Triangulation
Supercalifragilisticexpialidocious!
Just the sound of that word seems to have an amazing affect. There are other such words, one being triangulation. Using this word can have the result of making one look like a math genius.
But regardless of whether it does or not, it is a perfectly good word – and a concept that is critical to our everyday lives. So let's learn about it.
Seeing all sides of the issue
Conduct a little experiment in the name of science. Try the following:
Find some object in the room. Look at it while standing, positioning your body so it is directly in front of you.
Without turning your head, move to one side. You will notice the object appear to move.
The idea that objects look like they are moving, only by changing positions, is called parallax. How far the item seems to move depends on a couple of things.
The further you move, the further the object seems to move.
The further away the object is, the less it appears to move. This is why, as you drive through the country, things near the road appear to zip by, while distant objects barely seem to move at all.
Scene from a moving car, notice the closer objects move faster and are blurred. (My apologies for the poor photo quality.)
The rest, as a professor of mine once said, is math.
The math (lite)
Imagine you are out hiking and you stop to enjoy the view of a beautiful mountain in the distance. A friend of yours is also walking somewhere else and he also stops to enjoy this same mountain.
The three of you – you, your friend, and the mountain – can be seen as being three points on a triangle.
Using geometry, one can work out the distance to the mountain, but you need to get some information.
You would need to know how far away you are from your friend.
You need to measure the angle between the direction to the mountain and your friend. Your friend then needs to do the same thing back.
From this, it is just a question of working through the math to figure the distances and then where the mountain is. This approach, using triangles to find distances and positions, is called triangulation.
So, what's the big deal?
Triangulation has value outside of a geometry class.
Look at something. When you do, both your eyes will look straight at it. But since each eye is in a different place on your head, they will point in a slightly different direction. Your brain uses those directions to figure out how far away the object is. It's called depth perception.
This is why we have two eyes.
For centuries, surveyors used triangulation to find distances between objects along with how high things are.
Seismologists use it to determine where an earthquake occurred.
Radio locators use this to locate where a radio signal is coming from.
GPS uses triangulation, off of satellites, to find your location.
Look at a star in the night sky.
As time goes on, the Earth goes around the Sun.
As it does so, the stars will appear to move a little bit. Measuring how far the star seems to move is used to figure out how far away the star is.
Clever!
Who knew the humble triangle could be so helpful?
On the web
Stellar parallax and measuring distance
This animation shows very simply the idea of parallax and how astronomers use it to find out how far away stars are from us. The last part gets into the math details, but the concepts get explained very basically.
Triangulation With Trigonometry
This one is for the math folk who want the math details explained.
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