Once upon a time, 10′ poles were a tool common to a number of trades including linemen and cemetery workers. What they touched with their 10′ poles – high-voltage power lines and corpses respectively – is not something most people would want to touch, not even with an 11′ pole.
Carpenters, however, were quite happy with the 10′, or as the drawing suggests, any length of stick divided into 10 equal segments. For in their hands lay a tool critical to the efficiency and accuracy of their layout work. As we discuss in our book “From Truths to Tools” a right angle can be formed by a triangle composed of three whole-number leg lengths. In the simplest triplet, the leg lengths are three, four and five “whatevers.” The 10′ pole simply employs a doubling of those numbers: six, eight and 10, which are measured in this case with the imperial feet of some long-dead king. (If you think feet stink, you could measure out the pole in the cubits {forearm lengths} of some even longer-dead pharaoh.)
As demonstrated below – lifted from the book – we can construct a “proof” of this particular triplet using a straightedge and dividers. Be aware that there are many more whole-number triplet combinations – perhaps an infinite amount.
The sketch below shows the pole in use aligning a post square (and therefore plumb) to a level floor:
It’s a simple enough procedure: After fixing the base of the post to the desired location on the floor system, you use the pole to lay out a mark 6′ up from the bottom of the post. Next, you lay out a mark 8′ away from the post on the floor. When the full 10′ length of the pole fits exactly between the mark on the floor and on the post face, your post will be exactly square to the floor. Turns out that this layout problem (among many others as you’ll discover in the book) can be beat with a stick!
— Jim Tolpin, byhandandeye.com