Steve Waterman: Difference between revisions

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

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Revision as of 09:18, 17 July 2026

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

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-| birth_date = {{birth date|1952|00|00|mf=y}}
+| birth_date = 1952
 | fields = [[Independent Researcher]], [[Cartographer]]
 | residence = Montreal, Quebec, Canada
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-My background stems from nearing 20 years of independent research into the packing of equally sized spheres. I continue to follow that path since then, trying to see when and where those might apply. I spent two years just figuring out that in a cubic close packing arrangement (ccp), that all distances between sphere centers was in the form or the square root of an integer. This allowed a simple algorithm to manifest a cluster by that sqrt of an integer value, as a point set. This point set then was made into a convex hull. [http://dogfeathers.com/java/ccppoly.html waterman polyhedron applet] made by Mark Newbold. A good write-up about them by Paul Bourke...[http://local.wasp.uwa.edu.au/~pbourke/geometry/waterman/index.html initial convex hulls and clusters] Later, one of these polyhedron was selected to manifest a world map. [http://watermanpolyhedron.com/ first page of my site]   In my attempts to find out more about the ccp, the path led to nuclear structure, and I was eventually confronted by my theories being questioned as they did not account for Relativistic concerns. That brings me towards today and my challenge to the math of the hardly ever heard of, Woldemar Voigt. In 1887, so pre-dating Einstein's 1905 paper by 18 years, Woldemar Voigt wrote a set of equations using x' = x-vt. This is mathematically challenged by this author, in a couple of forms. First, a 2 1/2 minute video. [http://watermanpolyhedron.com/videoforweb101.html math challenge of x' = x-vt] Then, perhaps a couple of short 'thought experiments" upon this same concern. [http://watermanpolyhedron.com/EinsteinsLeftBehind.html Einsteins Left Behind] and [http://watermanpolyhedron.com/WoldemarAppointment.html The Appointment that Woldemar never kept]. I guess I will even include this too as part of introducing myself here at NPA...[http://www.watermanpolyhedron.com/ODE.html my overall perspective ( as a poem )]
+'''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|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==
+* [http://watermanpolyhedron.com/ Waterman Polyhedron (official site)]
+* [http://dogfeathers.com/java/ccppoly.html Waterman polyhedron applet by Mark Newbold]
+* [http://local.wasp.uwa.edu.au/~pbourke/geometry/waterman/index.html Waterman polyhedra write-up by Paul Bourke]
+* [https://en.wikipedia.org/wiki/Waterman_butterfly_projection Waterman butterfly projection (Wikipedia)]
+* [https://en.wikipedia.org/wiki/Waterman_polyhedron Waterman polyhedron (Wikipedia)]
+* [http://watermanpolyhedron.com/videoforweb101.html Math challenge of x' = x-vt (video)]
+* [http://watermanpolyhedron.com/EinsteinsLeftBehind.html Einsteins Left Behind]
+* [http://watermanpolyhedron.com/WoldemarAppointment.html The Appointment that Woldemar never kept]
+* [http://www.watermanpolyhedron.com/ODE.html Overall perspective (as a poem)]
 [[Category:Scientist|Waterman Steve]]