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Math and Map Making

How we view the world depends on what map(s) we use. A map good for navigation might not be good at showing the true size of countries or continents.

What Does Earth Look Like?

Michael Stevens has an interesting look at perception and how our maps have shaped the perception of the Earth. Use the YouTube link to access all the resources he mentions in the video.

YouTube URL
https://www.youtube.com/watch?v=2lR7s1Y6Zig
larger image of http://math.rice.edu/~lanius/pres/map/

image of http://math.rice.edu/~lanius/pres/map/

Mathematics of Cartography

Most teachers integrate some math concepts, such as scale, into the study of maps. Cynthia Lanius offers some imaginative applications of math in cartography. For instance, if students are circumnavigating the globe in 80 days with various vehicles, how many miles need to be covered each day? Suppose 3 evil dictators could be placed the farthest apart from each other on the globe; where would they live? She has included links about the history of cartography and the "best" Web sites in this field.

larger image of http://cdn.twentytwowords.com/wp-content/uploads/africa.jpg

image of http://cdn.twentytwowords.com/wp-content/uploads/africa.jpg

Africa vs. the world

Africa doesn't look that big on the map.

In reality, Africa is bigger than the United States, China, India and a couple of European countries ... combined!

larger image of http://bramus.github.io/mercator-puzzle-redux/

image of http://bramus.github.io/mercator-puzzle-redux/

Mercator Puzzle

A fun on-line game to show how the Mercator projection changes the apparent size of a country depending on its latitude. The goal of the game is to drag the countries into their correct location on the map. Not as easy as you might think, especially with the smaller countries.

Drag the country outline over your location to compare how large that country is compared to your state or region.

If you don't know the position of a country, double click it to let the computer place it. This version of the puzzle displays different countries with each refresh.

You can easily integrate some math concepts, such as scale or navigational geometry, into the study of maps.

Map Projections of The Earth

Cartographers face the "orange peel" problem when mapping the surface of Earth onto a flat piece of paper. The mathematician Euler proved that this can not be done without distortion – using an actual orange peal. (clip is from the PBS show "Life by the #s")

YouTube URL
https://www.youtube.com/watch?v=X4wgFSHZXBg
larger image of http://www.thegreenwichmeridian.org/tgm/articles.php?article=9

image of http://www.thegreenwichmeridian.org/tgm/articles.php?article=9

The Quest for Longitude and the Rise of Greenwich

In 1492 when Columbus crossed the Atlantic, although latitude could be measured (typically from observations of the Pole Star), there was no reliable way of measuring a ship's longitude once out of sight of land. Charts were inaccurate and incomplete and much of the World remained unexplored. This article explores the various ideas for measuring longitude, using everything from the Moon to the satellites of Jupiter to the need for royal observatories.

larger image of http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html

image of http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html

Map Projections

For older students, this site goes more into the math and geometry of map projections. Which is the right way to depict South America?

larger image of http://prizedwriting.ucdavis.edu/past/1992-1993/the-mathematics-of-map-making-in-the-renaissance

image of http://prizedwriting.ucdavis.edu/past/1992-1993/the-mathematics-of-map-making-in-the-renaissance

The Mathematics Of Map-Making In The Renaissance

Good for older students, this paper looks at the problem of map making and navigation – coming up with a way so that a ship's course could be plotted using a ruler. Today we know it as the Mercator projection.

These particular sites may or may not be appropriate for the grade level you teach, but they will surely spur your imagination towards getting the most mileage from your study of maps.

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