# B Carpenter's math problem

1. Jan 21, 2017

### arydberg

A carpender wants to install molding on the cealing of a room. He needs it to turn a 90 degree corner. In the old days the molding had a trianglar cross section and he had to cut it at a 45 degree setting angle. This was simple.

Today however the molding comes in a flat section. It has to be placed on the wall at 45 degrees to the wall and 45 degrees to the cealing with a trianglar air space behind it. Now he needs it to turn a 90 degree corner.

The way to do this is to cut the molding with a compound angle saw. That is the saw is angled with respect to the center line of the molding called the setting and the saw is tilted with respect to the plane of the molding.

The question is how do you figure out the angle of the tilt and the angle of the blade setting.

I think the answer involves the dot product.

btw In the real world the saws simpley come with the angles marked on the saw.

2. Jan 21, 2017

### Staff: Mentor

I don't believe it does.
What I would do is put together a fixture that holds the molding at an angle of 45° off of vertical, the same way the molding goes on the wall and ceiling, then turn the saw blade 45° and make the cut. The cut for the other molding piece should be the mirror image of the first cut.

3. Jan 22, 2017

### Svein

No. If you have the standard formula for the planes (a point in the plane and the normal vector), the cross product of the normal vectors results in a vector along the intersection line. Unfortunately the answer is not quite that easy, since you do not have planes but three-dimensional objects...

4. Jan 22, 2017

### Staff: Mentor

@Mark44 = his answer is exactly what is done. Those fixtures he refers to are called "jigs" by woodworkers and carpenters. Ex: cutting crown moulding for a complex china closet without a jig would be a very expensive operation: lots of wasted pieces at \$20USD per board foot.

5. Jan 22, 2017

### arydberg

My question is how do you use mathametics to solve the problem?

6. Jan 22, 2017

### Staff: Mentor

My answer uses geometry.