http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

Introduction• Map projections are attempts to portray the surface of

the earth or a portion of the earth on a flat surface. Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projection are attempts to only moderately distort all of these properties.

Globes versus maps

Advantages of a globe1. Shapes of things are true2. Areas are true3. Scale is constant4. Directions are trueIn a map, one or more of these is lostIt is difficult to accurately “flatten” a sphere

Example of map “problem”A

B

C

A is true shape and size on a globe

A and B are same shape butdifferent in area

A and C have same area butare different in shape

Map projections: methods for “flattening” the sphere

Projections• Shape (Conformality)

– When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps.

• Distance – A map is equidistant when it portrays distances from the center of the projection

to any other place on the map. • Direction

– A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions.

• Scale – Scale is the relationship between a distance portrayed on a map and the same

distance on the Earth. • Area

– When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map.

Map projections fall into four general classes

• Cylindrical• Conic• Azimuthal• Miscellaneous

Cylindrical Projection

• Cylindrical projections result from projecting a spherical surface onto a cylinder.

• When the cylinder is tangent to the sphere contact is along a great circle (the circle formed on the surface of the Earth by a plane passing through the center of the Earth)..

Cylindrical projections

Least distortion along line of tangency,where projection surface touches globe

Conic Projection

• Conic projections result from projecting a spherical surface onto a cone.

• When the cone is tangent to the sphere contact is along a small circle.

Conic projections

Least distortion along line of tangency,where projection surface touches globealong standard parallel.

Azimuthal Projection

• Azimuthal projections result from projecting a spherical surface onto a plane.

• When the plane is tangent to the sphere contact is at a single point on the surface of the Earth.

Planar projection

Least distortion atpoint of tangency,where projectionsurface touchesglobe

In a polarprojection, thepoint of tangencyis the pole.

Miscellaneous Projections

• Miscellaneous projections include unprojected ones such as rectangular latitude and longitude grids and other examples of that do not fall into the cylindrical, conic, or azimuthal categories

Cylindrical Projections

Mercator • The Mercator

projection has straight meridians and parallels that intersect at right angles. Scale is true at the equator or at two standard parallels equidistant from the equator. The projection is often used for marine navigation because all straight lines on the map are lines of constant azimuth.

Peters Projection

The Peters projection is a cylindrical equal-area projection that de-emphasizes area exaggerations in high latitudes by shifting the standard parallels to 45 or 47 degrees.

Comparing Mercators to Peters Projection

The Peters Map vs The Mercator Map

The Greenland Problem Greenland: 0.8 million sq. miles

Africa: 11.6 million sq. miles

The North compared to the South The North is 18.9 million square miles.The South is 38.6 million square miles.

Europe compared to South America

Europe is 3.8 million square miles.South America is 6.9 million square miles.

Africa compared to the Former Soviet Union

The former Soviet Union is 8.7 million square miles. Africa is 11.6 million square miles.

Greenland Compared to ChinaGreenland is 0.8 million square miles.

China is 3.7 million square miles.

Important characteristics of the Peters Map • The Peters Map is an equal area map. • This new map shows all areas -

whether countries, continents or oceans - according to their actual size. Accurate comparisons become possible.

• The Peters Map is an equal axis map. • All North-South lines run vertical on

this map. Thus, geographic points can be seen in their precise directional relationship.

• The Peters Map shows equal positions.

• All East-West Lines run parallel. Thus the relationship of any point on the map to its distance from the equator or the angle of the sun can readily be determined. Fairness to All Peoples

• In the complex and interdependent world in which nations now live, the people of the world deserve and need an accurate portrayal of the world.

• The Peters Map is the map for our day.

Conclusion

• Why is Europe at the top half of maps and Africa at the bottom? Although we are accustomed to that convention, it is, in fact, a politically motivated, almost entirely subjective way of depicting a ball spinning in space. Maps do not portray reality, only interpretations of it. To begin with, they are two-dimensional projections of a three-dimensional, spherical Earth. Add to that the fact that every map is made for a purpose and its design tends to reflect that purpose. Finally, a map is often a psychological projection of the historical, political, and cultural values of the cartographer--or of the nation, person or organization for which the map was created.