By Hand & Eye Discovery

[Jim Koepke]

I have been reading By Hand & Eye By George R. Walker & Jim Tolpin. Going through the construction of angles and geometric shapes at the end had me a little puzzled. So there is a set of drafting instruments in my office/computer room/library/man cave.

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The pair of dividers, under the beam compass, was taken to my bedroom since that is where much of my reading is done before falling asleep.

I hadn't given them much attention in the past since there are many others out in the shop that get used all the time. The little wheel between the legs got me curious. Turns out it might be a fine adjustment for the legs. It only changes the span by 1mm. That is likely enough for many purposes.

One thing I wish the book, By Hand & Eye, did would have been to better explain the constructions. The write up on the construction of a 45º angle doesn't explain the point above the vertex of the angle is a ghost construction of a 90º angle. It also doesn't explain how stepping off two radiuses on one of the arcs creating the ghost angle produces a 45º angle. Believing it works is one thing, but for me knowing why has it's values.

In the construction of polygons, for many polygons stepping off with a pair of dividers may be the best way. Though in high school my instructor showed us an easy way of constructing a pentagon using a compass and straight edge.

jtk

[Eric Brown]

I have been reading By Hand & Eye By George R. Walker & Jim Tolpin. Going through the construction of angles and geometric shapes at the end had me a little puzzled. So there is a set of drafting instruments in my office/computer room/library/man cave.

100_4243.jpg

The pair of dividers, under the beam compass, was taken to my bedroom since that is where much of my reading is done before falling asleep.

I hadn't given them much attention in the past since there are many others out in the shop that get used all the time. The little wheel between the legs got me curious. Turns out it might be a fine adjustment for the legs. It only changes the span by 1mm. That is likely enough for many purposes.

One thing I wish the book, By Hand & Eye, did would have been to better explain the constructions. The write up on the construction of a 45º angle doesn't explain the point above the vertex of the angle is a ghost construction of a 90º angle. It also doesn't explain how stepping off two radiuses on one of the arcs creating the ghost angle produces a 45º angle. Believing it works is one thing, but for me knowing why has it's values.

In the construction of polygons, for many polygons stepping off with a pair of dividers may be the best way. Though in high school my instructor showed us an easy way of constructing a pentagon using a compass and straight edge.

jtk

Good for you Jim. I enjoyed the three-book set so much that when my Grand-Niece said she liked math, I sent her a new set along with a wood sector, compass, protractor and aluminum ruler with six scales. (She's 12).
My nephew got home from work and said she had the biggest smile on her face. She wants to show her math teacher. Hopefully it opens her eyes and she has a better understanding of how math can be used.
The paper sector My Walker makes available is good for demontrations but I personally prefer something more solid.

Enjoy. Eric

[Jim Koepke]

The paper sector My Walker makes available is good for demontrations but I personally prefer something more solid.

The file is a free download at > www.byhandandeye.com < but the site isn't up at the moment, so the URL to the file isn't know to me right now.

It is scaled to be printed on an 11X17 sheet if my memory is working. I'm not sure how far I would have to drive to find a shop to print a piece that size.

Maybe print it in sections and tape it together. Then it wouldn't be too difficult to transfer the scales to wood. It could also be glued to wood and given a coat of shellac.

jtk

[Scott Winners]

Building a sector is a piece of cake. Mine is, standby, about 21 inches long. I started with a well seasoned 2x4, ripped in half, let it unwind for a few days and then made the two halves s5s. Little hinge from the home store, the center of the hinge pin is the origin point. The step marks on mine are about 1 5/16, I just divided my available 21 inch length by the 13+ increments I wanted, set my dividers and stepped it out. Mine is line of lines only. If I someday need a sector with the line of circles or etcetera I will just buy the $400 thing.

I did play with the 45 degree angle construction in _Hand and Eye_ for the first time jut now. It is on page 126 in my copy of the third printing. I dunno why it works. I think Jim's observation that point three is directly above the point of interest on the baseline is spot on. That is to say a line from P3 to the point of interest will always be perpendicular to the baseline. But P3 is not (at my house) the same distance away from the Point of Interest that P1 and P2 share. So we are working with a ghost right angle, but we are not, that I can see, just bisecting the ghost right angle as shown at the top of page 127 in my copy.

All I remember for sure about geometry is David Lee Roth was the lead singer for Van Halen that year, I got to sit next to Susie W because we were seated alphabetically in that classroom, and the teacher talked about triangles for the entire school year. The nice thing about the _Hand and Eye_ books, for me, is I don't have to do the proofs. I can just learn the tools and use the tools without having to learn Greek letters. Good luck and best wishes to Jim K for wanting to dig a little deeper.

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Looking at my image again I wonder if the leg P1 to POI and the leg POI to P2 aren't two sides of a square that haven't been folded up yet, but we can ghost the fold and get the 45 without having to construct and bisect the 90. Can you imagine somewhere centuries ago somebody was tired of drawing the 90 so (s)he could bisect the 90 and get to 45 degrees, after thousands of repetitions? So (s)he came up with a faster easier way. I bet there was alcohol involved.

