Villanova University, Department of Mathematical Sciences

Cartographiometry (MAT 1210/ GEO 1700)

(©  copyright 1996-1999, Timothy G. Feeman and Elaine F. Bosowski.)

Azimuthal Equidistant Projection: Supplemental questions

(azilabq.htm)

The following questions concern the mathematical construction of the base graticule for an azimuthal equidistant projection of one hemisphere centered at a pole. The questions assume that the graticule is designed using a model globe of radius 1 unit (so R=1).

1. On  a globe of radius 1 unit, what is the circumference of the equator? How far is it from the north pole to the equator travelling along a meridian? What is the circumference of the circle that represents the equator on an azimuthal equidistant projection based on this globe?
2. On  a globe of radius 1 unit, how far is it from the north pole to the parallel at latitude u° north travelling along a meridian? What is the radius of the circle that represents this parallel on an azimuthal equidistant projection based on this globe?
3. Find the radii for the circles on the graticule that represent the parallels at 30 and 60 degrees. What are the polar coordinate equations for these two circles?
4. The distance from any point to the pole is shown correctly, but other distances, as well as shapes, are distorted. Are distances between non-polar points shown proportionally shorter or proportionally longer than they really are? Explain. (Use your finished map as a visual aid.)
5. Explain why each meridian is shown  as a half-line emanating from the center of the map.
6. Describe how a classical Greek geometer could have constructed a graticule for this projection using only a straight-edge and compass (the sort of compass used to draw circles, not the sort you use to locate north).