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Sooooo..... being nonprofessional, I found myself doing a double-take when
magazine articles use the word "width" when I would have expected "length",
or vice versa.

It took a couple decades, but I finally came to the conclusion that "width" means "across the grain"...."length", along it.....irrespective of the actual dimensions of the board (a board could be much wider than its length, and up until my new understanding I would have reversed the words, to apply "length" to the longest dimension).

And then p29 in the current WOODSMITH, in discussing how to make crossgrain splines, says to "cut the splines to width (length)." aaaaack! I do see what, in their normally helpful way, they are talking about.....but got me to thinking.

Which led to my overthinking things and now I have a need to know.

Let's say you have a board that is 1" thick, 3" wide, 6" long. The "ends" are where the grain shears off. The "edges" are the thinner sides. The "faces" are the wider sides.

But if I were to rip a thin strip off ...say 1/2" wide, so that the smaller "board" is 1 x 1/2 x 6...have the "edges" and "faces" changed places? Is the "edge" still the thinner (1/2") side? If I rotate that board axially, the wider side (1") looks like a "face" to me. Or is there some subtle grain differentiation that I don't get?

Or did I overthink myself into stupidity?

john

On 03/24/2010 11:18 AM, snipped-for-privacy@triton.net wrote:

Personally I'd say yes. The edge should be the thinnest side that shows long grain.

Of course it gets tricky if you have pieces with a square cross-section. :)

Incidentally, for cabinetmaking plywood the second dimension is the grain direction. So an 8x4 sheet has the grain going the short way.

Chris

Do what a purported disconnected number recording at MIT once advised:

"The number you have called is imaginary, Please rotate your phone 90 degrees, and try again."

No, I don't 'mean' that. :)

If I'd said that, it would***not*** have been acurate reportage of the story
_as_I_heard_it_.

Admittedly, it is a complex subject.

But, even with 'pure' imaginaries, it's still a matter of degree.

what's sqrt(-i), for example? "imaginary in the 2nd degree"?***GRIN***

I must be doing something wrong: ( sqrt(2)/2 - sqrt(2)/2***i ) ****2

=(sqrt(2)/2)******2 -*((sqrt(2)/2*sqrt(2)/2*i) - (sqrt(2)/2***i)****2
= 2/4 -2*(2/4*i) - 2/4***(i***i)
= 2/4 - 4/4*i + 2/4
= 1-i

I'm tempted to make a facitous remark about an 'off by one' error. :)

Admittedly, I haven't played with this stuff for 30+ years, but I've got a vague recollection of 'j' (the 'hyper-imaginary'??) as sqrt(-i).

Of course, on my first exposure to the imaginary exponential, I immediately and rather vehemently questioned "exp(2***pi***i) = 1". As follows:

exp(0) = 1 by definition exp(2***pi***i) = exp(0) 2 thins equal same thing, equal to each other
(2***pi***i) = 0 if bases (non-zero, and non-multiplicative-
identity) equal, exponents equal.

This rather upset the 8th grade math teacher. He***knew*** my reasoning
was incorrect, but pointing out__ _where_ __the flaw was was not obvious.

Simple reasoning on complex issues can lead one to into trouble. <grin>

Once it was clarified that '2***pi' was angular measure, things clarified
It is true that 2***pi == 0 (plus 1 revolution), even though neither of
the multiplicands is zero.

Robert, Nice Try! The line above should be 2/4 -2*(2/4*i) +2/4***(i***i)

= 2/4 -4/4i -2/4 = -i, as advertised. You had me worried for a moment.

Yes, you assumed that the function e^x is 1-to-1. And it is definitely not. It wraps the imaginary axis around the unit circle infinitely often. Indeed, it maps every horizontal strip of height 2PI in the complex plane onto the whole complex plane minus the point 0. I use this property of e^x as a building block to help construct other mappings which are infinity-to-one. Of course, there is nothing special abought e^x in this context, any exponential function a^x (a>0, a!=1) may be written in the form e^(kx) for some real number k so similar properties hold for a^x. What is special about e^x is that d/dx (e^x) = e^x, and only constant multiples of it have this property (of being equal to their derivative on a suitable domain).

..Not obvious to an 8th grade math teacher. They have their hands full trying to convince students that (a+b)^2 is not a^2 + b^2!!! Tough job!

Actually, my 8th grade math teacher was one of my favorite teachers, K-12.

It is of course Not true that 2*pi =0. What is true is that e^(2pi*i) e^0=1.

What is also true is that, for real values x, e^(ix) = cos(x) + i sin (x), which I see is what you were referring to by "plus 1 revolution" above.

