Challenge 6 - Triangulation on Topographic Maps

The Challenge:

• Locate the Getty and the two houses on the topographic map using triangulation.
• Locate yourself on the topographic map using the tower and the building by the sea.
• You will need an alidade, a map, a sheet of tracing paper and a pencil.
• You will have to go to the Anderson School view deck and the Math Sciences roof top.
• Have fun and don't fall off!

What to sight on at the Getty:

The photographs that follow show two different sighting targets at the Getty. Pick one or the other and use it consistently. The corner of the southern building is probably the clearest and the best to use.

Locating yourself:

If you have a working GPS device it will give you the latitude and longitude. From this you can plot your position on a topographic map. Before the days of GPS you had to do this by taking bearings to known objects and working backwards to find your position. Even in the days of GPS these techniques are still useful. You may not have a GPS with you. It may not be receiving satellite signals. You may misread its coordinates. It may be wrong. Note that the first screen on your GPS unit disclaims any responsibility for the accuracy of its measurements. It is up to you to confirm that the GPS information is correct. For this reason it is useful, if not essential, to locate yourself using several different systems and see if they agree. Much of the scientific method rests on the notion of confirmability. If you use several completely different methods to locate your position and they all agree, you can increase your confidence that you really know where you are.

This method is called "triangulation." If you can identify two points on the landscape and the same two points on a map, all you need to know is the bearing (angle) between you and the two poins on the landscape. This is called triangulation because the two points and your location form the vertices of a triangle. The three points on the real landscape will form a triangle that is similar to (it has the same shape as) the three points on the paper map. The angles in the real and map triangles are identical. Therefore if you transfer the real angles that you see between your location and the two points on the landscape to the map, the lines on the map will cross at your location on the map.

Locating a landmark:

This situation is theoretically not much different from locating yourself. The difference is that in this case you must know your location on the map. From your location find the angle to an unknown landmark. Then copy that same angle to the map starting at your location on the map. The unknown landmark must be somewhere on the map along that line. You won't know how far out along that line the object is unless another known line crosses it. If it crosses a mountain ridge, a shore or a visible roadway, the landmark is at the intersection of the two lines on the map. If not, you need to take another bearing to the unknown landmark from another known position on the map.

Stereopsis:

Closely related to triangulation is perspective. Differences in perspective seen by the right and left eyes are perceived as depth, or stereopsis. When we look at an object up close, the right and left eye views are different. Look at your hand against a distant background while alternatively blinking your right and left eyes. Note the changes in perspective. A distant object doesn't show much perspective distance between your right eye and your left. That is why a view through binoculars looks so flat. If we take two photographs of that object from two widely separated places and artificially deliver them to each eye, we can see as much depth as if we were holding a miniature in our hands. Since many of the image pairs below were photographed from widely separated places, they provide an opportunity to demonstrate the phenomenon.

Two ways of viewing a stereo pair without any equipment:
Cross-eyed: right eye - left eye Hold your finger exactly half-way between your eyes and the screen. Focus on your finger. Shift your attention to the middle of the three images you see. Or, look cross-eyed at the screen until you see two sets of image pairs floating about. Adjust your vision so the closest images of each pair overlap. Shift your attention to the center image of the three images you see. Your eyes must be level - tilt your head to make the images line up. Practice on the images below:	Wall-eyed: left eye - right eye Hold your finger exactly half-way between your eyes and the screen. Focus on the images. Move your finger so your left eye cannot see the right image and your right eye cannot see the left image. Or, look wall-eyed through the image as though you were looking at a distant mountaintop. Slowly shift your attention to the center image of the three images you see. Your eyes must be level - tilt your head to make the images line up. Practice on the images below:
right eye - left eye	left eye - right eye

FROM THE ROOF OF MATH SCIENCES

xxxx Enter the Math Sciences building and take the elevator to the top floor. Exit onto the roof with the telescope domes.

THE GETTY x LEFT <-----> RIGHT x RIGHT <-----> LEFT On the North edge of the roof, take one bearing from the extreme Western (left) corner and another from the extreme Eastern (right) corner. There is not much parallax between the two images of the Getty, so the stereoscopic depth is weak.

PEAKED ROOF HOUSE x LEFT <-----> RIGHT On the North edge of the roof, take one bearing from the extreme Western (left) corner and another from the extreme Eastern (right) corner. If you view the image pair wall-eyed, you will see stereoscopic depth. x RIGHT <-----> LEFT If you view the image pair cross-eyed, you will see stereoscopic depth.

FLAT ROOF HOUSE x LEFT <-----> RIGHT On the North edge of the roof, take one bearing from the extreme Western (left) corner and another from the extreme Eastern (right) corner. If you view the image pair wall-eyed, you will see stereoscopic depth. x RIGHT <-----> LEFT If you view the image pair cross-eyed, you will see stereoscopic depth.

RED & WHITE KCBH RADIO TOWER x LEFT <-----> RIGHT On the North side of the roof, take one bearing from the extreme Western (left) corner and another from as far East (right) as possible (next to the drain).

BUILDING BY THE SEA x LEFT <-----> RIGHT On the South side of the roof, take one bearing from the extreme Western (right) corner and another from as far East (left) as possible. x x 1100 Wilshire Boulevard at Ocean Avenue, the building by the sea.

Finalizing the location.