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It's not my fault! (Geometric Right Angle Guage)

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Project by Tootles posted 04-19-2012 08:16 AM 2121 views 7 times favorited 13 comments Add to Favorites Watch

It’s not my fault ;-). Dusty 56 started it. Then Jaykaypur did it. And finally JR45 did it too. I just couldn’t help myself … (sob)

Really though, I have had a bit to say on Dusty56’s and JR45’s posts about this guage being based on a theorem of circle geometry (an angle inscribed in a semi-circle is always a right angle), not on the Pythagorus sum of squares theorem. Sure Pythagorus is valid, but he came well after the geometry, especially if a guage such as this was used by the Egyptians to build the pyramids some 2000 odd years earlier.

I also posted in JR’s project 5 steps (see below) to make this guage so I figured that I should put my money where my mouth is and test the process. And while I’m not going to deny that JR’s laser guided block plane might have made the job a whole lot easier, I just don’t have one of those so I had to rely on my dusty rusty old No. 4 – like the ancient Egyptians would have had to since lasers hadn’t been invented back then. (!)

The five steps that I followed to make the guage were:

  1. First make the short arm, complete with pointy end and hole for the pivot bolt.
  2. Cut the long arm more than double the length of the short arm and drill the pivot hole in the centre of the arm – some error can still be tolerated at this point.
  3. Align the short arm along the long arm in one direction, then use the short arm to mark the shape of the long arm.
  4. Align the short arm along the long arm in the opposite direction, then use the short arm to mark the shape of the long arm.
  5. Shape both ends of the long arm using the short arm to check that the ends of the long arm are accurate.
  6. Apply finish, in this case wax because it is quick, easy and I still love the feel of it.

Okay, I lied – there is a sixth step. After all I am posting this as a project which requires it to be completed, not just half-done. I did take photos, so if the instructions are not clear enough, and if enough people ask nicely, I could do a blog.

So now the ultimate question, what am I going to do with it? And well you might ask!

Actually, the most useful thing I can think of to do with it is take to to school if and when I ever teach the geometry of circles as a demonstration of the practical application of maths (you weren’t expecting me to say that now, were you?). The next most useful thing would be to use it in my woodwork class to check the squareness of some sliding lid boxes that my students will be making this term. I could use it to dazzle my students with my brilliance – in my dreams! But more realistically, it could be useful when I assess their work because it is a quick check using a guage that actually fits into the boxes

Whatever I do with it, it was a fun way to spend a little time in my workshop this afternoon. And isn’t that just what it’s all about?

Oh, materials are a strip of oak that I had in my scrap bucket and a bolt, washer and wing nut that I had on my shelves. So while I suppose the bolt and wingnut cost me something sometime, the effective cost for today is $0.00.

At 10” long, I’m guessing the woodpeckers one would be about $25. So special one-time offer, $12.50 anyone?

-- I may have lost my marbles, but I still have my love of woodworking





13 comments so far

View Jim Rowe's profile

Jim Rowe

558 posts in 964 days


#1 posted 04-19-2012 10:33 AM

I hope you used quarter sawn oak for stability. These tools rely on top quality materials to give consistent readings. Look how well the pyramids have stood the ravages of time!
Jim

-- It always looks better when it's finished!

View Tootles's profile

Tootles

704 posts in 1153 days


#2 posted 04-19-2012 12:31 PM

Mate, it’s Australian Oak. As we’re prone to saying Down Under, she’ll be right

-- I may have lost my marbles, but I still have my love of woodworking

View jaykaypur's profile

jaykaypur

3338 posts in 1059 days


#3 posted 04-19-2012 12:55 PM

An excellent project and very good looking but .......like JR45 pointed out, can it stand the ravages of age.

Take mine for example….its pivot point is the party of Lincoln, I can take it apart and micro-sand with it and…....and…..I can wear it! LOL

Good job on this.

-- Use it up, Wear it out --------------- Make it do, Or do without!

View Tootles's profile

Tootles

704 posts in 1153 days


#4 posted 04-19-2012 01:04 PM

Well what can I say other than “time will tell”. I mean, I’m going to take it to school and show it to students – that could be serious wear and tear.

And as I’m sure the Egyptians would have said, “Don’t worry about the guage, I can make another of those. It’s the pyramid that I’m worried about because that’s a bit more work”

:)

-- I may have lost my marbles, but I still have my love of woodworking

View Sylvain's profile

Sylvain

553 posts in 1151 days


#5 posted 04-19-2012 03:16 PM

In another post there was a link about the math behind this tool.

