The Mercator projection

This page is a sub-page of our page on Stereographic Projection.

Related sources of information:

Map at Wikipedia
Map projections – a video lecture GIScienceRIT at YouTube, 2 Sept 2014
The three main families of map projections at
Geocart Projections at
Images for Map Projection Types at Google
Different views of the world at
Visualizing the world in different projections David Madore on YouTube, 25 Nov 2013
Worldmapper at
The Mercator projection at Wikipedia
The man behind the Mercator projection – Stuff of Genius on YouTube
The Transverse Mercator Projection at Wikipedia
Universal Transverse Mercator (UTM) coordinate system at Wikipedia
Loxodrome (= Rhumb line) at Wikipedia
Stereographic projection at Wikipedia
Loxodromic navigation at Wikipedia
Tissot’s indicatrix at Wikipedia


The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.


Map projection of Earth .avi (ALAzharSEG on YouTube):


Why all world maps are wrong (Vox on YouTube):


The Mercator projection

/////// Quoting Wikipedia / Mercator projection:

The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for nautical navigation because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians.

Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects (making it a conformal map projection), the Mercator projection distorts the size of objects as the latitude increases from the Equator to the poles, where the scale becomes infinite.

So, for example, landmasses such as Greenland and Antarctica appear much larger than they actually are, relative to landmasses near the equator such as Central Africa.

/////// End of quote from Wikipedia / Mercator projection


Gerardus Mercator: Three ways the influential cartographer changed the way we look at the world:

Robin Show on YouTube, 5 March 2015


The Mercator projection:

The interactive simulation that created this movie.

Mercator projection (first step): Projecting a loxodrome into a logarithmic spiral:

The interactive simulation that created this movie.

Mercator projection (second step): Mapping the logarithmic spiral into a straight line
(by exponentiating it):

The interactive simulation that created this movie.

An alternative interactive simulation that shows the same thing.

Combining step 1 and step 2 to get the Mercator projection:

Reading from left to right takes you from the navigator’s map to the actual curve on the globe (the loxodrome) that it corresponds to.

Note: Unfortunately, I cannot connect the left and middle panes to the video in the pane to the right. For that I would have needed three independent panes. In that case you would have seen the points moving “in synch” in all three panes.


History of navigation :

History of navigation

Medieval age of discovery

Majorcan cartographic school 
• • Angelino Dulcert (fl. 1339)
• • Abraham Cresques (1325–1387)
• • Jehuda Cresques (1360 – 1410)
• • Catalan atlas and Abraham and Jehuda Cresques
• • Other Jewish cartographers 
• • Catalan atlas

The Age of Discovery
Age of exploration
• • Prince Henry, the Navigator (1394 – 1460)
Portuguese maritime exploration

Rhumbline network
Portolan chart

Bartolomeus Dias (c. 1450 – 1500)
• • Voyage around Africa
Vasco da Gama (c. 1460s – 1524)
• • First voyage
• • Second voyage
• • Third voyage and death

Pedro Nunes (1502 – 1578)

Piri Reis map

Treaty of Tordesillas 1494
League (unit)
Traditional French units of measurement 

Treaty of Tordesillas – Antimeridian: Moluccas and Treaty of Zaragoza
Treaty of Tordesillas (1524) – Wikipedia 
Treaty of Zaragoza 1529

Christopher Columbus (1451 – 1506)
• • Geographical considerations
• • Nautical considerations

The discovery of the Celendrical dateline
The International Date Line 
•• The International Date Line – Historic alterations 

Antonio Pigafetta (c. 1491 – c. 1531)
Ferdinand Magellan (1480 – 1521)
• • Juan Sebastián Elcano (1486/1487 – 1526)

Loxodromic navigation
Gerardus Mercator (1512 – 1594)
John Dee (1527 – 1608)

Francis Drake (c. 1540 – 1596)

Willem Schouten (c. 1567 – 1625)
Jacob Le Maire (c. 1585 – 1616)
• • Cape Horn

History of longitude
• • John Harrison (1693 – 1776)
• • • Lunar distances versus chronometers
• • • Nevil Maskelyne (1732 – 1811)

James Cook (1728 – 1779)
• • First voyage
• • Second voyage

History of cartography 
Werner projection of the world 
Stereographic map projection
Tissot’s indicatrix
Shen Kuo 
Gerardus Mercator 
Arnold Mercator 
Rumold Mercator
Johannes Stabius


Spice trade
Overview of the 16th century

• Treaty of Tordesillas (1494): This article is about the 1494 treaty between Portugal and Spain that divided the world as then understood between the two.
For the treaty signed in 1524 between Spain and Monaco, see Treaty of Tordesillas (1524).

Background: the Moluccas issue

Conflict (1520 – 1529): The conflict began in 1520, when expeditions of both kingdoms reached the Pacific Ocean, because no agreed meridian of longitude had been established in the Orient.

• Treaty of Zaragoza (1529): The Treaty of Zaragoza, also called the Capitulation of Zaragoza (alternatively spelled Saragossa) was a peace treaty between Castile and Portugal, signed on 22 April 1529 by King John III of Portugal and the Castilian emperor Charles V, in the Aragonese city of Zaragoza. The treaty defined the areas of Castilian and Portuguese influence in Asia, in order to resolve the “Moluccas issue”, which had arisen because both kingdoms claimed the Maluku Islands for themselves, asserting that they were within their area of influence as specified in 1494 by the Treaty of Tordesillas.

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