Making a Maths Field Kit
I’ve been meaning to do something maths-related with the girls for a while, but they’ve not been that interested so I’ve waited; these last few weeks, however, they’ve started to show some enthusiasm for maths and so we’ve been thinking about ways to use it out in the real world.
It seemed to be a lot more fun to make a kind of “field kit” than to do abstract maths and one of the most obvious uses for a field kit is trigonometry; after all, measuring the height of things provides some immediate results and can easily be checked on Google.
To find the height of a building using trigonometry we need to be able to do a couple of things: measure a distance across the ground and work out an angle from where we’re standing to the top of a building. The easiest way to measure a long distance across the ground is using a trundle wheel (a project for a later date) but we had to make do with a folding ruler. One of the girls had the idea of measuring and counting pavement slabs—which saved us a lot of time—but we still needed to make something that could measure the angle.
In the end we came up with the device on the left: a tube with a small hole at one end and a cross hair made of thread at the other, strapped to an iPhone with a spirit level app. This worked pretty well and was an improvement on earlier versions without the small hole and cross hairs. One of the first things we talked about was how to get the greatest accuracy; we found a whole list of things to improve by testing the equipment at home.
We went to the Arc de Triomf to do our measurement because it is well known enough to be on Wikipedia and because it has a lot of space around it.
First we measured the distance from the Arc to somewhere far enough away to get a good view (using the pavement slab method). Next we measured the angle from where we were up to the top of the monument using our special device. We also had to measure the distance from the measuring device to the floor so that we could add this on later. Finally, we needed to do some maths: we learned that the way to work out a missing part of a triangle (in this case the side opposite) was to use Sine, Cosine and Tangent. The way to remember which we needed to use is “SOHCAHTOA” (Sine=Opposite over Hypotenuse, Cosine=Adjacent over Hypotenuse and Tangent=Opposite over Adjacent).
We’d measured the side between us and the Arc (the Adjacent) and we wanted to know the Opposite side, so the bit of SOHCAHTOA we needed was the “TOA”. By rearranging the formula we knew that tangent of the angle we measured, multiplied by the length of the Adjacent side will give us the height of the Opposite side.
Luckily we had a vintage calculator with us (much cooler than an iPhone) and so we were able to work this out; using the calculator we were able to find out that the height of the Arc de Triomf was 28.5 metres.
Looking it up on Wikipedia we discovered that it was actually just over 29 metres so we were pretty pleased with our efforts. Being about a metre out seemed good to us although Olive is a bit of a perfectionist and would have been happier if we’d been spot on.
Anyway, this our first attempt at some maths fieldwork. If you know of anything else we could make to measure or otherwise understand the real world then please add a comment.
