Map making

Yinduo Ma (Mandy)

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• We can make a cylinder on the flat.

History Ancient Chinese map 200 B.C The Greeks understood that the earth was a sphere. 150 A.D Ptolemy proposed a system of projections and coordinate systems that are still used today. 16 century Mercator created a map- the Mercator Projection 20 century Aerial photographs, computers, electronic distance-measuring instruments, inertial navigation systems, remote sensing, and applications of space science create new extensions of cartography's reach.

Mathematics Topics

• Scale

• Coordinate Systems

• Projection

Mercator Projection• cylindrical map projection

• It became the standard map projection for nautical purposes .

• the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects .

Mercator Projection

Mercator Projection

• Formula

Mercator Projection

• the Mercator projection distorts the size and shape of large objects, as the scale increases from the Equator to the poles, where it becomes infinite.

• Greenland takes as much space on the map as Africa, when in reality Africa's area is 14 times greater and Greenland's is comparable to Algeria's alone

Gall–Peters projection

• specialization of a configurable equal-area map projection known as the equal-area cylindric or cylindrical equal-area projection.

• Maps based on the projection are promoted by UNESCO, and they are also widely used by British schools.

Gall–Peters projection

Gall–Peters projection

• Formula

Gall–Peters projection

• Popular culture

• American show – The West Wing

• Military strategist – Thomas Barnett

Winkel tripel projection• a modified azimuthal map projection.

• arithmetic means of the equirectangular projection and the Aitoff projection.

• minimizing three kinds of distortion: area, direction and distance

Winkel tripel projection

whereλ is the longitude minus that of the central meridian of the projection, φ is the latitude, φ is the standard parallel for the equirectangular projection, and

α is the unnormalized cardinal sine function (with the discontinuity removed). In his proposal, Winkel set :

A closed-form inverse mapping does not exist, and computing the inverse numerically is somewhat complicated.

Winkel tripel projection

Winkel tripel projection

• Winkel tripel fares well against several other projections analyzed against their measures of distortion, producing small distance errors, small combinations of Tissot indicatrix ellipticity and area errors, and the smallest skewness of any of the projections they studied.

Winkel tripel projection

• Winkel tripel projection as the standard projection for world maps made by the National Geographic Society.

Projection• Azimuthals and related• Conics• Cylindricals• Pseudoconics• Pseudocylindricals

Azimuthals and related

Conics

Cylindricals

Pseudoconics

Pseudocylindricals

Question

• Gall–Peters projection and Mercator Projection belong to what kind of projection.

• Answer – Cylindrical