>>12385236Just a math guy, not a carpenter. In this equation, S is the length of a side of the inscribed square and d is the diameter of the circle?
The equation is certainly correct for a square inscribed in a circle. Some obvious sources of possible error in cutting a real log would include:
(1) Non-circularity of the log,
(2) Distance from vertices of square to true circumference of circle
(3) Deviation from right angles,
(4) Measurement of circumference
(5) Measurement of side length
(1) is what you mentioned in the OP and is probably a large source of error for real trees. Even if a tree looks extremely round, it is probably not a circle. One shape that can look circular is an ellipse with relatively small eccentricity. In that scenario, you would get a rectangle, not a square, and the dimensions would depend on the angle the sides make with the major axis of the ellipse. An exact equation to deal with this is not so easy to understand (it is non-elementary), sadly. There may be useful empirical equations out there.
(2) Depends on the process of cutting a log. I couldn't cut a sheet of paper, so I can't tell you if this is reasonable or not. It will be *some* source of error in any case.
The other three are measurement errors. These are probably the three you have a best handle on. If these could account for what you are seeing, I expect you wouldn't have asked the question.
Even if none of these five errors can individually account for the live edge you see (at a corner, I guess?), consider that the errors can compound. On the other hand, there could easily be something I didn't think of. Or you could just be a shit carpenter. Who knows?
