Viking Navigation

Marlys Henke developed the following multicultural activity for her mathematics class:

"VIKING NAVIGATION

Background Information: The Vikings were the first of the European seafaring explorers. From about 800 A.D. to 1100 A.D, they invaded the coastline of all of Europe from Russia--where many of the Swedish Vikings called the Rus settled at Navgorod and Kiev--and around Germany to France, Spain, and Italy. They invaded the British Isles, where they had strong cultural impact. They sailed across the Atlantic Ocean to Iceland, Greenland, and North American. For 300 years, they were great explorers and plunderers.

If the Vikings were such fearless adventurers, why didn't they sail south to explore Africa, Central America, and South America? Their navigation depended upon sighting the North Star, Polaris, so they had to stay north of the equator. Actually, at the equator they would be at 0 degrees latitude and couldn't see Polaris, so they probably tried to stay north of 15 degrees N or 20 degrees N.

Activity: To find out what latitude you are at using the same method as the Vikings, you need two meter sticks, a nut and bolt, a level, and a protractor. Fasten the two sticks together at one end using the bolt. Use a level to line up one stick parallel to the Earth. Sight along the other stick to Polaris and tighten the nut on the bolt. Measure the angle of elevation, Angle 1. This is your latitude.

Star Gazer with Angle 1 between eye level and the Star Polaris

To understand why this is true, you need to refer to the following diagram of the Earth. In the diagram, you are at point P. Line Segment OC and Line Segment PN point to the North Star. Owing to the great distance to Polaris from the Earth, Line Segment PN may be considered to be parallel to Line Segment DC, the axis of the Earth. The vertical Line Segment OG is perpendicular to the horizontal Line Segment PA.

diagram for problem

Problem: Prove that the measure of Angle 1 (the angle between the meter sticks) = the measure of Angle 2 (the latitude of P).

Reference: A Sourcebook of Applications of School Mathematics, National Council of Teachers of Mathematics, 1980, p. 149."

Developed by Marlys Henke.