PETE'S CONCEPTION OF WORLD WALLPAPER

Pete decided to donate a special world map to the Bren Events Center. He will mount it on the largest wall in the main auditorium for campus events. Within a month, his map of the world covering the wall took preliminary shape. He expected to tessellate a special matting on the wall with Mercator maps of the world. Special lighting would create the impression the maps continued over the wall from floor to ceiling, and off beyond the wall to both the left and to the right. The seed for the tessellation would be a central Mercator map. Identical replicas of it would fill the wall to the left, right, bottom and top. This, he thought, would allow him to draw exact illustrations of his trips. The history of his band's tours would be one long path along the wall.

Four Mercator
maps in a rectangle, one in each corner.
Figure 1: Pete's First Try

First he tried stacking maps one on the other, and from left to right (Figure 1). This, however, was unrealistic. For example, consider his last summer trip to Rovaniemi, Finland, across the Arctic circle, followed by a plane flight over the arctic cap. This trip has no representation on such a simple tessellation of Mercator maps. Once he crosses the Arctic Circle, the map presentation forces him to jump to the South Pole (Figure 2).

Figure 1 with
an arrow starting in Rovaniemi, Finland,  stopping when it
crosses the Northern edge of the Mercator maps
Figure 2: Artic Circle Dilemma

Therefore, Pete saw his tessellation required the northern edge of the central Mercator map to touch the northern edge of another Mercator map above it. This forced the effective unit of tessellation to be a Mercator map right side up, and above and below it another map, upside down (Figure 3).

Two
<i>upside-down</i> Mercator maps atop two normally aligned
Mercator maps
Figure 3: The New Tessellation

Fixing, however, one problem brought immediate new problems. For instance, a trip from Miami, Florida to London, England, has two possible routes (Figure 4). Both look equally good for a plane trip. Yet, these trips are different distances. This new tessellation repeatedly distorts trip distances.

Figure 3 with
two arrows illustrating trips
Figure 4: The Discrepancy

In an interview, Pete explained his World Wallpaper goal. Convential maps wouldn't satisfy him.

"I thought about using just one Mercator Map. Yet, I wanted to move on it as though it were a real globe. Consider what would happen with one large map. If my band traveled from India to Hawaii, the line representing this trip would start in India and continue to the eastern side of the map. Then, the line would have to jump to the other (western) side of the map, for the group to continue to Hawaii (Figure 5). This jump defies what happens when I travel."

A single
Mercator map illustrating the <i>jump</i>
Figure 5: The jump


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