teaching machines

Bathroom Angles

Our bathroom gave me a math problem, and I failed. Herein I document my failure and visualize the answer I should have provided.

When we bought our home, the bathroom had carpet but no baseboard. This combination makes painting the walls difficult. As we are preparing to paint, I decided to install some baseboard. Measuring, cutting, and hammering… These seemed like things I could do.

The only gotcha is that one of the corners between walls isn’t a 90-degree angle. It’s a 45-degree chamfer. I knew that I wouldn’t be able to just put two baseboards with perpendicular ends together at this corner. I’d end up with a join like this:

The red board and magenta boards overlap, which is a physical impossibility.

I could have them meet at the front instead, like this:

But this leaves an unsightly gap, which is an aesthetic impossibility.

My intuition kicked in and told me I needed a 45-degree cut on the board that was up against the chamfer. I obeyed and unwittingly birthed a monster. The boards aligned at the ends, but the fronts didn’t match up at all.

After some reflection, I realized that I was lining up the side of a 45-degree right triangle with the hypotenuse of a 45-degree right triangle, and they would necessarily not be of the same length.

To ensure that both ends had the same length, I would need to cut each at the same angle. In this case, I needed to split those 45 degrees between the two boards, cutting each with a 22.5-degree bevel.

This looks so much better.

One of the reasons I got into computers is so that I could play around with ideas without wasting materials on my mistakes. If only I’d done so here. This is what miter been.

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