Frequently Asked Questions About
The Fuller Projection
Index
What is meant by
'no visual distortion'?
When transferring geographic data from the globe
onto a flat plane, distortions will always occur in
either shape, size, area, distance or direction.
On projections such as the Mercator map, the further
north of south of the equator one goes, the more extreme
the distortion becomes. When comparing the Mercator
map to a globe, it is easy for everyone to see that
Greenland, for example, is much larger on the flat
Mercator map than it is on the globe.
However, when visually comparing land masses on Fuller's
map to that of a globe, the land masses appear to
have their correct size.
The Peters projection, on the other hand, sacrifices
shape to preserve relative accuracy in overall land
area; distortions are obvious when comparing it to
the globe. However, there are no visible shape discrepancies
in any of the land masses on Fuller's map when it
is compared to a globe.
Minute area and shape distortions can be detected
mathematically and are equally distributed throughout
the map. Visually, however, these distortions are
negligible.
Why an icosahedron?
A polyhedron is a many-sided 3-dimensional object.
An icosahedron is a polyhedron with 20 equilateral
triangular faces. Of the five Platonic polyhedra (all
of which have equal faces in size and shape), the
icosahedron most closely approximates a sphere.
Fuller found that the best way to lay various polyhedra
flat while keeping all the land masses unbroken was
to use the icosahedron. With only two exceptions,
all the breaks needed to lay the icosahedron flat
occur completely within the oceans, and, therefore,
keeps the division of land masses to a minimum.
With minor adjustments to two triangular faces, Fuller's
Dymaxion Air-Ocean World Map provides us with a flat
view of all the Earth's land masses as unbroken islands
in a single world ocean.
Why are the oceans
broken up?
Try peeling an orange while keeping the skin in one
piece. Then lay the skin out flat. Notice how it needs
breaks, or 'sinuses' in many different places in order
to lay flat. The more breaks introduced, the flatter
the orange peel will lay.
When an icosahedron is unfolded and laid flat, breaks
need to be introduced, just as in the case of the
orange peel. The question is then where to introduce
these breaks? One way of doing this is to introduce
the breaks in the oceans as much as possible. This
provides a world view in which the land masses are
unbroken.
Fuller's map was actually designed to have all of
the icosahedron's triangles separable. This allowed
the map to be dynamic. By rearranging the triangles,
with the South Pole at the center of the map, navigation
routes by sea become readily apparent, just as air
routes across the North Pole are obvious in the original
configuration.
Fuller explored more than 25 different useful configurations
of the Dymaxion Air-Ocean World Map. Each configuration
introduces breaks in different places and allows different
aspects of the world to be emphasized.
Why are the
mean low temperature zones shown?
The Fuller Projection defines our world not in terms
of political boundaries or physical features but by
temperature zone. Buckminster Fuller was interested
in the history of human migration and the geographical
areas of technological innovation as it related to
temperature.
Looking at the yellow band closest to the North Pole
we find that the mean low temperature ranges from
23 degrees to 41 degrees Fahrenheit. Fuller found
that throughout history, humans migrated east to west
along the 32 degree freezing line and that the majority
of the dominant centers of modern civilization can
be found to lie somewhere within this optimum temperature
band. He felt that social patterns, human preoccupations
and economic customs are determined by how cold it
gets, not by how hot.
Buckminster Fuller then realized that: (I ) the colder
an area gets the larger the fluctuation in temperature
is to be found, and (2) the more a geographical area's
temperature varies, the more technologically inventive
must humans living there become in order to survive.
(For example, they must learn to build boats to cross
a lake in summer, as well as design sleds to cross
the ice in winter.)
Fuller's Projection
Method
Fuller superimposed a spherical icosahedron grid
onto the Earth's sphere. Each of the grid's edges
are arcs of "Great Circles" which show the shortest
routes between two points on a sphere's surface. 
When the Great Circle arcs are unfolded, the arc-edges
of the spherical icosahedron become the straight edges
of the regular icosahedron and the twenty spherical
triangles become twenty plane triangles. Since the
arc-edges are unfolded, their lengths remain undistorted.
Minute distortion in the middle of each triangle is
distributed evenly throughout the map.
The Fuller Projection is not a 'shadow' projection
as most maps are because the world is not projected'
onto a regular icosahedron but rather unfolds into
an icosahedron. Thus, Fuller preferred to call his
map a "transformation". During this transformation,
the line from the sphere's center through the sphere's
surface and out to the zenith point is kept at a constant
90 degree angle with respect to the map's surface.
Fuller referred to this as a "constant zenith projection."
© 1992 Buckminster Fuller institute
For more information, please contact:
Buckminster
Fuller Institute
|
