Fundamental Rules

Formula. Our lives are defined by formula. The mathematical depiction of reality.

E = mc2


s = ut + (1/2)at2

So many of these derived so long ago, and yet still perfectly accurate. Nature defined.

There is one that is again, so simple, so exact. a2 + b2 = c2 This one has only been around a short while….about 2500 years! Known as the Pythagorean theorum, by the philosopher and mathematician Pythagoras of Samos.

Italiano: Busto di Pitagora. Copia romana di o...

Pythagoras of Samos (Photo credit: Wikipedia)

It is such a simple rule, a theorem in geometry that states that in a right-angled triangle the area of the square of the hypotenuse is equal to the sum of the areas of the squares of the other two sides. And the easiest version to remember is a 3-4-5 triangle. If your triangle follows this rule, you are guaranteed that the angle between the two shorter sides is a perfect right angle.

So if this rule is so perfect for ensuring you have a right angle, then why not have a tool based on such a perfect formula?

As a limited run (also known as “One-Time Tools”) from Woodpeckers, they have released a range of “Pythagoras Gauges“, available through Professional Woodworkers Supplies. The link takes you the set of all the sizes available as a set, but you can also purchase them individually, pricing ranging from $30 to $100.

They are accurate (I don’t know to what degree, but Woodpeckers don’t work to coarse tolerances!), and a lot cheaper than the equivalent square. The largest is around 1 metre (on the longest side): a square made to the same tolerances, to the same size would cost a fortune! Or be as (in)accurate as a carpenter’s square. The smallest is 178mm on the longest side, perfect for small boxes.

They look unusual compared to a traditional square, but what is important is accuracy and functionality.

If all three points are each touching a side (or corner), then the object is perfectly square. If not, then it is very easy to see not only which way the side needs to move to achieve ‘squareness’, but by how much.

I see one improvement that could have been made: additional marks on either end of the long side would have been possible to demonstrate to a very fine amount how much off from square the object is.

But other than that, a very interesting application of such an ancient theorum!

I’ve had an idea…..

After playing around with the ability to angle tools to the workpiece on the Torque yesterday, I’ve had another thought.

I was chatting to Larry (Lazy Larry (QLD)) about surfacing and it is very much trial and error to get the cutting plane of the surface mill bit parallel to the X & Y directions of travel.  As much as that is often how we have to do woodworking, I’m all for precision where it is practicable.  And when it comes to precision, I don’t think there is a system anywhere that can compete with the precision of Incra.

I’ve been toying around with some different ways the Incra rails can be combined, but what came to mind today was to do with the angling of tools, and in particular because I’ve put a less-than-ideal self-lubricating pad into place I was thinking of ways to positively lock the tool at the chosen angle.  What came to mind was the Incra Miter Gauges.

My idea then, is whether something like the Miter V27 could be used in a vertical orientation (or at least that concept)

Incra Miter V27

It would conceivably mount behind where the tool angle is determined currently (to the right of the drill in the following image)

Setting Tool Angles

Probably an idea that won’t go any further, but I’m always interested in how products from complementary companies can be symbiotically combined, and this is one example where the significantly versatile Torque workcentre could combine with the ingeniously simple concept behind Incra’s precision positioning.

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