Thursday, 19 May 2016
I have a very strange history with maths. I did advanced maths at high school, and the hardest maths level at HSC level, and I always walked out of the tests and exams feeling completely confident that I knew exactly what I was doing and I'd passed. But half the time I'd get the test or exam back and discover I'd got some ridiculously low score like 14%. It was very un-nerving. By the time I reached the end of year 11 I'd lost so much confidence that it at least didn't surprise me when I failed the final exam and had to repeat the subject the next year.
I was so un-nerved by this experience that when I was forced to do some maths units at uni half a decade later I panicked.. I was completely paranoid that I'd fail and get thrown out of my course. I worked so hard to avoid that outcome that I actually received university awards for both the maths and statistics units. What the?? So I still don't know if I'm good at maths, or if I'm an idiot. Or maybe I'm average, and everyone else at uni that year were idiots. Who knows. It could have been that the uni subjects contained a lot more statistics and things like queuing theory which I really enjoyed for their more obvious real life applications (gambling and anywhere with queues), whilst the algebra and trigonometry at HSC perhaps seemed more abstract, and less applicable to real life..
So - what I'm trying to say here (in this long winded introduction), is that the last time I did trigonometry I had a spiked haircut (short on top, long at the back) and Australia had not yet celebrated its bicentennial. In fact when I closed my answer booklet at the end of the HSC maths exam (2nd time around) I probably thought that my troubled relationship with Sines, Cosines, Quadratic Equations and the rest of the trigonometric palarva was over..
But here we are 30 years later, and my current woodworking project involves making a frame for a mirror. A circular mirror. And the frame is made up of lots (35) bits of wood pointing outwards. Like that sketch below
So to work out how to cut these peices of wood so they fit nicely (or nice-enoughly) together, I've had to pull some maths out of the dusty reaches of my brain and work out some angles. Using Pi, tan, and arctan. Thank goodness the internet has sprung up since I solved my last trig problem - not that it could solve the problem for me, but it could remind me of the tools I could use to do it. If you're interested, I worked out the outside diameter and then the inside diameter. Turning the inside into a percentage of the outside, I could work out how much length each piece would need to 'cut in' on either side. What I really wanted was the angle to put my dropsaw onto though. So using my two values I used a tan equation (I had adjacent and opposite lengths). From there it was a matter of using arctan to determine what the angle was. Therefore the angle to set my dropsaw was 90 minus the value I'd found. Phew!
And did it work? Yeah - pretty much. It was a bit of a pain that I had about 7 different widths of wood - so I had to repeat the calculation each time - if I hadn't chucked out my scientific calculator all those years ago I would have used it so I could just plug in the lengths. Of course calculating the angle down to two decimal points wasn't all that useful, as the drop saw only really had 1 degree settings, but I could at least eyeball an approximate setting. It wasn't perfect, but it wasn't too bad. I'm sure the imperfectness of my woodworking skills that I'll be using to complete this project will far outweigh any errors I've made in my calculations and cutting.