Trigo-what?

I haven't posted in awhile, so I'm going to shake things up a little with some geekiness. Here goes.

Amber bought some pictures she wants to hang along our staircase. Here's a little sketch. I've labeled generally where she wants the pictures in blue.

I hate home improvement, so I left this exercise largely to her. She carefully measured the width of each of the frames and the dimension of the staircase (her measurement is shown above in red). After doing some arithmetic, she figured out where she wanted to hang each picture so they'd be centered. We started hanging the pictures following her math.

After the first picture was hung, something occurred to me. I hadn't really been paying attention to what she'd been measuring or her calculations, so I asked:

Chris:	"Did you use trigonometry to figure this out?"
Amber:	"Trigo-what?"
	<dramatic pause>
Chris:	"If you didn't use trigonometry this isn't going to work"
	<pause while Amber looks at the wall and envisions the rest of the pictures being hung according to her math>
Amber:	"This isn't going to work"

Here's the reason: she measured the dimension of the staircase on an angle, but measured the width of the frames not on a angle. So you can't just subtract these numbers. You either have to remeasure some of the dimensions or you have to use trigonometry to make them compatible.


Thus, to calculate the compatible value, a, we'd need to measure the angle above and multiple by it's cosine.

So, higher math does actually come up in real life! Albeit rarely.

To get even nerdier, you can break out some elementary vector calculus. Model the dimension of the staircase as the vector s with

In this case, the length a above is the projection of s along the abscissa basis vector i.


Ah! I knew I took two and half years of calculus in college for something. I just didn't think it would be for interior design.

(The formulas above are written with LaTeX using an online formula editor.)