You might also be interested on how to find the arc of circle from which a line segment is viewed under a given angle.

This is called in French the “arc capable”. Sorry it is not shown in the English version of wikipedia.

http://fr.wikipedia.org/wiki/Fichier:ArcCapableConstruction.png
Draw the line “T” making the desired anggle alpha at point A. Draw a perpendicular to “T” and find the center “O” of the circle. Draw the circle. It is that easy.

I still have to find a use in woodworking, (unless you are building special instruments) but
It can be used in navigation if you have three known points in view and on the map, if you can mesure the angle of view between the points, you station is then at the intersection of the two “arcs capables” drawn on the map.

(just in case the battery of your GPS is out)

-- Sylvain, Brussels, Belgium, Europe - The more I learn, the more there is to learn

View TopamaxSurvivor's profile

TopamaxSurvivor

14742 posts in 2327 days


#6 posted 04-19-2012 06:19 PM

Nice work Tootles ;-) I wonder why Woodpeckers misnamed their gauge? Suppose semicircle-square gauge did sound as complex as Pythagoras ;-)

-- "some old things are lovely, warm still with life ... of the forgotten men who made them." - D.H. Lawrence

View seiner's profile

seiner

2 posts in 880 days


#7 posted 04-19-2012 08:12 PM

Yes – Thales’ theorem http://en.wikipedia.org/wiki/Thales'_theorem

-- Vitezslav / Czech Rep.

View Tootles's profile

Tootles

704 posts in 1153 days


#8 posted 04-20-2012 06:42 AM

Topamax – most people have heard of Pythagoras, and maybe even remember what the theorem is all about. But go ask a cross section of people and I can almost guarantee that most will tell you that they don’t like maths, and often geometry in particular. And remember that marketing is all about creating a warm and fuzzy feeling that gets people to buy the goods by whatever means possible – the complete truth and technical accuracy (even assuming the copy writer knows those two things, which is unlikely if he “doesn’t like maths”) is entirely optional.

Sylvain & Seiner – Thanks for the links to some interesting maths. I must admit that I was not familiar with there being a Thale’s theorem since it is, as the wikipedia article says, just a special case of the inscribed angle theorem that I referenced. I’ve always just learned and worked with the more general theorem and that is all that I would normally teach as well.

-- I may have lost my marbles, but I still have my love of woodworking

View Jorge G.'s profile

Jorge G.

1526 posts in 1126 days


#9 posted 04-20-2012 08:07 AM

Ok, here is the thing, as presented the gizmo is not really of much use, but I am wondering if there is a way to make one so that one would get the golden ratio. If I recall correctly ( and please feel free to correct me if I am wrong) the golden ratio is 1/1.6 or .625. If instead of making the shorter arm equal to one half the length of the large one, if one makes it Lx(.625) then we might have a useful gizmo to determine golden ratio distributions. What do you all think?

-- To surrender a dream leaves life as it is — and not as it could be.

View Tootles's profile

Tootles

704 posts in 1153 days


#10 posted 04-20-2012 08:22 AM

JGM - what you’re looking for I think is a Fibonaci Guage. Grumpy did what looks like a good post on one, certainly it references a few others. I think Stevinmarin also did a video of one on his woodworking for mere mortals site.

-- I may have lost my marbles, but I still have my love of woodworking

View Roger's profile

Roger

14556 posts in 1455 days


#11 posted 04-20-2012 12:43 PM

This sure beats the un Godly amount o money they want for this tool. Very good. Thnx for sharin

-- Roger from KY. Work/Play/Travel Safe. Kentuk55@bellsouth.net

View nomercadies's profile

nomercadies

507 posts in 990 days


#12 posted 04-20-2012 04:59 PM

I don’t know why you would make one when you can buy one … wait, did I say that right?

Woodcraft just sent me an advertisement with the least expensive commercial version, on sale, at twenty dollars.

But you are able to pay $140 if you would like a set with several sizes.
That is a “maths” I pay attention to.

-- Chance Four "Not Just a Second Chance"

View PaBull's profile

PaBull

928 posts in 2316 days


#13 posted 04-23-2012 11:27 PM

I might just build this “thing” some time to say:”I did it”.
Thanks for the post.
Pb.

-- rhykenologist and plant grower

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