tetrahedron (Lee) 1983, 2016 Stereographic 1999, 2011 Droop 2010, 2012 Wreath 1989 Eisenlohr 2000