Best, Bill

ARGH!!! like I said, "I must be doing something wrong' <wry grin>

I inverted the sign on the last term__ _and_ __left the i^2 in. one or the
other, but not both. Takes more than 2 i's to find it. :)

Well, It__ _is_,__ for exponents without an imaginary component. The concept
of multiplying something by itself an imaginary number of times is utterly
lacking in any intuitive foundation.

His own fault!__ _He_ __was the one that sprung it on me, cold, and wanted me
to agree it was true. I'd stuck my head in the classroom, after school
was out, to ask him something, and he threw that at me, from the middle of
a discussion he was having with somebody else -- "e to the two pi eye
equals one, right?" I thought for about half a second and said, firmly,
"no". He asked "why not?" And I wrote the above 'disproof' on the black-
board. Finding -where- to kick a hole in it is difficult. Every line __
_does_ __follow validly from the prior one. It's merely that the 'meaning'
of the numbers changed.

HUH?????

I think my 5th or 6th grade class spent -maybe- one afternoon on that. Re-write the '^2' as an explicit multiplication, and apply the distributive property (a total of 3 times) to eliminate the parens, then consolidate the like terms.

The error is also 'painfully obvious' if you simply work through a couple of 'concrete' examples.

Admittedly, I was learning this stuff _just_before_ the "new math" teaching started. (My younger brother, 3 years behind me, got a***very*** different math
education!)

Depends on what you mean by '='. <grin type='Clintonesque'>

They're both the same "direction". "equal" in that sense.

Anything derived from the point-value (ignoring the 'path' that got you there) is the same for both.

Quoting a line from an old comic strip -- where they got it absolutely wrong (unintentionally!) in context: "How do you tell a pilot he's 360 degrees off-course?"

Yes, think of expressions like 2^i as exp^(i *ln 2), then you can use your intuition a little more once you are adequately aquainted with the function e^x.

What you REALLY mean is that: 2*pi radians ~ 0 radians!

0 and 2*Pi are complex numbers, different ones, which are over 6 units apart in the complex plane. We save "=" for when the numbers coincide.

Again, The terminal side of angle of 0 degrees is the same of one of 360 degrees. But, turning a gear or the steering wheel of your car 360 degrees or -360 degree or 0 degree are 3 different things, right? I agree it probably doesn't matter how a pilot turns west, if west is the direction he is supposed to go! : )

Best, Bill

#### Site Timeline

- posted on March 24, 2010, 5:18 pm

It took a couple decades, but I finally came to the conclusion that "width" means "across the grain"...."length", along it.....irrespective of the actual dimensions of the board (a board could be much wider than its length, and up until my new understanding I would have reversed the words, to apply "length" to the longest dimension).

And then p29 in the current WOODSMITH, in discussing how to make crossgrain splines, says to "cut the splines to width (length)." aaaaack! I do see what, in their normally helpful way, they are talking about.....but got me to thinking.

Which led to my overthinking things and now I have a need to know.

Let's say you have a board that is 1" thick, 3" wide, 6" long. The "ends" are where the grain shears off. The "edges" are the thinner sides. The "faces" are the wider sides.

But if I were to rip a thin strip off ...say 1/2" wide, so that the smaller "board" is 1 x 1/2 x 6...have the "edges" and "faces" changed places? Is the "edge" still the thinner (1/2") side? If I rotate that board axially, the wider side (1") looks like a "face" to me. Or is there some subtle grain differentiation that I don't get?

Or did I overthink myself into stupidity?

john

- posted on March 24, 2010, 5:25 pm

Personally I'd say yes. The edge should be the thinnest side that shows long grain.

Of course it gets tricky if you have pieces with a square cross-section. :)

Incidentally, for cabinetmaking plywood the second dimension is the grain direction. So an 8x4 sheet has the grain going the short way.

Chris

- posted on March 24, 2010, 6:31 pm

wrote:

Thanks, I learned something today.

Thanks, I learned something today.

--

Nonny

Suppose you were an idiot.

Nonny

Suppose you were an idiot.

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- posted on March 24, 2010, 7:17 pm

wrote:

Lowe's has some 4X4 sheets. What is one to do?

Max

Lowe's has some 4X4 sheets. What is one to do?

Max

- posted on March 25, 2010, 2:04 am

Do what a purported disconnected number recording at MIT once advised:

"The number you have called is imaginary, Please rotate your phone 90 degrees, and try again."

- posted on March 25, 2010, 3:03 am

wrote:

But of course. Why didn't I think of that.

