When a neighbor offered us an old outbuilding—one that was in fairly good repair but that he’d no longer wanted—Pythagoras, the Greek mathematician and philosopher, was not foremost in my mind. I did have some deep philosophical questions, though. “Did we really want an old hand-me-down chicken coop?” was one. And, “If we did want an old hand-me-down chicken coop, why did we want one?” was another.
We didn’t have chickens but we certainly could have gotten one. Okay three. Including the rooster. Besides, the building hadn’t been a chicken coop for some time. The owners had cleaned it out, spruced it up and it had served as a kids’ playhouse. But both the chickens and the kids had long since grown up and moved away.
It took little time and debate to make the decision that we did want an old hand-me-down chicken coop, and we’d already picked out the location for it. And a name. You see, once we’d acquired it it was to be referred to, quaintly of course, as “the cabin.” That’s because we would be staying in it occasionally while finishing the house.
So the big question was this: What does a brilliant, if ancient, Greek philosopher have to do—posthumously of course—with relocating an old chicken coop onto a half-arsed homestead? Well, it wasn’t long before I needed his help. The 10′ by 20′ building was well-constructed and substantial enough that it would take a sizable crane to move it in one piece. And prepping a suitable foundation to receive it might call for some attention to detail.
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Our neighbor had a beautiful piece of land with an old farm house and several outbuildings. The gift building, though, he pointed out, he’d never gotten onto a proper foundation but had just propped onto some field stones. New England weather and soils being what they are, the little structure would heave and pitch with the seasons like a small boat buffeted in super slow motion on a solid but movable sea. If Pythagoras and I were to have our way there’d be none of that in the new location.
With all that in mind, the first task at hand was to decide what material to use for the foundation. One option was to go with the tubular forms available from building suppliers. These over-sized paper-towel tubes are heavy-duty and the general idea, of course, is to dig a hole, place the tube upright into the hole then pour concrete into it. Another choice would have been to stack large stones in the holes to form pillars.
I didn’t have sufficient stone available, and since the tubular forms would have been an additional expense, I opted to work with materials already on hand. That meant cinder blocks. I figured I’d stack them and pour concrete into the vertical cavities to form the piers.
Up to this point Pythagoras hasn’t been a lot of help. For one thing, I had to make all the decisions about materials on my own, and I figured there was little hope that he was going to offer to help with the digging. Anyway, the next task was to mark the location for six 42-inch-deep holes, one for each corner and one midway between each of the two corners. In our region, the base of a foundation should be at least 42 inches below the ground surface. This helps prevent the frost heaving and shifting problems our neighbor had had with the building.
I knew that I could’ve driven four stakes into the ground in a more or less rectangular shape to mark the corners. I figured I might have even been able to get my stakes set to exactly the distances apart they needed to be. But there’s a problem with that approach. Even with all the correct distance measurements to and from each stake, the corners might be only approximately at right angles. Worse, they could be off by a considerable amount. The point was that eyeballing it just wouldn’t do. I certainly didn’t want to find out on moving day that the foundation was out of kilter. This is where Pythagoras began to help out a little, though not with the digging mind you. He was more concerned with where to place the holes.
Mr. Philosopher had been on break for so long I’d lost track of him altogether. I’d used his formula before but was definitely rusty with it. Fortunately, though, I’d planned ahead and had remembered to carry along something special in the truck. Before I divulge what that something was, and is, I should state a disclaimer. I’d be the last one to try to plug or pitch or endorse a particular product in an article like this, unless there were to be large sums of cash in it for me—or unless I truly had a deep emotional attachment to the item in question.
Either way, I’ll leave it for you to decide that and I’ll divulge right now what the something is. It’s my cherished copy of Reader’s Digest Back to Basics—How to Learn and Enjoy Traditional American Skills. Mine, as the subtitle suggests, is the original edition. If you sense that I just might have a special place in my heart for this book you just might be right. I could go on about it but promised myself I wouldn’t.
So how do you like your math dished out? Do you like it in abstract and mind-numbing mathematical formulas? Or do you prefer it in the straightest, most practical and simplest of terms?
I seem to recall—from another lifetime—the phrase “Pythagorean theorem” as uttered by a math teacher. The teacher had written the equation out on the board and this caused me to cock my head and gape quizzically at the strange glyphs, the way a dog might react to something curious but incomprehensible.
If the same teacher were to have stretched a measuring tape from one of my foundation stakes to the stake diagonal from it and said, “Your corners won’t be square until this measurement is exactly equal to the other diagonal measurement; that’s the Pythagorean theorem,” I would’ve suddenly realized that I’d become the math genius I had always wanted to be. (Also, if Back to Basics had been my textbook I would’ve been a much better and happier student all around.)
Well, with stakes in the ground and a three-pound hammer in my hand, all of that “let this be side ‘x’ and let this be side ‘y’” mumbo-jumbo from math class turned into something tangible and began to make sense. My side “x” was 20 feet, and my side “y” was 10 feet. (The other way around would have worked just as well, as it turns out.)
