Cutting a board square

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Steve Maskery

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If you have an MFT then move on, you already have an excellent solution.

This is for the rest of us.


The first thing I ever filmed when I got my first camcorder was a gadget for checking a square corner. I never did find out what it was called, so I've called it the Square of Thales. Mr Thales was the first recorded philosopher, and is credited with being the first person to recognise that the corners of a triangle always add up to 180 degrees. This gadget works on that principle.

A Square of Thales is a pointed stick with a swinging arm. The points line up exactly at both ends. That's it.

P1040823.JPG


When all three points touch, the angle is 90.00000000 degrees. It has to be. I can give you a mathematical proof if you want. But it is.

So it's great for checking an internal corner. If the big arm is too loose, the angle is too big, if the small arm is too loose, the angle is too small.

But I have long wanted to use it for an external corner. It's taken me years, but, like so many ideas, I've come up with a way that could not be simpler. I just convert the external angle into an internal one.

In this example I am trying to set my saw track square to an edge. So I have my track, my Square of Thales, and a length of wood with a rebate cut along its length.

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1 Mark where the track is to cut, and align the track to that point.

2 Put the rebated strip up to the back edge of the track and hold it in place, either with a clamp or just with your manly thigh.

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3 Push the Square of Thales into the corner and adjust the track until all three points touch

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Job done. If you doubt it you can check with the biggest square you have, but it will be right.

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I love it when a plan comes together.
 

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Worthy of a short vid.

Now if you had too much time on your hands you could make a fancy one out of a nice hardwood with coplanar points, each with a brass insert, also a roll pin pivot in stainless bushes would be nice.
 
I can't get my head around that, but will make one anyway to see if I then understand

assume the pivot needs to be exactly mid point of the long stick

So I:

fix the short stick to the longer one via a pivot
clamp two ends and make a vee cut through both
twissle the short one (now with a vee) around to the other end and use that to mark the cut that end to match

Correct?

Edit: the trigonometry has just "clicked" :lol:
clever =D>
 
Thats a very neat cheap solution, triangles are a wonderful thing.

They could also use maths and measure but I think your thales sticks are probably even quicker.

Gotta be worthy of including in a new video... hint hint...

I bought a nice large glass makers square which is enormous and bang on accurate (well as accurate as my eyes are anyway) as I wanted a quick reliable solution to marking out 8x4 sheets to cut with the track saw. Works perfectly but your item would have saved me a lot of money
 
Looks like lots of people will be busy in the workshop this weekend.

Pete
 
Adam9453":ha83wvma said:
Thats a very neat cheap solution, triangles are a wonderful thing.

They could also use maths and measure but I think your thales sticks are probably even quicker.

Gotta be worthy of including in a new video... hint hint...

I bought a nice large glass makers square which is enormous and bang on accurate (well as accurate as my eyes are anyway) as I wanted a quick reliable solution to marking out 8x4 sheets to cut with the track saw. Works perfectly but your item would have saved me a lot of money

Where did you buy your Glass makers square from?

I need a decent large square for site work and I've been looking for a good glaziers one for a while.
 
I've been wring this up for my Italian friends, so here is a bit extra.
Why it works:
We have three triangles here, the big one defined by the three points (T3), and two smaller ones, one each side of the swinging arm (T1 and T2).

square of thales 1_1.jpg


Each triangle has corners that add up to 180 degrees., so T1 and T2 together make 360 (that is six corners in total).

At the pivot point, there are two angles, one from T1 and one from T2. We do not know what size they are, but we do know that together they make half a circle, 180 degrees. This means that the other 4 corners must add up to the other 180 degrees.

But wait a moment – look at the two smaller triangles. What do you notice about the two remaining corners in each triangle? They are the same. The two remaining corners in T1 are the same as each other, and the two remaining corners in T2 are the same as each other.

So if two of each add up to 180 degrees, one of each must add up to 90 degrees, and that is exactly what we have in the corner. One from T1 and one from T2. 90 degrees exactly.

square of thales 2_3.jpg
 

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Zeddedhed":p9umfziy said:
Adam9453":p9umfziy said:
Thats a very neat cheap solution, triangles are a wonderful thing.

They could also use maths and measure but I think your thales sticks are probably even quicker.

Gotta be worthy of including in a new video... hint hint...

I bought a nice large glass makers square which is enormous and bang on accurate (well as accurate as my eyes are anyway) as I wanted a quick reliable solution to marking out 8x4 sheets to cut with the track saw. Works perfectly but your item would have saved me a lot of money

Where did you buy your Glass makers square from?

I need a decent large square for site work and I've been looking for a good glaziers one for a while.

This looks to me very much like a common framers square that has had a removable wooden bar added to allow it to have one edge butted up to the outside of a sheet as a normal smaller square would.

Don't buy a silverline framers square though as they are anything but, buy a decent one unless you don't mind spending the time to true up a very cheap one - it can take a while, take my word for it.
 
Zeddedhed":1zfwnrsk said:
Adam9453":1zfwnrsk said:
Thats a very neat cheap solution, triangles are a wonderful thing.

They could also use maths and measure but I think your thales sticks are probably even quicker.

Gotta be worthy of including in a new video... hint hint...

I bought a nice large glass makers square which is enormous and bang on accurate (well as accurate as my eyes are anyway) as I wanted a quick reliable solution to marking out 8x4 sheets to cut with the track saw. Works perfectly but your item would have saved me a lot of money

Where did you buy your Glass makers square from?

I need a decent large square for site work and I've been looking for a good glaziers one for a while.

It was from Bohle, they only sell to businesses so bear that in mind when contacting them.
I went for the square with the brace as it had a higher accuracy level.
Was about £80 incl the Vat and carriage if I remember rightly.
They do various sizes Upto about 2.5 metres if I remember correctly.
I went for the 1350mm one as it was in stock and great for marking out large sheets.
Here's the link to the one I went for;
https://www.bohle-group.com/en-gb/produ ... race-black
 
I don't need to do it often but if I need to square across a sheet I use an offcut from another sheet to mark from. I can't see an occasion I would need more accurately than that.
 
That's fine providing your offcut is square. A lot of sheets aren't actually cut square so would give you an iffy result if you trusted their squareness
 

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