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## Challenge: Measure angles in a large room (file:- ChallGym.htm)

This page sets out a simple challenge for groups to have fun with. It gives a group of individuals or small teams the chance to measure a bunch of angles. Probably, they will have made their own tools for doing the measuring, and comparing results will give them information about how successful their tools and techniques were.

It follows on from a simpler map making challenge. You might want to study that one first, to get the basic idea, before seeing what follows.

An organizer will have to do some setting up, and some "traffic directing" on the day.

The reasons for elements of the design below may not be immediately obvious... but there are reasons for many things.

We need a largish room, with few barriers to looking across the whole of the room. A gym would be perfect.

## The set up...

I will speak of "the north wall", etc in what follows. Your room can, of course, have any orientation. It would only be the "north" wall in my room, and we'll assume the diagram here was made with north at the too.

In a large rectangular room, set up...

Along the north wall some "targets"... an "X" on the wall made with masking tape would be fine. (If you're sure the paint on the wall won't be damaged!)

I've shown targets "V" and "X" on the wall in the diagram, and marked in U and T as dotted entities. I'm trying to imply that you can have as many targets as you wish.

You also need some targets on the east wall. One in the corner probably makes particular sense, but if there's "stuff" in the corner, making it difficult to put one there, it is no big deal.

The targets should be easy to see from across the room, and they should be labeled with letters, working backwards from "Z" at the lower left, and proceeding counter-clockwise. (As in the diagram!)

Moving on...

The diagram has two blue lines, with "A", "B", "C"... on them. The letters mark "stations". You don't need to mark out any lines. But the stations should be on lines. Lines parallel to the side of the room.

Participants will stand at the various stations. And measure the angles which are defined by any two of the targets and the station they are at... the station being at the apex of the triangle. I've drawn in a few of the MANY angles which can be measured on the diagram. I made those lines red. For example, the angle "VDY".

How you mark the stations for your participants will depend on the room you are in, and the measuring tools they are using. I suspect that an "X" in masking tape on the floor will be fine. If your participants are making their own angle measuring tools, give them plenty of warning about how the room will be set up, so that they have a way to position their tool accurately.

The stations need to be far enough away from the wall they are near that the participants can get behind their instruments, and sufficiently far apart that participants don't get in one another's way.

## The coordinates...

I've marked a suggested coordinate grid on the diagram. The southwest corner of the room is (0,0). Examples of "how it works": station "B" is at 2,6. Target "X" is at 18,8

(The units might well be meters, and you could of course measure more accurately than merely to the nearest meter.)

For the basic exercise this set up is proposed for, you don't need the coordinates. In no case, do the stations or targets need to be at places where "whole number" x's and y's cross.

It will soon be helpful if the three vertical lines in the diagram (two walls, and the line A-B) are all parallel. And if the three horizontal lines are.

If you set things up that way, a secondary exercise can be executed...

The participants can measure the position of each station and target, using the coordinate system described. With just a little sense on the part of the participants, a FEW could be working on measuring the positions' coordinates directly, while most participants measured angles. (The participants measuring dimensions would have to avoid blocking the sight lines of those measuring angles.) If each participant measured just a few dimensions, with who- measures- what coordinated by the organizer, then in the course of the time of the exercise, all the dimensions could be collected. (This approach would also help with the problem of finding more than one or two good tape measures with sufficient length. Getting mini-teams of four participants to measure the X and the Y of a point at the same time would heavily reinforce just what we mean by "X" and "Y", if that would be useful to your participants. On the other hand, the Y of C, D, E, F, G... only needs to be measured once, of course... if you trust the measurer to get it right. Multiple measurements helps you know if a particular measurement is right.

With those dimensions, a map of the room could be drawn, the boring way. From that, a second way to measure the angles becomes available.

However, on a much higher plane, with those numbers, the size of the angles can be calculated! For some groups, doing those calculations would be a useful exercise.

If you know anyone teaching (or enjoying) computer programming, an amusing exercise would be to create a program which could take the dimension numbers and generate a list of the angles, with their sizes.

Let's say that station D is at 5.5, 2. V and X are at 9,12 and 18,8, as you can see.

A "simple" computer program... on which a bigger one could be built... would have a way to input the 3 sets of coordinates...

• 9,12
• 5.5, 2
• 18,8

(The programmer would be allowed to assume that the user would enter the coordinates of the vertex of the angle as the second set.)

When three sets of coordinates were present, the computer should output the size of the angle. (If you attempt this, please have your program calculate the answer in degrees, not radians.)

(To keep the programming problem simple, for beginners, you will need to specify some constraints... I'm sure you can see them, if you think about it. But do. (Think about it.))

A fancier program could be set up to take all the dimensions from a carefully structured text file, and generate a list of all the angles participants might have measured. (Do a lot of thinking, and planning, before starting THAT program!)

## In conclusion...

This page explains an exercise which could be conducted in isolation... a chance for some participants to measure a bunch of angles, compare the results they obtain.

But it will be more fun in a larger context. It might "merely" be in the context of learning how to measure angles with plane tables, or with self-made theolodites. Or even in the context of making maps by triangulation.

I would love to get reports that someone, somewhere tried this... and feedback on any bits which could be improved.

If you enjoyed this simple challenge, and there's someone willing to set things up, I have a more complex challenge for you.

In a completely separate sphere, I have a different challenge... I've worked up most of what a programmer would have to think about in order to create computer program which could generate a table the size of all of the angles from some measurements that could be taken in the room. It would be, for some, an amusing exercise, whether or not anyone ever organizes the "measure angles with theolodite" exercise for some participants.

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