Much of our contemporary furniture designs tend to strip away as much as possible letting the bones lay bare. What this points to, both period and contemporary is that the simple shapes that define a design are what makes it. Up until very recently those simple shapes were in the realm of artisan geometry, produced with a compass and straightedge. Today we have digital tools to design with, but that digital technology is limited if it doesn’t have the mastery of artisan geometry to go with it. Sort of like using a calculator without knowing how to add.

Regardless if you work with an eye towards the future or to the past, this knowledge is still key to becoming the best artisan you can be. We wrote our most recent book, From Truth to Tools with that in mind and now are offering a video series that introduces this artisan geometry through the building of a basic layout kit. Come along with us and you’ll gain a nice set of layout tools and learn the same design language that produced the most iconic works of all time.

George R. Walker

]]>Sharpening has always been one of those gateway skills into the ordered side of woodworking, but to our ancestors, artisan geometry was the gateway into that world of the unknown. That place where we could explore ideas in our imagination and refine them into something our hands can make real like a chair or a spoon or a cathedral. Oddly enough, artisan geometry has its own gateway. Our ancestors became familiar with artisan geometry by making their own set of layout tools using the truths of geometry to birth each tool. And amazingly as each tool came to life in their hand, the truth and mystery and beauty of geometry came alive in their minds.

We’ve put together a video series about making these tools. But It’s not only about making a great set of tools. It’s about stepping out of the boat into the unknown.

George R. Walker

]]>Not only will you get a great set of layout tools uniquely suited to woodworking, but also gain a deeper understanding of artisan geometry. Jim Tolpin and I have been working on a video series “Building Tools from Truths” to walk you through the build process for making your own tool set. Our first offering covers tools for the layout of straight lines. Here’s a link if you are interested in learning more.

George R. Walker

Cross posted from Design Matters Blog

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In this excerpt from our latest book, “From Truths to Tools”, we show how the carpenter’s of antiquity used the simplest of tools–those mentioned with almost annoying alliteration in the title–to solve for an unknown distance. Note that the solution does not necessarily require a number, it just needs to reveal the length of rope or timber needed to reach the span point. Here’s the excerpt:

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Here’s what the publisher, Christopher Schwarz, says the book is about:

Good books give you a glimpse of small truths – about workbenches, joinery or sharpening, for example. Great books, on the other hand, stitch together seemingly disparate ideas to present a new way of looking at the world as a whole, from your marking awl, to your hand or to the line of the horizon.

“From Truths to Tools” by Jim Tolpin and George Walker is a hand-illustrated work that masquerades as a children’s book. There are funny drawings. There aren’t a lot of words. You can read the entire 208-page book in one sitting.

But “From Truths to Tools” somehow explains the craft, the entire physical world, our language and geometry in a way that makes you feel like the authors have revealed a huge secret to you. One that has been sitting in front of you your entire life.

The book begins with an explanation of a circle and a single point and show how those simple ideas can be used to create an entire set of layout tools – a try square, a straightedge, dividers etc. that allow you to build furniture.

Once you understand the language behind your tools, very complicated things become easy to understand. Compound joinery. Fitting odd miters. Making curves that taper.

And once you get those ideas in your head, it’s a short hop to how those same ideas can be applied to building anything of any shape imaginable – skyscrapers, boats, bridges. When you can calculate if a tree will hit you when you fell it in the forest you’ll be able to calculate the circumference of the earth.

“From Truths to Tools” is the third book from the geometry-loving team of Jim Tolpin and George Walker. Their first book “By Hand & Eye” makes the case that simple whole-number ratios are the underpinning to the built world and our furniture. The second book, “By Hound & Eye” gives you the exercises that open your eyes to the way geometry and ratios govern our world. And the third, “From Truths to Tools,” shows how geometry creates our tools and, once understood, leads to a deeper grasp of the things we build, the world around us and even our language.

“From Truths to Tools” is printed in the United States to exacting standards. The pages are sewn and glued so the book will last a long time and can rest flat on your bench. The pages are protected by heavy paper-covered boards. The book is designed to last several generations.

As always, we hope our retailers in North America and elsewhere will carry the book, but the decision is up to them. So as of today, we don’t know which retailers will stock it.

*— Christopher Schwarz, editor, Lost Art Press*

I first stumbled on the sector as a layout tool through an article by Tom Casper in Woodwork magazine that appeared in the late 90’s. My curiosity engaged, I went through all the woodworking books in my considerable collection and couldn’t find a single reference. It turned out that the sector is essentially extinct. But as Tom pointed out, it was–and is–incredibly useful. The sector could effortlessly divide–with no measuring and therefore no math (fractional, decimal or otherwise involved)–a certain space up into whole number segments. When I presented the sector in my book “Measure Twice, Cut Once”, I showed how to locate drawer pulls two-fifths of the way in from either end of a drawer face.

