Global Positioning System Reference
In-Depth Information
portant works. He made maps of Lorraine, now lost, and of the British Isles,
before producing a masterpiece, his map of Europe. Fifteen years later, in
1569, he made a world map ''ad usum navigation'' (for the use of navigation)—
the only occasion he employed the Mercator projection.
Mercator, who coined the word atlas to describe a group of maps, died
aged 82 in Duisburg.
The Mercator projection probably precedes Mercator, and the theoretical
underpinning was done by others, notably Edward Wright at the end of the
sixteenth century. However, credit for the projection accrues to Mercator be-
cause of the excellent quality of the map he made with it. While this map bene-
fited travelers and geographers, through precise measurement and high-
quality production (Mercator discarded many of the historical errors that clut-
tered medieval world maps), the Mercator projection was ahead of its time
and would not really benefit navigators until the eighteenth century because
marine navigators lacked the means to measure their location at sea. Once the
longitude problem was solved and magnetic declination understood, Merca-
tor projection maps permitted ships to sail the world's oceans secure (if not
quite safe) in the knowledge that they knew where they were going.*
* Crane (2002) provides a detailed biography and cartographic history. Taylor (2004)
portrays the times in which Mercator lived. Shorter biographical sketches can be found in,
e.g., Encyclopaedia Britannica and Encarta Encyclopedia , s.v. ''Gerardus Mercator.''
The regular polyhedra are highly symmetrical 3-D objects that are made
up of a number of regular polygons (equilateral triangles, squares, or pen-
tagons). For example, six squares can be used to construct that most famil-
iar of regular polyhedra, the cube. Four equilateral triangles can be used to
construct a tetrahedron; eight make up an octahedron; twenty make an
icosahedron. Twelve pentagons form a dodecahedron. The octahedron and
the dodecahedron are illustrated in figure 4.10, which also illustrates how
they unfold so that they lie flat.
Here lies the utility of such polyhedra. Because a single piece of paper
can be cut and folded to form a polyhedron, we can project our globe onto
the polyhedron and so form a map. In figure 4.10 you see that we can place
a sphere inside the polyhedron so that each face of the polyhedron is
tangent to the globe. Clearly, the more faces a polyhedron has (i.e., the
more polygons that are used to construct it), the closer it can be made to
 
 
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