Max (hitting himself in the forehead)

But of course. Why didn't I think of that.

Max (hitting himself in the forehead)

- posted on March 25, 2010, 3:04 am

wrote:

Cute. You mean multiply it by exp^(i \PI /2). I've never seen the word imaginary and degrees in the same sentence--no, never before. Obviously undergraduate MIT students... I guess you could use the cord for the initial side of the angle of rotation---but, what if you only have a cell phone?

Bill

Cute. You mean multiply it by exp^(i \PI /2). I've never seen the word imaginary and degrees in the same sentence--no, never before. Obviously undergraduate MIT students... I guess you could use the cord for the initial side of the angle of rotation---but, what if you only have a cell phone?

Bill

- posted on March 25, 2010, 7:53 pm

No, I don't 'mean' that. :)

If I'd said that, it would

Admittedly, it is a complex subject.

But, even with 'pure' imaginaries, it's still a matter of degree.

what's sqrt(-i), for example? "imaginary in the 2nd degree"?

- posted on March 25, 2010, 8:27 pm

Robert Bonomi wrote:

sqrt(-i) = exp(-PI/4) or exp(3PI/4). Not "purely imaginary" at all--the real part is +/- sqrt(2)/2. It's as plain as a point on the unit circle. You could double-check that if a = sqrt(2)/2 - sqrt(2)/2*i, or b=-a, then a^2=b^2=-i. Simple trig and De Moivre's Theorem...

Bill

sqrt(-i) = exp(-PI/4) or exp(3PI/4). Not "purely imaginary" at all--the real part is +/- sqrt(2)/2. It's as plain as a point on the unit circle. You could double-check that if a = sqrt(2)/2 - sqrt(2)/2*i, or b=-a, then a^2=b^2=-i. Simple trig and De Moivre's Theorem...

Bill

- posted on March 26, 2010, 12:43 am

I must be doing something wrong: ( sqrt(2)/2 - sqrt(2)/2

=(sqrt(2)/2)

I'm tempted to make a facitous remark about an 'off by one' error. :)

Admittedly, I haven't played with this stuff for 30+ years, but I've got a vague recollection of 'j' (the 'hyper-imaginary'??) as sqrt(-i).

Of course, on my first exposure to the imaginary exponential, I immediately and rather vehemently questioned "exp(2

exp(0) = 1 by definition exp(2

This rather upset the 8th grade math teacher. He

Simple reasoning on complex issues can lead one to into trouble. <grin>

Once it was clarified that '2

- posted on March 26, 2010, 2:16 am

Robert, Nice Try! The line above should be 2/4 -2*(2/4*i) +2/4

= 2/4 -4/4i -2/4 = -i, as advertised. You had me worried for a moment.

Yes, you assumed that the function e^x is 1-to-1. And it is definitely not. It wraps the imaginary axis around the unit circle infinitely often. Indeed, it maps every horizontal strip of height 2PI in the complex plane onto the whole complex plane minus the point 0. I use this property of e^x as a building block to help construct other mappings which are infinity-to-one. Of course, there is nothing special abought e^x in this context, any exponential function a^x (a>0, a!=1) may be written in the form e^(kx) for some real number k so similar properties hold for a^x. What is special about e^x is that d/dx (e^x) = e^x, and only constant multiples of it have this property (of being equal to their derivative on a suitable domain).

..Not obvious to an 8th grade math teacher. They have their hands full trying to convince students that (a+b)^2 is not a^2 + b^2!!! Tough job!

Actually, my 8th grade math teacher was one of my favorite teachers, K-12.

It is of course Not true that 2*pi =0. What is true is that e^(2pi*i) e^0=1.

What is also true is that, for real values x, e^(ix) = cos(x) + i sin (x), which I see is what you were referring to by "plus 1 revolution" above.

Best, Bill

- posted on March 27, 2010, 2:29 am

ARGH!!! like I said, "I must be doing something wrong' <wry grin>

I inverted the sign on the last term

Well, It

His own fault!

HUH?????

I think my 5th or 6th grade class spent -maybe- one afternoon on that. Re-write the '^2' as an explicit multiplication, and apply the distributive property (a total of 3 times) to eliminate the parens, then consolidate the like terms.

The error is also 'painfully obvious' if you simply work through a couple of 'concrete' examples.

Admittedly, I was learning this stuff _just_before_ the "new math" teaching started. (My younger brother, 3 years behind me, got a

Depends on what you mean by '='. <grin type='Clintonesque'>

They're both the same "direction". "equal" in that sense.

Anything derived from the point-value (ignoring the 'path' that got you there) is the same for both.

