The Hundred-Year Chair · a chapter

Two Triangles

Wendy had found the problem by sitting down. I could see the rear foot slide when she leaned forward, and the seat flexed as well. Telling her the chair was fine would not stop it moving. I had to change something.

The legs raked to the front and back. Under load they pushed outward against the floor, which had to supply enough friction to keep the feet in place. Leaning forward bent the front legs and took weight off the rear feet. With less weight on a rear foot, there was less friction to keep it from sliding.

Side view of the stave chair, with black labels identifying rear-foot sliding, front-leg bending, and seat flex at the nose.
The movement I was trying to stop: the seat flexed, the front legs bent, and a lightly loaded rear foot could slide. The arrows identify the movements; the drawing does not show their magnitude.

Rubber feet were the obvious thing to try. Claude and I had already discussed them while I was working on the preceding version. I had replied, "relying on the rubber feet is not an heirloom strategy...feet come and go."

An heirloom? A few days earlier I had only been trying to use up scrap. Somewhere between that pile and a chair I liked enough to send a photograph to my sons, I had begun imagining something that might outlast me. Now even a rubber pad had to answer to that ambition. It could wear out or fall off, and I did not want the chair's stability to depend on someone finding a replacement. I wanted the structure itself to keep the feet in place.

Picture standing on ice with your feet spread and about to go, then tying a rope between your ankles. The rope takes the outward pull instead of asking the ice to resist it. In a chair, a stick connecting the feet can do that job. The stick is called a tie. Two legs and a tie can make a triangle.

Thinking about triangles brought back the voice of Peter Grove, my son Jamie's elementary-school science teacher. Peter taught for thirty years at Friends' Central outside Philadelphia. His classes launched hot-air balloons and waded in streams. The children hauled his car up a hill with a pulley system they rigged themselves. When his lessons turned to structures and bridges, his whole doctrine was one word, delivered as a mantra: triangles.

Peter died on May 6, 2026, a few months before this project began. He never saw the chair. My best chairs all contain his triangles.

The reason for Peter's mantra is easy to see with four sticks. Pin them together at the corners of a square and you can push the square into a parallelogram without breaking a stick. The corners simply turn. Add a diagonal and you divide the square into two triangles. Now the corners cannot turn without stretching or shortening a member, or making a connection give.

An unbraced frame at rest in gray and pushed sideways in color, with its corners turning.
Sideways movement in an unbraced frame. The gray outline shows its starting position; the colored members show the lean as the corners turn.

Engineers call that folding movement racking. A chair encounters it when someone shifts, leans, or tips onto two legs to reach something. Making the legs thicker is not much help if the connections still let the frame fold.

Triangles are not the only answer. Walking to my office months later, I noticed a Fyrn stool whose metal brackets made another approach unusually easy to see. Instead of adding a diagonal, the designer had made the corners resist turning. Rietveld had done that with broad overlapping boards and many screws. For my narrow sticks, I wanted to see what triangles could do.

reproduction permission pending; Karl to shoot or license a replacement
Another way to resist racking: Fyrn's metal brackets restrain rotation at the corners. Placeholder image; reproduction permission still needed.

On the evening of August 5, I went back and forth with Claude over drawings of the frame. The first moves stayed close to the chair I had built. What if the front leg stood more upright, parallel to the back? What if the rear leg changed slope too? Each change moved the intersections and altered the bracket that held the boards together.

Then I proposed putting the seat and back between two side frames. The bracket grew into a broad panel with legs attached, a trestle. It was starting to look like farm equipment. I could see how the panel might stop the movement, but I was putting a lot of plywood back into a chair I had been reducing to narrow sticks.

"Well, if you're going to do that," I wrote, "then just put a horizontal shelf between the front and back legs at 150mm from floor. Actually the whole thing becomes a truss ...no brackets."

A truss is a framework braced with triangles. I was looking for a way to make the chair's ordinary parts do the bracing, rather than adding large brackets to hold the corners. The shelf was another version of the tie between the feet. It also gave me something else to move around in the drawing.

What if the shelf tilted and met the bottom of the back at the same point as the rear leg? Three members would meet at one junction. I asked Claude to draw that. Then I saw another move:

"Run the back leg all the way to the seat. Terminate the front leg when it tees into the rear leg. Voila. Two triangles."

It had been little more than an hour since I proposed changing the front leg's slope. I had not calculated my way directly to this arrangement. I had proposed a shape, looked at the drawing, asked what it would do, and proposed another. The triangles gave me a useful direction without prescribing the chair.

