Polynomial Roofs without the math
In a previous post I did some math to figure out how to cut wooden beams for a specific type of roof and ended up with a 4th-degree polynomial. Then I saw my landlord build a similar roof in our backyard with basically the same technique and I thought: "No way is he doing 4th-degree polynomials in his head, he knows some trick!" A bit more thinking and I came up with the trick myself :) This is one of those "academia smarts" vs. "street smarts" stories I think, like the (false) story of the inkpens in Space.
To keep this post short, I'll explain the technique in a series of images. For simplicity, we assume that one side of the roof is already done and we want to fit the beams of the other side, but this also works for the first beam by putting something at a right angle on the center of the middle beam so you have the necessary contact point.
Make sure your beam touches the other beams at the red contact points:
Draw the red line from the top corner of the beam vertically down, and cut away the red area:
Now we have two parallel sides and can move the new beam to the right until it touches the beam on the other side:
This is the most complicated step: Draw in a bunch of vertical lines as shown, then draw a perpendicular line that hits the intersection point circled in red. This gives you the distance , which you then have to apply at the top contact point:
Cut out two more sections as shown in red:
Now you have these neat pockets and can move the beam straight down:
And you are done:
