Contour Maps Visualizing 3 dimensions A contour map is a good way to represent a surface on a 2 dimensional sheet of paper With practice interesting information such as highpoints maxima lowpoints minima and saddles can be detected Contour maps are a good way to see complicated surfaces Below are some examples of contour maps plus some discussion all topo maps are from www mytopo com Humphreys Peak Arizona Note the nested behavior of the contours all counting up to the summit elevation 12 633 feet The map shows dark contours every 200 feet lighter contour intervals every 40 feet The consistent spacing of the contours suggest a uniform shape to the mountain s slopes it s an old extinct volcano See the local maximum marked 12 089 at the bottom Can you identify the saddle a bit to its upper left What is the approximate elevation z value of this saddle Contour Maps Math 211 Surgent ASU 2009 Mather Point South Rim Grand Canyon Arizona Mather Point is the most popular overlook at the South Rim of the Grand Canyon the first one you ll come to once you enter the park Note the broad spacing of the contours in the lower left suggestion generally flat ground the contours are at 40 foot intervals Now note the multitude of intervals everywhere else this of course is the canyon Contours are never supposed to touch but in this picture the resolution seems to indicate they do These would be the nearly vertical cliffs while the slightly spaced apart contouring would be the slopes between the cliffs You can see the dramatic drop in elevation change in z value Mather Point is at 7 118 feet while less than a mile to the north northeast is a point with an elevation of 4 968 feet a nearly 2 200 foot drop Pipe Spring is below 3 800 feet Yes the canyon drops steeply Contour Maps Math 211 Surgent ASU 2009 Arizona State University Tempe Arizona The contour lines here are in brown but there aren t many to be seen suggesting our university is on mostly flat ground the purple coloring is for man made objects In the lower left is a spot elevation benchmark at the railroad tracks on Broadway road behind Tempe High School 1 161 feet above sea level To the right is a spot elevation benchmark at the corner of Broadway and Rural 1 172 feet above sea level This is an 11 foot change in elevation z value in about 1 25 miles a very small slope indeed It seems flat to us but there is a very slight downhill to the west The Tempe Buttes A Mountain can be seen at the top These contours are crammed together tightly suggesting a very sudden increase in elevation these are steep little hills Contour Maps Math 211 Surgent ASU 2009 Great Salt Lake Desert Western Utah This exciting topographical map shows one of the flattest natural regions anywhere in the world the Great Salt Lake Desert of Utah Water always will settle to exact level and when it evaporates leaves behind a level salt field The red box is a one square mile section used by surveyors to mark off the land the thick red lines are Interstate 80 and the Western Pacific Railroad is also shown This particular section is not far from the famous Bonneville Race Track where land speed records are set requiring a near perfect level ground Note the spot elevations at each corner of this section all reading 4 218 feet above sea level There is some variation within the box though The problem with a map like this is the contour spacing they are miles apart since the gradient is so slight Hence mapmakers will put in more spot elevations for reference purposes Contour Maps Math 211 Surgent ASU 2009 Weather Maps A weather map is a good example of a contour map The colors here suggest the contouring pinks and whites being hottest yay Phoenix and reds oranges and yellows being cooler in this example Similarly for Dewpoints Contour Maps Math 211 Surgent ASU 2009 Scoliosis Detection http www pubmedcentral nih gov articlerender fcgi artid 2367415 Scoliosis is a lateral or torsional curvature of the spine A common way to detect scoliosis is to make a height map of the back A normal back would be close to symmetrical while in patients with scoliosis there will be asymmetry In the above image the person s shoulder blades jut out at different heights a difference of nearly 15 mm and not symmetrically with the center of the back This imaging can be used for cases when the scoliosis may be slight and not immediately obvious to the eye Contour Maps Math 211 Surgent ASU 2009