How square is your square

[Tellurian]

I saw this and thought of @Steve Maskery.

https://fb.watch/IEh3ZucO32

(Apologies to Farcebook avoiders)

 

[Dr.Al]

While I can definitely see the benefits of Steve's Square of Thales, that seems like a convoluted way of checking a square when you can just use it to draw a line square to a straight edge & then flip it over & make sure the line still reads square.

 

[Tellurian]

While I can definitely see the benefits of Steve's Square of Thales, that seems like a convoluted way of checking a square when you can just use it to draw a line square to a straight edge & then flip it over & make sure the line still reads square.

I did think this as well and to be honest, in a workshop I expect the flip test would be the one most would use. But this method doesn't depend on your straight edge being accurate, eliminates any systemic errors from the flip test, but most importantly (to me anyway), it's a really elegant (and cool) demonstration of classical geometry proving a right angle from first principles.

 

[Sheffield Tony]

Aren't you still assuming the base line was drawn straight.

It is interesting to consider how you can get to precision from nothing. After all, humans have somehow achieved making straight edges, squares and much more complex things without so much as a straight line to start with. Planing 3 pieces of wood so that all pairings meet without gaps gets you to a straight edge (with 2 spares). Then you can either tune a 90 degree square by repeated flipping and adjustment, or if you can strike a circle from a line drawn using the straight edge, you can do what he does. You can also generate 60 degree angles by striking chords. I always found it fascinating what my Dad could draw; templates for cutting sheet steel that somehow folded or rolled into 3D forms, all with a rule, compass and squares, but little maths.

 

[Dr.Al]

It is interesting to consider how you can get to precision from nothing. After all, humans have somehow achieved making straight edges, squares and much more complex things without so much as a straight line to start with.

There's a superb book on this subject, called "The Foundations of Mechanical Accuracy" by Wayne Moore. Sadly printed copies are like hen's teeth, but you can find a PDF online (albeit with quite low resolution & grainy photos). I was lucky enough to borrow a printed copy & I read it cover-to-cover before I returned it but I've never seen one for sale at a sensible price (if I had it would be on my bookshelf now!).

 

[Tellurian]

Aren't you still assuming the base line was drawn straight.

No because you are using the square itself to draw the line, if the edge you use isn't straight, then the line won't be straight and it will be obvious there's a problem with the square when it doesn't fit the theorem.

It is interesting to consider how you can get to precision from nothing. After all, humans have somehow achieved making straight edges, squares and much more complex things without so much as a straight line to start with. Planing 3 pieces of wood so that all pairings meet without gaps gets you to a straight edge (with 2 spares). Then you can either tune a 90 degree square by repeated flipping and adjustment, or if you can strike a circle from a line drawn using the straight edge, you can do what he does. You can also generate 60 degree angles by striking chords. I always found it fascinating what my Dad could draw; templates for cutting sheet steel that somehow folded or rolled into 3D forms, all with a rule, compass and squares, but little maths.

I've always found all this stuff fascinating. My problem these days is that I can't remember the process. I'll know that it's possible to get a 60° angle by striking chords but I'd have to look it up to get correct technique.

 

[Tellurian]

There's a superb book on this subject, called "The Foundations of Mechanical Accuracy" by Wayne Moore. Sadly printed copies are like hen's teeth, but you can find a PDF online (albeit with quite low resolution & grainy photos). I was lucky enough to borrow a printed copy & I read it cover-to-cover before I returned it but I've never seen one for sale at a sensible price (if I had it would be on my bookshelf now!).

It seems to be available here: https://www.scribd.com/doc/267930763/Foundations-of-Mechanical-Accuracy

 

[Dr.Al]

It seems to be available here: https://www.scribd.com/doc/267930763/Foundations-of-Mechanical-Accuracy

Yep, that's the one. The pictures look to be similar to those in the PDF I've got. The photos in the real book are much better quality. Unfortunately, some of the photos are quite important in aiding understanding of the concepts being explained, so the grainy pictures in the online version are quite unhelpful.

It's still possible to buy the book new in the US, but it's $250 so you've really got to want a copy! Alternative there's a used copy on abebooks for about twice as much as the brand new one! I keep hoping to stumble across a copy in a charity shop but I know that's a bit of a pipe dream

 

[SteveMP]

Interesting. I have used the pythagorean theorum for large projects like outdoor patios, laying out concrete or pavers etc. Probably the only math i learned in school that i still use

 

[Sheffield Tony]

Interesting. I have used the pythagorean theorum for large projects like outdoor patios, laying out concrete or pavers etc. Probably the only math i learned in school that i still use

I have done similar when building a hut. But, you do need to be able to measure distance accurately for that. Alternatively you could strike out a straight baseline (chalk line), and perpendicular reference line by marking a point on your baseline, striking out an arc to a point each side of it on the baseline, then striking a longer radius arc from each of these two points and taking the intersections. This gives you two orthogonal reference lines with no measurement or square.

 

[Lurker]

My engineering squares are as square as a square thing. My woodwork squares are good enough.

 

[SteveMP]

I have done similar when building a hut. But, you do need to be able to measure distance accurately for that. Alternatively you could strike out a straight baseline (chalk line), and perpendicular reference line by marking a point on your baseline, striking out an arc to a point each side of it on the baseline, then striking a longer radius arc from each of these two points and taking the intersections. This gives you two orthogonal reference lines with no measurement or square.

Yeah exactly. Oftentimes I am building something adjacent to the house for example so will use one wall of the exterior, or the concrete foundation/footing, and use the formula to layout a perpendicular string line(or chalk line) for example

 

[Steve Maskery]

This is not doing it from First Principles, although it is a nice illustration of the Theorem.
My alpha/beta explanation IS from First Principles.
As no-one has yet posted it in this thread, I feel morally obliged to plug my film again...

Enjoy!