Notes on the gallery

Maps from my Christmas cards

Ring of Fire. The great chain of volcanoes is usually depicted as surrounding the Pacific Ocean. Here the perspective is reversed and the volcanoes surround the continents.

Jerusalem shall be inhabited as towns without walls for the multitude of men and cattle therein: For I, saith the Lord, will be unto her a wall of fire round about.     -- Zechariah 2:4-5

Jerusalem Trefoil. Three circles of different sizes are drawn on the globe roughly to encompass each of three continents, with each circle passing through Jerusalem. Then the circles are stretched conformally into trefoil leaves. 1995 Christmas card.

Way to go. On this map for shepherds and magi a line from any point to Bethlehem shows the great-circle direction to Bethlehem (but not the great circle itself). Within the inner hemisphere directions are conventional; north up, east to the right. Within the outer hemisphere they are inverted--north down, east still to the right. Peter McIlroy suggested this arrangement of the hemispheres, which are usually presented as two conventionally oriented sheets.

Morphomap. An animated map that morphs from infinite beanpole to lemon, basketball, pumpkin and ultimately to infinite in all directions.

Conformal polygonal hemispheres

Big star. Northern and southern hemispheres are pentagons.

Sea whirled. Hemispheres are triangles, with which the plane can be tiled continuously. The orientation here (hemispheres bounded by 80°E and 100°W; vertices at 90°S and 30°N) is chosen to display the continuity of the major oceans. In an extended tiling, the coastlines of North America and Eurasia would be trebled like Antarctica's.

These projections belong to a family whose underlying math was published by H. A. Schwarz in 1869. The first application of Schwarz's formula to cartography mapped hemispheres to squares (C. S. Peirce, 1879). Triangles came considerably later (O. S. Adams, 1925) and pentagons not for a century (J. P. Snyder, unpublished). My map program can draw the 3- through 8-sided members of the family.

Word squares

These squares, which I found by exhaustive search in Webster's Collegiate Dictionary, were nominated as best of their sizes by the nonpareil word-gamester, Dmitri Borgmann; see A. Ross Eckler, Making the Alphabet Dance, St. Martin, 1995. More squares have been published in Word Ways; see my bibliography. A C program for the search still exists, simplified from the original, which had to be contorted to squeeze into a tiny DEC PDP-11.


Doug McIlroy's home page
Modified October 23, 2012.