Artisan Geometry | Popular Woodworking Magazine

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Craft geometry. The model used to establish the “square” in this shop-made wooden test square was generated with a little help from artisan geometry.

The universal and timeless structure of our imagination.

WThe work activity extends all over the world and is a common thread that connects human beings through the centuries. This boat shares a basic tool kit over time and space with more similarities than differences. A craftsman from feudal Japan might suspiciously see a western saw, but would still recognize it as a saw. Tools such as chisels, planes and saws are universal and work in parallel with a universal design language integrated both in the tools and in the way we carry out the project.

This language, which I call “artisan geometry”, has been used and handed down by builders since the early days. The language of this blue collar builder has been used both in the design process to display ideas and at the practical level used in the actual layouts on the workbench.

In our high-tech world it can easily be confused with an ancient method or a set of rules that could limit creativity. Far from it. Geometry is the structure that elevates our imagination just like the roots and stem of a plant support the flowering of a flower.

This is not the geometry that you were forced to memorize in third grade with theorems and tests. This is an artisan language expressed with a pair of dividers, a length of string and a straight stick. Yes, it was written, often in the opening chapters of the first books on construction such as Roubo’s treatise on carpentry (“l’Art du Menuisier”) or “The practical geometry of Natte”.

It is also lurking just below the surface, embodied in common layout tools created by the user such as test squares, straights and marking indicators.

Highway of imagination

Building 101. The first books on art almost always started with geometry lessons.

Today’s carpentry shop can purchase accurate layout tools and even laser-equipped machines. What need is there to learn this craft geometry? The short answer is that this is the basic knowledge behind our trade. On a daily basis we could use a calculator to solve math problems. But that doesn’t mean we wasted time in elementary schools learning to add, subtract and multiply. On the contrary, the calculator is a powerful tool precisely because we understand the math behind it. But this goes much deeper than just checking out some fundamentals.

I was always struck by the fact that ancient layout tools were often made by the user. At first I thought it was a practice born out of necessity. After all, tools such as test squares, oblique gauges, straight edges and winding sticks could be made from scraps of wood. But I wondered if there was anything else. Could the realization of these tools be a door in this artisan geometry?

In an attempt to deepen my understanding, I decided to create my layout tools using only handcrafted geometry to make them come out of nowhere. I’m not talking about the use of an engineer’s precision square as a master. This would have defeated what I needed to learn. Instead, I used craft geometry alone to find the real square.

Multiple methods. Here are three ways to evoke a right angle from nowhere. What construction was used to build the test square in the opening photo?

That proved to be a fundamental step. The act of using my hands to create physical tools that embodied geometric truths such as points, lines and planes allowed me to cross a new threshold. I am now convinced that the craftsmen made these tools not because they were frugal but because everyone needed to cross that threshold.

There is something about craft geometry that involves imagination in unique ways. It is a language spoken with our hands. It is revealed by scribing circles on the clean face of a pine board or by using an awl to hit a series of points to mark an important carpentry shop on one leg of the table. This face-to-face connection with the brain is a powerful conduit that awakens the imagination, that part of our mind that can see images in space. Think of it as a playground where you allow your ideas to rub against reality. Reality flows from the tip of our fingers as we start with a point and then a line. By connecting these lines they become planes which eventually turn into solids. We take it for granted, but this is a raw primordial thing like eating wild strawberries harvested from the forest floor. These are deep and fundamental truths at the root of everything we know about the material world. Even the simple act of using a compass to write a right angle pushes us into something at the basis of reality itself.

More than a solution

Buildings. Everything we build can be reduced to points, lines, planes and solids.

On a purely practical level, artisans who can speak this language can quickly find different ways to solve problems on the workbench.

Take the simple right angle as an example. Suppose you have to write a right angle at a narrow point too small to fit into your test box, or you need an accurate right angle to lay the foundation for a new laboratory, something beyond the scale of your test square. Or you simply want to create your own wooden square like our ancestors did.

On the left are three geometric layouts that use circles and a row to create a right angle. Note that they can be drawn on a small scale with a compass or on a large scale by swinging the arches with a rope attached to a stake anchored to the ground. Each is drawn showing its entire circle, but in reality, once you understand them, you can simply write small sections of circles in the space where important intersections are to be located.

Take a few moments and draw each time several times until it sinks into your memory and understanding.

The top one uses two identical circles that overlap. In this case, the center of the second circle is located on the circumference of the first. A line connecting the two centers will be perpendicular to a line connecting the point where the circles intersect.

The middle example uses circles to draw a 3-4-5 triangle that will always contain a right angle. On a straight line, go down five equal spaces. Place the cardinal point on the first sign and write a circle using the third sign to resize it. Then open the compass to extend all five signs and reset the compass point to the fourth sign, then draw a circle. The resulting triangle is 3-4-5.

Finally, draw a circle and then a line that crosses the circle through its center. Any two straight lines connecting the end points of the diameter and the edge of the circle will create a right angle.

Now go out and build a wooden test square or lay the foundation for that dream shop you’ve been thinking about for years. You have power with a little help from craft geometry.

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