Steve Waterman

Steve Waterman
Steve Waterman
Born	1952
Residence	Montreal, Quebec, Canada
Nationality	USA / Canadian
Known for	Relativity, Mathematics, Cartography, Sphere Packing
	Scientific career
Fields	Independent Researcher, Cartographer

Steve Waterman (born 1952) is an American-Canadian independent researcher, mathematician and cartographer based in Montreal, Quebec, Canada. He is best known as the originator of the Waterman polyhedra and of the Waterman "Butterfly" world map projection, both of which grew out of his study of the packing of equally sized spheres. He is also a critic of the mathematical foundations of Relativity.

Biography

Waterman describes his work as stemming from nearly twenty years of independent research into the packing of equally sized spheres, a line of inquiry he has continued to pursue in an effort to determine where such geometry might apply. He spent two years establishing that in a cubic close packing (ccp) arrangement, all distances between sphere centers take the form of the square root of an integer. This observation led him to a simple algorithm that generates a cluster of sphere centers as a point set, from which a convex hull can be constructed.

His interest in cubic close packing subsequently led him toward questions of nuclear structure. When his ideas in that area were questioned for not accounting for relativistic effects, he turned to examining the mathematics underlying relativity theory. In particular, he has focused on the work of the physicist Woldemar Voigt, who in 1887 — eighteen years before Einstein's 1905 paper — published a set of transformation equations using the relation x' = x − vt. Waterman challenges this mathematics in several forms, including a short video argument and a pair of "thought experiments."

Work

Waterman polyhedra

The Waterman polyhedra are a family of polyhedra that Waterman introduced around 1990. A Waterman polyhedron is generated by packing spheres according to cubic close packing (also known as face-centered cubic packing), removing the spheres whose centers lie farther from a chosen center than a given radius, and then taking the convex hull of the remaining sphere centers. Because the squared distances between centers are integers, successive polyhedra can be indexed by that radius value. An interactive applet illustrating the polyhedra was written by Mark Newbold, and an early description of the clusters and their convex hulls was prepared by Paul Bourke.

Waterman butterfly world map

Waterman selected one member of the polyhedron family, the W5 polyhedron — a truncated octahedron — as the basis for a world map projection, first published in 1996. Unfolding this polyhedral globe produces a "butterfly" arrangement that presents the continents with minimal interruption of the major land masses. The design follows the butterfly-map principle earlier developed by the cartographer Bernard J. S. Cahill (1866–1944) in 1909, and it invites comparison with R. Buckminster Fuller's 1943 Dymaxion projection. The map can be shown in several profiles, typically joined across the north Pacific or north Atlantic oceans.

Abstracts

2002 - "Waterman Polyhedra"

External links