I left it at that until just a few years ago when, on the recommendation of Joe Youcha (www.buildingtoteach.com), I got a copy of *The Victorian Cabinetmaker’s Assistant *published in the mid 1800’s. Here I learned that not only could the “Line of Lines” provide multiplication and division solutions along line lengths but it could also lay out (or find) whole number proportional relationships.

At this point having become rather obsessed with this tool, I sought out even earlier manuscripts from the 1700’s that described further workings of the sector. When I finally understood that the geometry of the sector allowed it to solve for unknowns among all sorts of ratios, I added another scale to a paper version that could provide solutions for the diameter, radius or circumference of a circle (i.e. the “Line of Circles”). The realization that the geometric truth underlying the six-sided figure (the hexagon) could produce another scale to provide the facet length of other polygons was exciting enough to keep me up half the night–and in the morning I added the “Line of Polygons” to the paper sector.

You can download a free template of this sector over in the shop section of this website–and you can also download a not-as-free, forty-page pamphlet that tells you how to use it. But you still can’t buy a “real” sector at Home Depot or anywhere else since they stopped making them (as far as I can tell) more than 100 years ago. Until now!

Due to the enormous efforts and talents of Brendan Gaffney of www.burn-heart.com), we now have a limited number of his solid maple-and-brass hinged sectors in stock. Read more about them over on our shop page where there is also a link to a video on working with it. This batch is the last of his first run so this is your last chance to get your hands on a first edition!

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In our book* By Hand and Eye*, we showed a simple straight taper–common enough in Roman columns and quite easy to generate. But some columns from Greek antiquity display a taper that follow a curve. As shown in the drawing below, the curves get more radical as you move from parabolic to elliptical to hyperbolic. All were developed, not from a numerically dimensioned layout, but from the generation of a relatively simple geometric construction familiar to ancient artisans.

The parabolic curve is the simplest and fastest to execute. As shown in the drawing, it is simply a matter of dividing up (with dividers of course) the inset amount of the top of the column into equal segments, than running straight lines (with a straightedge or string) from these points to the corner of the column shaft at the base. You then create station points at evenly spaced, horizontal intervals drawn across the length of the column. (I show only four intervals here for clarity–plus I’ve compressed the height-to-width ratio to exaggerate the curve).

To create the elliptical curve, the artisan drew a half circle to the diameter of the bottom of the shaft, then segmented the half sector into six even slices. Lines drawn vertically from the intersection of the horizontal segments with the rim of the arc create your station points above.

The hyperbolic curve station points arise from evenly spaced segments stepped along the circumference of the half circle.

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Step 1: Establish the baseline (via a stretched string) and set a pin (a sharpened stick works) at the focal point to which the angle will converge.

Step 2: Make a loop at the end of a non-stretchable rope (i.e. avoid nylon) and run it out along the baseline from the base pin. Measure out 57-feet, 2 ½-inches from the pin along the rope and make a mark with a sharpie or tie on a piece of string. Also set a pin at the baseline at that distance.

Step 3: Now arc the rope away from the baseline in the direction you want to lay out the angle.

Step 4: Set the base of the ten-foot pole at the base line pin and orient it to the rope. When the eight-foot mark on the pole passes over the mark on the rope the angle to the baseline is (drum roll) eight degrees.

So how does this work you might ask? As my friend Joe Youcha of buildingtoteach.com explained to me: “The answer is buried in the math we were all injected with in grammar school.” We were all told about the “transcendental number” called “pi” which when inputted into your calculator would provide you with either the circumference of a circle based on its diameter or vice versa.

Artisans of antiquity, however, had no knowledge of the decimal number pi. In fact decimal numbers in general had not been described in detail in the western world until the late 1500’s by the mathematician Simon Stevin. But artisans did have an excellent working relationship with the straightforward (non-cendental?) proportional ratio system. In the case of the relationship of the diameter of a circle with its circumference, they would just step out the diameter into seven segments and know that twenty-two of those segments would, to a high level of accuracy, give them the length of the circumference. Good enough for government work (such as the Parthenon) as they say.

Since we apparently need to work with degrees (probably because the architect speced out the angle in degrees instead of the length of a chord as they would have in antiquity) we would need to know what number of segments the diameter would be if the circumference were stepped out to 360 segments. (That number is, of course, an arbitrary but widely accepted convention since Babylonian times as a convenient way to divvy up a circle. We like it as it can be evenly divided by so many whole number divisions–though for a time Europeans were quite fond of 400 degrees.

But I digress, back to how it works: If you go to the trouble of physically stepping out along the circumference of a circle with dividers, you’ll discover that when three hundred and sixty segments do the trick, one hundred and fourteen and five twelfths of another segment will define the diameter. Of course, using al-Jabr ( given to us by the Islamic mathematicians), we can quickly solve for this result using an algebraic equation to solve for an unknown.

For this purpose we’ll use half of the diameter segments–fifty seven and three and one half twelfths–to lay out the radius length on the rope. The bottom line: We find that a radius of 57 feet, 3 ½ inches produces a circumference length of 360 feet. So for every foot we swing the arc, we produce an angle of one degree.

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