I didn’t know where Pythagoras had gotten off to; I really thought he’d have been around for this part of the project. Anyway, I did have my bible so I turned to page 20, where it cited the curmudgeon, and it indicated that I should take my side “x” and square it. That gave me 400 (not in cubits but in feet). I was then to take my side “y” and square that. That gave me 100. Then I was to simply add them together. And that gave me 500.
The elegance of all this is that the figure 500 is the length of my diagonal, or line “z”—squared. In other words, it’s as if I had known the length of the diagonal all along and simply squared it just as I had done with the two sides. So the picture is simply one of two identical triangles sharing the diagonal line. Take away the diagonal line and it’s just a rectangle.
There was only one math task left to do—find the square root of 500. Wherever Pythagoras had gone off to he evidently had taken my slide rule. Fortunately I’d had a calculator in the truck so I traded the book for that, punched in 500, hit the square root key and got 26.36 (only with more numerals after the decimal point).
Since my tape measure wasn’t marked in decimals—and since measuring to the nearest eighth of an inch would be plenty good enough—I rounded the .36+ to .375, or three-eighths of an inch. So my diagonal measurement was 22 feet and three-eighths of an inch. Whew.
Well, Pythagoras was still nowhere to be found but we got through all this anyway. At this point the “we” includes my brother who’d come to help. So we had tweaked the stakes and now all the distances between them were correct, including both diagonals. This told us where to dig. Then a fortuitous thing happened. We remembered that an excavator would be working at the house site the next morning doing much bigger jobs. If the operator would be willing to burn about ten minutes with his machine and scoop out these holes for us it would save some manual digging. So I made a quick call and he agreed to it.
We returned to the site a day or two later and the machine had come and gone. We had four good holes at the corners. The only thing was that we’d taken the center stakes out along the 20-foot dimension to make clearance for measuring the corners and had never put them back. So the operator dug only where there were stakes and didn’t dig the centers. Shoot! Moving day was fast approaching and this meant we really had to concentrate on the corners and just block those sections up temporarily later, right on the ground surface. (Isn’t that what I said I didn’t want to do?)
Anyway, after cleaning out and fine tuning the holes at each corner, we stacked cinder blocks, with each stack sitting on a thick, solid concrete block for a firm base. It was necessary, then, to do a little more digging by hand to shave the walls and get the holes’ depths to where we could level the blocks. And, of course, the same diagonal measurement was then necessary in order to tweak the outermost corners of the block piers, but that was now routine.
Once we’d done all that, leveled and plumbed the blocks and mixed and poured the concrete, the only thing left right then was to sit and watch the concrete cure. My brother had brought us some refreshments for that phase of the operation.
With the foundation all set, backfilled and its concrete cured sufficiently, we were ready to set the building on it. Now all we had to do was to set the building on it. And for that all we needed was a 30-ton crane and a huge flatbed tractor-trailer rig. Oh, and an experienced crew to rig and secure everything and to carry out the entire operation.
Darned if just such a contingent didn’t come rumbling down our road more or less at the appointed time. Things on the home front don’t always work out so smoothly but we had done our prep work on this, too. We’d checked around and lined up a crane service that came highly recommended.
The neighbor is about a quarter of a mile down our narrow, dead-end dirt road through the woods. And the driveways—both his and ours—presented what we thought might be a serious challenge for the crew. (Actually, the crew that day was a crew of two—a father and son.)
They were the consummate professionals, though, and made pretty short work of rigging, lifting, loading and transporting the building. The thing that I think impressed me the most was how they negotiated the tight turn coming up the hill from the neighbor’s place into our driveway. It had seemed almost impossible but they did it with only a few back and forth adjustments and without going into the ditch. And we’d lost many a good contractor in that ditch.
After they’d gotten the whole bundle of joy into the driveway, the finishing stroke went pretty quickly. In very shortorder the building was sitting on its new foundation. I can’t say for certain whether the poor thing liked its new home or not, but I do know that the rest of us were fairly pleased about it.
When I say “the rest of us” I can’t speak for Pythagoras, though he must have been very proud. Or completely indifferent. Who’s to say. The bum never did really show up. I suppose I should go a little easier on him, though, because maybe he was there in spirit. At the very least his formula was in the good book and that was a huge help.
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Well that’s about it, except for some loose ends I alluded to earlier but didn’t cover in detail. So here they are in a nutshell: Not only do the foundation piers, or posts, have to be perfectly square, they also, of course, must be plumb or straight up and down. And they all must be at the same level if the building is to sit level.
As it turns out there’s a remarkably simple yet effective device to help accomplish the leveling, and it’s at least as much fun to use as is the Pythagorean theorem. It’s a garden hose water level. Pythagoras didn’t invent this, I did. Actually I didn’t but I like it so much I want to have invented it.
Perhaps these things are best left for another article, but in lieu of that they’re in Back to Basics for anyone who might want to refer to them there. In the meantime consider this: the next installment in this series of fascinating articles is going to cover particle physics and differential calculus equations as they relate to black holes and homesteading.
Or maybe weeding would be a more practical topic.