Quoting a line from an old comic strip -- where they got it absolutely wrong (unintentionally!) in context: "How do you tell a pilot he's 360 degrees off-course?"

- posted on March 27, 2010, 3:02 am

Yes, think of expressions like 2^i as exp^(i *ln 2), then you can use your intuition a little more once you are adequately aquainted with the function e^x.

What you REALLY mean is that: 2*pi radians ~ 0 radians!

0 and 2*Pi are complex numbers, different ones, which are over 6 units apart in the complex plane. We save "=" for when the numbers coincide.

Again, The terminal side of angle of 0 degrees is the same of one of 360 degrees. But, turning a gear or the steering wheel of your car 360 degrees or -360 degree or 0 degree are 3 different things, right? I agree it probably doesn't matter how a pilot turns west, if west is the direction he is supposed to go! : )

Best, Bill

- posted on March 25, 2010, 9:46 pm

On Wed, 24 Mar 2010 21:04:19 -0500, the infamous
snipped-for-privacy@host122.r-bonomi.com (Robert Bonomi) scrawled the following:

Lay her down, roll her over, and do it again?

I like it! I wonder how many people actually tried that. <g>

-- If we attend continually and promptly to the little that we can do, we shall ere long be surprised to find how little remains that we cannot do. -- Samuel Butler

Lay her down, roll her over, and do it again?

I like it! I wonder how many people actually tried that. <g>

-- If we attend continually and promptly to the little that we can do, we shall ere long be surprised to find how little remains that we cannot do. -- Samuel Butler

- posted on March 24, 2010, 6:52 pm

On 3/24/10 12:18 PM, snipped-for-privacy@triton.net wrote:

Sorry, this is a tangent....

A pet piece of mine is when "woodworkers"-- especially ones on TV shows-- say the word, "heighth."

They think that somehow, because length, width, and depth, have a "th" sound at the end, then so does height. Sometimes, I'll jokingly say, "Hey, height only has two H's."

Sorry, this is a tangent....

A pet piece of mine is when "woodworkers"-- especially ones on TV shows-- say the word, "heighth."

They think that somehow, because length, width, and depth, have a "th" sound at the end, then so does height. Sometimes, I'll jokingly say, "Hey, height only has two H's."

--

-MIKE-

"Playing is not something I do at night, it's my function in life"

-MIKE-

"Playing is not something I do at night, it's my function in life"

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- posted on March 24, 2010, 7:18 pm

Ehh... you need to be careful for what purpose is the statement being
made.

Face and edge mean very specific things when you are considering grain. Edge grain is very different than face grain in terms of apperance and somewhat structurally when gluing. However, even that has some ambiguity because you cut wood from round logs.

So if you cut a 4" square timber from the center of an 8" round log it has face grain on 4 faces.

However, if you slice a 1" thick board from the same round log (rather than a 4x) it has face grain on the wide "faces" and edge grain on the thin sides. The face always shows edges of rings to varying degrees while the edge shows to varying degrees the faces of rings. The piece cut from the center of the log will have an edge grain with almost completely the face of a ring. Confusing enough?

An edge to edge glue joint is super strong. A face to face glue joint is super strong. An edge to face glue less strong. This last sentence is conjecture on my part but it seems to bear out in my experience but matbe because edges are usually narrow and faces usually wide so the joint has available leverage to break it.

On Mar 24, 10:18 am, snipped-for-privacy@triton.net wrote:

Face and edge mean very specific things when you are considering grain. Edge grain is very different than face grain in terms of apperance and somewhat structurally when gluing. However, even that has some ambiguity because you cut wood from round logs.

So if you cut a 4" square timber from the center of an 8" round log it has face grain on 4 faces.

However, if you slice a 1" thick board from the same round log (rather than a 4x) it has face grain on the wide "faces" and edge grain on the thin sides. The face always shows edges of rings to varying degrees while the edge shows to varying degrees the faces of rings. The piece cut from the center of the log will have an edge grain with almost completely the face of a ring. Confusing enough?

An edge to edge glue joint is super strong. A face to face glue joint is super strong. An edge to face glue less strong. This last sentence is conjecture on my part but it seems to bear out in my experience but matbe because edges are usually narrow and faces usually wide so the joint has available leverage to break it.

On Mar 24, 10:18 am, snipped-for-privacy@triton.net wrote:

- posted on March 24, 2010, 8:22 pm

On 03/24/2010 01:18 PM, SonomaProducts.com wrote:

Your conjecture is false.

The fact that longer pieces confer more leverage doesn't imply anything about the strength of the joint itself.

