Just did a reference with a student who asked a simple question I feel I should have a better answer to... for map projection properties, why is an equal distance projection not also inherently an equal area projection or vice versa?
I understand the issues with map transformations and the preservation of the various characteristics of a globe based on those transformations. But when I thought about the question I realized how intuitive that assumption is, if distance is preserved in all directions and area is a function of measuring distance around some boundary then an equal distance map should also give you equal area. The answer I think has to do with the fact that even equal distance maps are often not equal in every direction, but I wasn't sure if there was a more robust answer than that.
What's your understanding of how equal distance and equal area differ?
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I understand the issues with map transformations and the preservation of the various characteristics of a globe based on those transformations. But when I thought about the question I realized how intuitive that assumption is, if distance is preserved in all directions and area is a function of measuring distance around some boundary then an equal distance map should also give you equal area. The answer I think has to do with the fact that even equal distance maps are often not equal in every direction, but I wasn't sure if there was a more robust answer than that.
What's your understanding of how equal distance and equal area differ?
أكثر...