The arrangement is easier to understand than that evening's route to it. Start with the seat and back, meeting at the hundred-degree angle I had chosen for sitting. A brace between the top of the back and the front of the seat would make a triangle, but it would also pass through the person. Extend the back below the seat instead. A diagonal underneath can close the triangle without occupying the sitter's space.

That upper triangle still needs legs. Extend its diagonal to the floor and it becomes the rear leg as well as the brace. Add a front leg and a low tie, meeting the diagonal on its other side, and there is the second triangle. One long member serves both.

Five stages showing a seat and back, a brace crossing the sitter's space, and the development of two triangles below the sitter.
A way to understand the arrangement after finding it. The first brace crosses the sitter's space; extending the back below the seat makes room for a triangle underneath. Extending the diagonal to the floor, then adding a front leg and tie, produces the second triangle.

Even then there were choices. The front leg could meet the diagonal at a right angle, which would simplify a joint. I asked for that version, then asked to see the front leg parallel to the back and the low tie parallel to the seat. "That one is pretty nice," I wrote.

Making the two triangles the same size and shape, or congruent, gave me those parallel pairs. They sit on opposite sides of the long diagonal, with their long sides overlapping. From the side, each short member has a partner pointing in the same direction. I liked the repetition. I also liked needing one set of angles rather than a different angle at every corner.

Two congruent triangles on opposite sides of a shared diagonal, with extensions forming the seat, back, and feet.
Turn the upper triangle through half a turn and shift it along the diagonal to get the lower one. The back is parallel to the front leg; the seat is parallel to the low tie. Their long sides overlap along one continuous member.

The next morning I asked to see a version with angles of 40, 61, and 79 degrees. Then I asked what we would give up to use 40, 60, and 80 instead. "I know we're gilding the lily," I wrote, "but where else can we indulge this kind of obsession? How you do anything is how you do everything."

I chose 40, 60, and 80. By then I was choosing among shapes close enough that a one-degree change deserved a drawing. First principles had helped me find a promising neighborhood. Finding the house I wanted to live in took a lot of looking around. There was no calculation that could tell me how much I should like those parallel lines.

On August 8 I opened another branch. During the pandemic I had made furniture from used wine barrels in Napa. I liked the oak more than the chair I had made from it. Now I wondered what those curves would look like in the two-triangle arrangement.

"we're not afraid of a little detour, right? It's just bits, not atoms," I wrote, before asking what would happen if the narrow members followed the arcs of wine-barrel staves.

"A detour into French oak is barely a detour at all," Claude replied.

The drawings bowed the members between their connections. I tried keeping the familiar joint angles, then reversing some of the curves. In two versions I liked, the curves swept in the same direction, giving the chair a sense of motion. I could imagine making one when I had suitable connectors. For now I wrote, "I think we can stub off this branch for now."

The exchange took less than forty minutes. I had not cut any oak. The drawings were enough to see a possibility worth keeping, and I could return to the straight-sided chair without pretending the curved one had been a mistake.

By then the project had produced several dozen versions. Some changed the way the chair carried weight; others changed a slope, a junction, or the way it looked. The drawings made comparisons cheap. They did not relieve me of choosing what to build.

Twenty-four chair side elevations at a common scale, from the early sitting envelope to the two-triangle design.
Twenty-four states of the design at one scale. Gray areas show brackets or panels connecting the colored members. In the third row, the front leg first tees into the diagonal; the next version adds the low black tie that closes the second triangle. These are side-view schematics, not joint details.

For the first full-size double triangle, I wanted a quick answer. I proposed cutting the ends of the plywood parts at their meeting angles and fastening them with brads. "This is a 100-hour solution not a 100-year solution," I wrote.

The assembly took more than brads. I used superglue to hold a joint, put in a brad, brought the full assembly into line with the measurements, and added more brads. Finally I put screws in all the joints for good measure. The result was another chair in black film-faced plywood, this time with the two triangles visible in its sides.

A full-size chair in black film-faced plywood, with two triangular side-frame openings sharing a long diagonal.
The two-triangle arrangement built in plywood. The first prototype was assembled with superglue and brads, then reinforced with screws.

On August 13 I sent Claude my report: "A lot of saw dust today. Strong validation for double triangle design. Feels very robust."

In the same message I had a question about cutting a fifty-degree miter on a saw I thought stopped at forty-five. I had found an arrangement I liked, and the first chair felt solid. Making its joints reliably match the angles in the design was going to occupy me for a while.

Notes

A chapter of The Hundred-Year Chair, drafted and refined in public. The same text lives in the book; the interactive tools and the fully-sourced technical notes live here. home · the book · the technical notes · hundredyearchair.com