And besides, an edge-to-edge joint with the same glue area has at least as much leverage potential--imagine holding onto the edges of a panel and bending it over your knee right along the glue join.

Generally speaking a well-constructed long-grain to long-grain glue joint is as strong as the wood itself regardless of growth ring orientation. This is a simplification, but one that works in the vast majority of cases.

Chris

Your conjecture is false.

The fact that longer pieces confer more leverage doesn't imply anything about the strength of the joint itself.

And besides, an edge-to-edge joint with the same glue area has at least as much leverage potential--imagine holding onto the edges of a panel and bending it over your knee right along the glue join.

Generally speaking a well-constructed long-grain to long-grain glue joint is as strong as the wood itself regardless of growth ring orientation. This is a simplification, but one that works in the vast majority of cases.

Chris

- posted on March 24, 2010, 8:44 pm

On 3/24/2010 2:18 PM, SonomaProducts.com wrote:

More importantly, most "boards" are cut from the "length" of round logs.

Tree cells are generally elongated and and that elongation is aligned to carry water and nutrients along the length of the tree trunk (log) and limbs.

"Long grain", running along the length of elongated cells structures, and "end grain" running across the elongated cell structure, are much better terminology for joinery/gluing purposes, IMO.

Not to quibble, but I would tend to disagree somewhat with that conjecture.

Long grain to long grain, whether it be on a "face" or "edge", should have the same relative glued strength characteristics for the most part and, MOST IMPORTANTLY, should also the same relative dimensional stability for joinery/gluing purposes (although the way it was cut from the log (i.e., flat, rift, QS, etc) will cause some differences in the latter)

Why? ... mainly because both have same elongated axis of cell structure exposed to the chemical reaction of gluing.

<CAVEAT: Not a botanist, but took two semester of botany in college, although 40+ years ago, that's how I remember it, and I'm sticking to it. :) >

More importantly, most "boards" are cut from the "length" of round logs.

Tree cells are generally elongated and and that elongation is aligned to carry water and nutrients along the length of the tree trunk (log) and limbs.

"Long grain", running along the length of elongated cells structures, and "end grain" running across the elongated cell structure, are much better terminology for joinery/gluing purposes, IMO.

Not to quibble, but I would tend to disagree somewhat with that conjecture.

Long grain to long grain, whether it be on a "face" or "edge", should have the same relative glued strength characteristics for the most part and, MOST IMPORTANTLY, should also the same relative dimensional stability for joinery/gluing purposes (although the way it was cut from the log (i.e., flat, rift, QS, etc) will cause some differences in the latter)

Why? ... mainly because both have same elongated axis of cell structure exposed to the chemical reaction of gluing.

<CAVEAT: Not a botanist, but took two semester of botany in college, although 40+ years ago, that's how I remember it, and I'm sticking to it. :) >

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- posted on March 24, 2010, 9:28 pm

Chris and Swing,

I stand corrected. I really started out just to say that width usually means face grain and actually never said it and tangented off into other topics. I've never done that before.

Who knows, maybe I am also wrong about the health care thing being another government sink hole for my money with minimal return. I hope I'm wrong.

Caveat: Not a real woodworker, I just play one on TV.

I stand corrected. I really started out just to say that width usually means face grain and actually never said it and tangented off into other topics. I've never done that before.

Who knows, maybe I am also wrong about the health care thing being another government sink hole for my money with minimal return. I hope I'm wrong.

Caveat: Not a real woodworker, I just play one on TV.

- posted on March 24, 2010, 9:38 pm

On 3/24/2010 4:28 PM, SonomaProducts.com wrote:

LOL ... in that regard, you're more than one up on me! :)

I really wasn't trying NOT to be a smart ass, sorry if it came across that way.

Ditto ... but I like what Upscale said:

"The US people made a choice on a particular leader and that leader has made a choice on healthcare. Cry in your soup as much as you want, but deal with it instead of doing all this shrill whining and running around that the sky is falling."

If you use your head for something besides a hat rack, you can't argue with that bottom line, and the perspective.

I'd also take exception to that ... your work speaks otherwise.

LOL ... in that regard, you're more than one up on me! :)

I really wasn't trying NOT to be a smart ass, sorry if it came across that way.

Ditto ... but I like what Upscale said:

"The US people made a choice on a particular leader and that leader has made a choice on healthcare. Cry in your soup as much as you want, but deal with it instead of doing all this shrill whining and running around that the sky is falling."

If you use your head for something besides a hat rack, you can't argue with that bottom line, and the perspective.

I'd also take exception to that ... your work speaks otherwise.

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