Villanova University, Department of Mathematical Sciences

Cartographiometry (MAT 1210/ GEO 1700)

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

The Mercator map: Supplemental questions

(mercmapq.htm)

The following questions concern the mathematical construction of the base graticule for a Mercator map centered on the equator and the prime meridian. The questions assume that the graticule is designed using a model globe of radius 1 unit (so R=1).

1. The construction of the Mercator map is described in Chapter 13 of the course notes. In the expression numbered (37) on page 79, what do the quantities  t  and  u   represent? What does the entire expression represent? Where does the factor of   Pi * t /180 come from?
2. Use a calculator or computational software to compute the value of expression (37) on page 79 if u = 40 and t = 5;  if  u = 40 and  t = 1;  if u = 40 and t = .5 . In what sense is the answer you get with  t = .5  better than the other two?
3. Mercator's map is conformal, which means that all angles are shown correctly. However, distances and areas are distorted. In what parts of your finished map does the distortion of areas appear to be the most severe? the least severe? Describe the distortions that you see. (Use your finished map as a visual aid.)
4. Why might a conformal map be useful to a person using a compass for sailing, orienteering, or hiking?
5. Mercator's map is often (these days) accused of being "Euro-centric".  Is this accusation fair? What is the role of  "map purpose"  in this accusation?