This page sets out a simple challenge for groups to have fun with.
The page explains how to set up some things to be mapped, in a simple classroom situation. Because the problem is so simple, the map can be made several different ways. But I hope that, among others, you will try to make the map by triangulation.
We need a largish room, with few barriers to looking across the whole of the room.
We need four "things" that we can place in the room which will create "little flagpoles". Alternatively, but probably not as good, strings could be hung from the ceiling, with weights on their bottoms; strings that came down to about 4' above the room's floor. Or you can modify the design when you understand better what we're setting out to do.
Whateve you use for the "flagpoles", the more you can protect them from being moved, once the challenge is launched, the better.
Three of the flagpoles ("A", "B", and "C") go in corners of the room. Not all the way into the corner... participants will need to be able to get between the room's corner and the flagpole. (If you want to add another, in the remaining corner of the room, fine.)
And one flagpole, the one marked "X" in the diagram, goes in the center of the room.
Good! the stage is set!
Now, the participants try to make a map.
Let's say that the room is 30' x 40'. And that flags A, B and C are each 5' from each of the walls it is near.
Drawing a map of that, to scale, would not be terribly hard. And you could put X on the map too, once you measured how far it was from one of the "north/south" walls, how far it was from one of the "east/west" walls.
But! What if you aren't allowed near flagpole x?!
Situations like that are common in "real world" map making.
But if you are using triangulation, there's no problem.
You can see some angles marked in on the diagram. If these were measured, in the room, and if the locations of A, B and C were done by the "simple" method, then you could draw in the angles, on the "map to be".
Take angle "BAX" (marked in green) as an example. The side "BA" goes from A exactly towards B. It just does. We have B and A already drawn on our map, and we know that when the angle was measured (in the real world), that side of the angle was lined up like that.
Now use a protractor to finish angle BAX. There is only one place the AX line can go. (Or else the angle on the map won't be right.
So far, we know what direction X is from A... but we don't know how far it is from A.
Take another angle. Let's use ABX... marked in yellow.
When that's drawn in, we get a pretty good idea of where X is.... it is where the lines AX and BX cross.
Now imagine that you've also measured two more angles: XBC and BCX. And drawn hose angles onto your map.
If you've made all your measurements accurately, the four lines passing through X will pass through it very neatly. They will cross at one point. If the lines don't quite cross all at the same point, as in the diagram, you can console yourself with the fact that you are only human, and were probably using a pretty crude device to measure the angles. Maybe only a plane table?
But the whole exercise will still have been worth it. If no one cheats (it is easy, in this simple challenge, you can compare your map with those of the other participants and feel you've done well, or that it was someone else's "day", as appropriate.
In real science, there isn't "one answer". Scientists have to "have a go", see how the attempt turns out, and then try again... trying to fix things that led to errors in what they've done. If you attempt the map a second time, can you get a better result? How were you measuring the angles? Can you improve on that?
If you enjoyed this simple challenge, and there's someone willing to set things up, I have a bigger challenge, which lets participants see well they can measure angles with a plane table, or check the accuracy of a theolodite they've made.
And beyond that, again if there's someone willing to set things up, I have a more complex challenge... one where "cheating" is difficult, among other things!
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