# I Don’t See How This Works

My experience doing flooring is limited to edge-to-edge boards. In fact, I’ve been terrified of doing tile because of the problem of making the edges meet the wall.

This video by youtuber This Old Tony (one of my favorites!) is pretty simple-seeming. In fact, it’s so simple I can’t figure out why it works at all. Or, I can’t figure out if it’s hard to figure out.

I keep going, “no wait there has to be more to it than that!” It doesn’t even appear to waste tiles.

“Why is there a large band of grout around the floor?”

1. xohjoh2n says

Hmm.

Imagine the wall is a “virtual, infinitely thin” wall.

Now imagine the tiles continue past it, tiling the plane in all directions.

Now imagine that you’ve not got just the one wall, but a series of parallel walls, at the same periodicity as the tiles themselves (though obviously not aligned by angle or by position).

Because the periods match, the whole system has translational symmetry in the axis perpendicular to the walls. As such the walls intersect/cut the tiles in exactly the same position relative to an individual tile within each period.

All the template is doing is showing where the next “virtual wall” would be, so you make the cuts there. Then translate those tiles one period in the other direction.

2. says

xohjoh2n@#1:
Now imagine that you’ve not got just the one wall, but a series of parallel walls, at the same periodicity as the tiles themselves (though obviously not aligned by angle or by position).

Aah! Lightbulb comes on!

So, that also answers Tony’s question in the video, whether it would work if the tiles were at a different angle. It should work regardless of angle as long as the tiles are “tiling” periodically.

3. consciousness razor says

It’s pretty simple. It is using the fact that the square tiling is regular (and squares are symmetric like xohjo2n said). If the tiles were various sizes or shapes, or they’re not forming a regular pattern, there wouldn’t necessarily be a way to line up the new tiles on top of the already-placed tiles and get a correct measurement for them. With squares or similar shapes, that’s not a problem. (The wiki page for tessellations is fun. Imagine how it would work or fail to work, with some of the tilings shown there.)
He said there was “no measuring,” but that’s exactly what he did on the cardboard piece before marking the (carefully placed/rotated) tiles with the appropriate measurements. It doesn’t need to be a special “measuring tape” (or stick) like you buy at the store, with numbers or other crap written on it, because the cardboard and the tiles themselves will do the job. (People often call these kinds of things a “guide” or a “jig,” not “measuring stick,” but it’s just one that’s customized for this purpose.)
Note that he also didn’t need a protractor or whatever, to measure the angle. If it’s not exactly 45 degrees relative to the wall like he said it was, that makes no difference…. It’s some angle or other, and there’s no need to figure out exactly what it is and write down a number somewhere. (You could pick different numbers for the same thing anyway … “45” degrees, “π/4” radians, “1/8” turns, etc. They’re not as useful as might think and sometimes just get in the way.) What’s needed is just for them to be at the same angle as the ones he’s already laid down on the floor, because the pattern is regular and the tiles (practically) identical in size/shape. That’s why he had to adjust them slightly, when he wasn’t happy with how they were rotated. Sliding probably isn’t a big deal, if you don’t go too wild while drawing the lines, since there’s enough friction to keep them in place.
It would be good to pay close attention to where you make the cut relative to the mark, because real cuts with an actual saw blade aren’t actually area-preserving like an abstract, geometrical line would be. The latter have 0 thickness and don’t eat away at the material, but really, a small amount of tile is lost with each cut — it’s chewed up and you can of course see the dust. Although it won’t be very much, it’s comparable to the width of the grout line, which is also something he tried to factor in (just by eyeballing it) when making the cardboard guide. So, I would make sure the cut doesn’t take any material from “inside” the mark (i.e., from the part of the tile that you’ll place on the floor there … because it’s okay if you shave off some of the leftover part).

4. lochaber says

ha! that’s pretty clever.

It looks to me like he’s just moving the line of the wall one tile-unit in wards, so that you can align the tiles and mark the cut line without the wall interfering.

consciousness razor @ 3>accounting for the width of the saw blade (I believe it’s called “kerf”?) is a pretty regular thing when working with wood (sometimes the “waste” side of a cut is marked), and I’d assume when working with other materials as well. It might be so common with someone who does a lot of woodwork/construction, that they didn’t even think to address it.

5. consciousness razor says

Yeah, I’d say it’s more important with carpentry and woodworking. If you’re doing it enough, it’s not even worth mentioning like you said. But I’ve seen plenty of novice woodworkers despair when they find gaps in their joints. They may have measured it all very precisely (a couple of times) like they’re supposed to, but it may not occur to them to be just as precise when accounting for the cut itself.
With tiles, I guess it’s not as problematic, because you want to leave a bit of extra room for expansion and so forth anyway. Plus, a baseboard (the wood trim at the bottom of the wall) will cover the edge of the tiles. It’s usually pretty thick — with some styles, another piece is tagged on at the bottom to make it extra-thick and thus idiot-proof — so even a fairly large gap between the tiles and wall will be hidden, not exposed like a joint on a piece of furniture or whatever.

6. consciousness razor says

Also…. One thing I assumed and didn’t say before (because it’s almost too obvious) is that the “wall” and “mark” edges of the cardboard have to be parallel to one another, not merely straight edges. It won’t do to have just any old quadrilateral. The thing is that he didn’t show how he made his piece of cardboard into that specific kind of shape — that was maybe a bit of misdirection, if you were mystified by how his magic trick works.
It would be fine as a trapezoid/parallelogram/rhombus, since the other sides don’t do anything important. But it’s probably best to make it rectangular (or square), since it’s relatively easy to make them parallel by constructing that out of two adjacent right angles. In this case, since you’ve got the square tiles, you’ve already got right angles to copy.

7. says

See also “spiling” and “joggle stick” (the latter is a tool for performing the former). There are a remarkable number of bad ways to transfer an edge-line to something you have to cut, and a few good ones.

8. cvoinescu says

Cool method.

When the tile edges are parallel to the wall, you simply use a tile as your “template”, the exact same way he uses his cardboard piece (add a spacer between template tile and wall before marking the tiles to cut).

This is a generalization of that for when the angle is not zero. He gets the math wrong, though: it’s not a grout line width you need to add, but a grout line width divided by the cosine of the angle between the wall and the tile. For 45 degrees, that’s a factor of sqrt(2) — call it one and a half if you eyeball it.

9. cvoinescu says

Actually, it’s not wrong, just unclear. If you add the grout line around both sides of the tile that meet at that corner, and mark the intersection, it works.