# Beach Ball Cartography

By Carmen Kracl Hood

Purpose:

To examine the difficulties involved in transferring a spherical shape to a flat surface.

Background:

The Mercator projection is the most familiar attempt at representing a 3-dimensional surface.

Materials:

• beach ball
• felt-tipped markers
• graph paper

Procedures:

1. Mark lines of latitude and longitude, on your beach ball in the following manner:
2. Identify a Prime Meridian extending from the top to the bottom of the beach ball.
3. Locate the International Dateline directly opposite the Prime Meridian in a like manner.
4. Divide each of these hemispheres in half once again (90o east and west) then divide each of these sectors in half (45o east and west and 135o east and west).
5. Locate the equator (0o)and the poles (90o north and south).
6. Locate the 30o and the 60o north and south lines of latitude.
7. In a similar manner located the 15o, 45o, and 75o lines of latitude.

Prepare your graph paper to represent a Mercator Projection by first taping two sheets of graph paper together lengthwise.

1. Using the middle horizontal line for 0o latitude, mark
• the 15o lines at the 10th block north and south
• the 30o lines at the 20th block north and south
• the 45olines at the 50th block north and south
• the 60o lines at the 90th block north and south
• the 75o lines at the 140th block north and south and end the map 40 blocks later.
2. For longitude lines use the middle vertical line as 0o and mark lines off every 15 blocks east and west in 15o increments from 0o to 90o.

Laboratory groups 1-4 should draw jack-o-lantern faces on their beach balls. Gorups 5-8 should draw jack-o-lantern faces on their Mercator Projection sheets. (Be creative!)

Each group should then transfer their designs from the beach ball to the map sheet and vice versa, by determining the latitude and longitude of the boundary points of their designs and plotting the points.

Interpretations:

1. Where do the largest distortions occur?
2. Where do the smallest distortions occur?