A map projection is a set of equations used to visualize the surface of the earth...
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A map projection is a set of equations used to visualize the surface of the earth on a two-dimensional map. The act of displaying a curved surface on a flat surface will always result in some sort of stretching, splitting or distortion. Think about the challenges of flattening an orange peel! The Mercator projection, proposed in 1569, is a very famous map projection. It was very popular because of how useful it is as a navigational chart. Any straight line on a Mercator map corresponds to a path of constant bearing, and such a path was easy to navigate! The big problem with the Mercator projection is that scale is highly distorted. On a Mercator map, areas far from the equator appear far larger than they actually are. Have a look at the map below. It looks like Greenland is larger than Africa, but Africa is actually 14 times larger. In this question, we'll look at the math behind the Mercator projection. In this projection, A, o will represent the longitude and latitude, respectively, of a point on the Earth's surface and (x, y) will represent the location of that same point on the map, where we will place the x-axis along the Equator and the y-axis along the Prime Meridian. If R is a positive scaling constant, then the y-coordinate on the map of a location with latitude o is given by (a) Evaluate y = Riu (tan (+2)) lim y to explain what happens as you try to map a point near the North Pole. Does this make sense? (b) Evaluated. Express your answer entirely in terms of the sin function. (c) Solve the above equation for o to give a formula that you could use to find the latitude of a location if you knew it's location on a map, that is, if you knew it's y-coordinate on the map. (d) Use your formula to determine the latitude of a point with y-coordinate equal to R/3. Find a location on earth with this latitude. Does it make physical sense that it would have a y-coordinate of R/3? A map projection is a set of equations used to visualize the surface of the earth on a two-dimensional map. The act of displaying a curved surface on a flat surface will always result in some sort of stretching, splitting or distortion. Think about the challenges of flattening an orange peel! The Mercator projection, proposed in 1569, is a very famous map projection. It was very popular because of how useful it is as a navigational chart. Any straight line on a Mercator map corresponds to a path of constant bearing, and such a path was easy to navigate! The big problem with the Mercator projection is that scale is highly distorted. On a Mercator map, areas far from the equator appear far larger than they actually are. Have a look at the map below. It looks like Greenland is larger than Africa, but Africa is actually 14 times larger. In this question, we'll look at the math behind the Mercator projection. In this projection, A, o will represent the longitude and latitude, respectively, of a point on the Earth's surface and (x, y) will represent the location of that same point on the map, where we will place the x-axis along the Equator and the y-axis along the Prime Meridian. If R is a positive scaling constant, then the y-coordinate on the map of a location with latitude o is given by (a) Evaluate y = Riu (tan (+2)) lim y to explain what happens as you try to map a point near the North Pole. Does this make sense? (b) Evaluated. Express your answer entirely in terms of the sin function. (c) Solve the above equation for o to give a formula that you could use to find the latitude of a location if you knew it's location on a map, that is, if you knew it's y-coordinate on the map. (d) Use your formula to determine the latitude of a point with y-coordinate equal to R/3. Find a location on earth with this latitude. Does it make physical sense that it would have a y-coordinate of R/3?
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a lim2 y As the latitude approaches the North Pole 2 the term tan4 2 grows without ... View the full answer
Related Book For
Intermediate Accounting
ISBN: 978-0324592375
17th Edition
Authors: James D. Stice, Earl K. Stice, Fred Skousen
Posted Date:
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