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- Waterman_butterfly_projection abstract "The Waterman \"Butterfly\" World Map is a map arrangement created by Steve Waterman. Waterman first published a map in this arrangement in 1996. The arrangement is an unfolding of a globe treated as a truncated octahedron, evoking the butterfly map principle first developed by Bernard J.S. Cahill (1866–1944) in 1909. Cahill and Waterman maps can be shown in various profiles, typically linked at the north Pacific or north Atlantic oceans.As Cahill was an architect, his approach tended toward forms that could be demonstrated physically, such as by his flattenable rubber-ball map. Waterman, on the other hand, derived his design from his work on close-packing of spheres. This involves connecting the sphere centers from cubic closest-packed spheres into a corresponding convex hull, as demonstrated in the accompanying graphics. These illustrate the W5 sphere cluster, W5 convex hull, and two Waterman projections from the W5 convex hull.To project the polyhedron to the plane, straight lines are used to define each 5 × 5 section onto this convex hull. According to annotations on modern versions of the map, the projection divides the equator equally amongst the meridians. Popko notes the projection can be gnomonic too. The two methods yield very similar results. Parallels of latitude are drawn as three straight-line sections in each octant: from pole to fold-line; from fold-line to longest line parallel to equator; and then to the equator. The longest line parallel to the equator also has equal-length delineations. Waterman chose a specific Waterman polyhedron and central meridian to minimize interrupting major land masses.Like Buckminster Fuller's 1943 Dymaxion Projection, an octahedral butterfly map can show all the continents uninterrupted if its octants are divided at a suitable meridian (in this case 20°W) and are joined, for example, at the North Atlantic, as in the 1996 version.".
- Waterman_butterfly_projection thumbnail W5_sphere_cluster.jpg?width=300.
- Waterman_butterfly_projection wikiPageExternalLink waterman.
- Waterman_butterfly_projection wikiPageExternalLink Waterman_.htm.
- Waterman_butterfly_projection wikiPageExternalLink Waterman-review.html.
- Waterman_butterfly_projection wikiPageExternalLink defPatA.html.
- Waterman_butterfly_projection wikiPageExternalLink projPoly2.html.
- Waterman_butterfly_projection wikiPageExternalLink CART5.html.
- Waterman_butterfly_projection wikiPageExternalLink methodp.html.
- Waterman_butterfly_projection wikiPageExternalLink watch?v=ajwR6ku5WGk&feature=related.
- Waterman_butterfly_projection wikiPageExternalLink waterman.
- Waterman_butterfly_projection wikiPageExternalLink waterman-butterfly.
- Waterman_butterfly_projection wikiPageID "30775660".
- Waterman_butterfly_projection wikiPageLength "4374".
- Waterman_butterfly_projection wikiPageOutDegree "27".
- Waterman_butterfly_projection wikiPageRevisionID "680446019".
- Waterman_butterfly_projection wikiPageWikiLink Architect.
- Waterman_butterfly_projection wikiPageWikiLink Atlantic_Ocean.
- Waterman_butterfly_projection wikiPageWikiLink Bernard_J._S._Cahill.
- Waterman_butterfly_projection wikiPageWikiLink Buckminster_Fuller.
- Waterman_butterfly_projection wikiPageWikiLink Category:Map_projections.
- Waterman_butterfly_projection wikiPageWikiLink Circle_of_latitude.
- Waterman_butterfly_projection wikiPageWikiLink Dymaxion_map.
- Waterman_butterfly_projection wikiPageWikiLink Equator.
- Waterman_butterfly_projection wikiPageWikiLink Geographical_pole.
- Waterman_butterfly_projection wikiPageWikiLink Globe.
- Waterman_butterfly_projection wikiPageWikiLink List_of_map_projections.
- Waterman_butterfly_projection wikiPageWikiLink Map.
- Waterman_butterfly_projection wikiPageWikiLink Map_projection.
- Waterman_butterfly_projection wikiPageWikiLink Meridian_(geography).
- Waterman_butterfly_projection wikiPageWikiLink Octahedron.
- Waterman_butterfly_projection wikiPageWikiLink Octant_(solid_geometry).
- Waterman_butterfly_projection wikiPageWikiLink Pacific_Ocean.
- Waterman_butterfly_projection wikiPageWikiLink Steve_Waterman_(mathematician).
- Waterman_butterfly_projection wikiPageWikiLink Waterman_polyhedron.
- Waterman_butterfly_projection wikiPageWikiLink World_map.
- Waterman_butterfly_projection wikiPageWikiLink File:W5_polyhedron.jpg.
- Waterman_butterfly_projection wikiPageWikiLink File:W5_sphere_cluster.jpg.
- Waterman_butterfly_projection wikiPageWikiLink File:Waterman_projection_(Pacific_centered).jpg.
- Waterman_butterfly_projection wikiPageWikiLinkText "Waterman butterfly projection".
- Waterman_butterfly_projection wikiPageUsesTemplate Template:Map_Projections.
- Waterman_butterfly_projection wikiPageUsesTemplate Template:Portal.
- Waterman_butterfly_projection wikiPageUsesTemplate Template:Reflist.
- Waterman_butterfly_projection subject Category:Map_projections.
- Waterman_butterfly_projection hypernym Arrangement.
- Waterman_butterfly_projection type MusicalWork.
- Waterman_butterfly_projection type Projection.
- Waterman_butterfly_projection type Projection.
- Waterman_butterfly_projection comment "The Waterman \"Butterfly\" World Map is a map arrangement created by Steve Waterman. Waterman first published a map in this arrangement in 1996. The arrangement is an unfolding of a globe treated as a truncated octahedron, evoking the butterfly map principle first developed by Bernard J.S. Cahill (1866–1944) in 1909.".
- Waterman_butterfly_projection label "Waterman butterfly projection".
- Waterman_butterfly_projection sameAs Q7974340.
- Waterman_butterfly_projection sameAs m.02qv4s0.
- Waterman_butterfly_projection sameAs Q7974340.
- Waterman_butterfly_projection wasDerivedFrom Waterman_butterfly_projection?oldid=680446019.
- Waterman_butterfly_projection depiction W5_sphere_cluster.jpg.
- Waterman_butterfly_projection isPrimaryTopicOf Waterman_butterfly_projection.