Some ideas about triangulation

David Coulson, 2014

Triangulation is about finding distances when you can’t simply go and measure them.

How far is it across the river to the door of the castle?

If you walk left or right along the ‘baseline’ until the viewing angle is 45 degrees, then the distance across the river is the same as the distance you walked.

Alternatively you could walk until the viewing angle is 60 degrees, and use a bit of maths to work out the distance.

Pythagoras can tell you the shortest distance.

The side lengths are the same, therefore the half triangle has a length half of the slanting side.

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That gives us the direct distance to the target.

This numbers turns out to be about 1.75 times the distance you walked

If you know some trig, you can walk any distance you like.

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The further you go, the more accuracy you’ll get.

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But this might not be practical.

Maybe you can only sight the target from two locations.

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2

Maybe you can’t even establish a perpendicular baseline.

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If you sight the Moon at sunrise and sunset, very precisely...

...You can estimate the distance from the Earth to the Moon.

And if you sight a star from opposite sides of the solar system, very precisely... ... You can estimate the

distance to the star.

The word triangulation used to be a scientific term but it has entered common language now.

Now it is used when two people are exchanging points of view about some other person or object or phenomenon, and describe how that thing appears to each of them.

Maybe someone is a pain-in-the-ass to me but he’s nice to you. At least now I know that he’s not a pain-in-the-ass to everyone, and that I should be thinking about how I interact with him.

I like to think of this as another example of how scientific thinking becomes common thinking, and how we can get along a little better if we take advantage of scientific ideas.

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dtcoulson@gmail.com