[Jim Koepke]

I bet there was alcohol involved.

LOL!

jtk

[Edward Weber]

I've heard of this book/s, though have not gotten a copy to read yet.
I'm a bit surprised that there is so much geometry included in a book with such a title as, By Hand and Eye. Curious

[Eric Brown]

I've heard of this book/s, though have not gotten a copy to read yet.
I'm a bit surprised that there is so much geometry included in a book with such a title as, By Hand and Eye. Curious

The real trick of the books is that while math is obviously behind the techniques, the tools do it without a calculator. With ratios and proportions the numbers don't matter so much as there relationships to each other.
So using a straight edge, a compas and a pencil, you can lay out projects that look good.

[Edward Weber]

Thanks, I might have to give it a look

[Jim Koepke]

I've heard of this book/s, though have not gotten a copy to read yet.
I'm a bit surprised that there is so much geometry included in a book with such a title as, By Hand and Eye. Curious

As Eric mentions, it shows ways to create layouts without having to make calculations with numbers.

The geometric layouts are only a chapter or two. It book explains the importance of learning the proportions used throughout history in the design of architectural elements and its relationship used in different styles of furniture from the past and present.

Laying out molding and other elements without a calculator can be very handy when developing a design.

jtk

[Scott Winners]

I've heard of this book/s, though have not gotten a copy to read yet.
I'm a bit surprised that there is so much geometry included in a book with such a title as, By Hand and Eye. Curious

It is a bit of an eye opener for sure. I ordered all three books in the series a few months ago and started with the 'comic book' version, by hound and by eye.

I am using the concepts to build a boot changing bench for my mudroom, see 'low boarded bench for mudroom' as a more or less contemporaneous thread today here in the Neander section. The bench I am building is going to be 2 handspans tall, about 17 inches. I have a standard "handspand" piece of furring strip floating around my shop at 8.5 inches long. The side planks on my build are going to be 1/3 the total height of the bench, or 2/3 of one handspan.

I have no idea what number in inches is 2/3 of 8.5 inches. I just pop my 'one hand span' furring strip into my sector at '12' and set my dividers to the marks at '8.' I could just as well drop the one handspan blank into my sector at '9' and make set my dividers to the marks at '6.' Two thirds is two thirds no matter how you derive it.

It is a mind boggling simple way of getting stuff done if you can let go of knowing the actual dimension out to 4 or 5 decimal places.

I just now am plugging it into a calculator, 2/3 of 8.5 inches is 5 2/3 inches. Or I can just set my dividers on the sector and carry my dividers to the table saw...

[Edward Weber]

Thanks Jim
I prefer to do as little actual measurement as possible. I find it better to get the overall size, then break it down by quarters or thirds, etc. For me, proportions come much easier to achieve by eye, than calculating measurements. It does sound interesting

[Jim Koepke]

It is a mind boggling simple way of getting stuff done if you can let go of knowing the actual dimension out to 4 or 5 decimal places.

A few things come to mind from Scott's revelation. The first is that I used to work in a silkscreen print shop. No, we didn't print on silkscreens. The screen holds a stencil that was made photographically and ink was forced through the stencil on the screen with a squeegee. On a large banner one customer was trying to get his cost lowered by complaining about the banner being 1/16" short. The resolution was when the shop owner and the manager asked to see his tape measure. They stretched out three tape measures and showed how over a long distance they were all different.

From that I learned to only have one measuring device being used on any project. This was about 50 years ago and the manufacturing of tape measures has likely improved. The other note on this is if a lot of tape measures from the same batch are used they may be in agreement.

When my woodworking journey began many years ago a tape measure was my guide. My marks were made to the 32nd of an inch. It didn't work out many times. My projects often made me look like a true wood butcher. Framing up a rabbit cage or a shed for ducks worked, but trying to make a nice set of shelves might have errors if a number was transposed or if the saw was set to the wrong side of a line.

Interestingly, my work seemed to improve when I switched to an old Stanley folding rule:

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I tend to use the other side. It needed restoration with a fine tipped Sharpie to redraw most of the lines. It was shortly after that when an article on using story sticks was read.

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My work has improved dramatically from the use of story sticks and using a shooting board to make two or more pieces of wood being the same size. Maybe the exact length or width isn't known. What is known is they are within a thousandth or two of each other and often that is more important than knowing the exact size.

jtk

[Scott Winners]

From that I learned to only have one measuring device being used on any project.

jtk

Preach it brother. Amen.

[Chuck Hill]

My favorite part of not using machines is avoiding most measurements. The part just needs to be the “right” size, it does not need to be a specific number. Dividers rock!

[Tom M King]

Not really about proportions, but here's a video my BIL made with me laying out handrail balusters with dividers. I use them all the time. These are just some cheap Generals that get left out all the time. The better ones stay in safer storage.

https://www.youtube.com/watch?v=oIn24ClUilY