Draw Celtic Knots by Using Lines and Circles

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December 29, 2006 at 12:16 pm #986137

Ok! Lookit! I'm actually ahead of schedule! Set up?

Let'southward start with working running borders in a circle. I tend to recollect of it as angle them. And while information technology appears really complicated, I detect it easier than working in a straight line in a lot of cases. Reason #1, no corners. Reason #2, it'south easy to sneak in an extra repeat or bend if you lot need it. And last but not least, reason #iii: Information technology creates a large visual touch with very petty endeavor.

The books on knotwork spend a fair amount of time & endeavour discussing how the aboriginal scribes did it, using minimal tools and using lots of geometrical terms that send this math-challenged girl into a tizzy trying to make heads or tails of what they're talking well-nigh. They as well spend a lot of time having y'all draw in "guides" that aren't needed in the long run. Now, while I fully support the idea of understanding *how* information technology was done in the past, I am also very very glad I'chiliad not living and so (I like electricity, indoor plumbing, and having a protractor!). That being said, there are a few geometrical terms/definitions you'll demand to go on in mind:

–Circles take 360 degrees.
–The diameter of a circle is the measurement from edge to edge.
–The radius of a circle is the measurement from the centre signal to the outside edge (it's *one-half* of the diameter)

There are couple of things to remember when working with curves: #ane: the arcs of the knots on the exterior edge are going to exist longer than those on the inside, so brand sure you aren't working then tight & small that the inside border will become incommunicable. #2: Whatsoever breaks in the pattern will be very obvious, so accept that into consideration when drafting your initial composition.

In the interest of not re-inventing the wheel, I'll get-go with a simple running edge you should feel comfortable with already: The braid. Hither it is in a direct line:

Nosotros won't worry well-nigh trying to brand it all one band at this stage. And to brand it easier, I'll show you how to plot the circle to resemble the graph paper. We'll need to draw iv concentric circles, 1/4" apart. In society to stay pocket-size enough you won't be overwhelmed & big enough you'll notwithstanding be able to see what you're doing, we'll make the outside circumvolve 4" in diameter. Here's the pace by step:

I've divided my paper in half, & picked a spot to exist the center of the circle. Mensurate 2" along the line (this is the radius) from the midpoint and make a tic marker. At present, make 3 more than marks 1/iv" autonomously moving back toward the eye. Using your compass, set the signal in the midpoint, and the pencil cease at the outside mark. Depict your circle. Now, keeping the point at the midpoint, set the pencil finish to the next mark, etc. In one case you've fatigued in these 4 circles, the largest will be four" in diameter, so 3 1/ii, iii, and lastly 2 1/ii .

Next, have your protractor & line the 0 mark upwards with your middle line and the center on your midpoint. At present make little tic marks every ten degrees. At this size, 10 degrees is roughly the same size as the 1/4" filigree of standard graph paper. I usually only make tic marks around ane half of the paper & use the midpoint to line upwards the ruler. This fashion, if my tic marks are a little off, it'll exist consistently off and still pass through the midpoint (of import when we go to the spirals). Use the ruler to draw in guidelines on both sides of the circle. I hope its looking a little familiar at this stage.

At present, only like you did on graph newspaper for the running borders demo, offset drawing in the "bones" of the braid.

Draw in your curves & kickoff the weave pattern.

Erase the "bones" and clean-up.

Now, retrieve the rule about braids? It won't be one ring of interlace when they connect if the number of curves on the outside edge tin can be evenly divided by 3. Since we used 20 degree segments per bend on the outside (tic mark every 10, and having the curves use 2 spaces like we did on the graph newspaper), our 360 circle has given us 18 curves. Which is evenly divided by iii. Then, to make this into ane band, if we make tic marks at 9 degrees, instead of 10, we would take 20 curves along the outside. Which *can't* be divided by 3.

With me so far? Fix to move on?

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/colour]
[FONT="Book Antiqua"]How does she do that??? Find out hither:[/colour] Celtic Art 101

Do not meddle in the affairs of Dragons, for y'all are crunchy and good with ketchup.[/left]

Dec 29, 2006 at 12:24 pm #1079361

It'south Challenge Time!

When we worked with the triangles & pretzels, I showed how to do knots without that center band. I did that for a few reasons. Primarily, equally yous start to design carpet pages and work with the knotwork in irregular spaces, grids and what-not are going to be harder and harder to come up by. The other reason is that I observe information technology actually fussy to *always* work it out on graph paper then try to arrange it to an actual piece. So here's the assignment: Tin you exercise a uncomplicated twist effectually a circle without using a centre line? And I'd like y'all to start getting used to using as few guide marks every bit possible (less erasing). I'll show you lot how to set information technology upwards. But lets practice a fleck first:

On your sketch paper draw 2 fairly long parallel lines, 1/ii" apart. Brand tic marks (height & bottom) every 1/two". Requite yourself as much room as you need to beginning feeling comfortable. At present, draw in your top & bottom curves, centered betwixt the tic marks and letting the right-mitt side cross over into the space for the next arc (remember the discussions on which direction the knots volition "pull"?). These will be the outer edge of your bands. Here'south how mine looks:

Side by side, depict in the inner edge of your bands on the elevation. Extend your lines a bit more. Observe how the inner edge is aligned. It should naturally go the outer edge of the lower curves & create the "over" portion of the twist. You may need to correct some angles & extend your lines. Don't worry if it looks a little messy. That's what erasers are for.

Now complete the lower curves. Try to keep the width of your bands consistent. You may need to right the angles and refine a flake. That's fine. Observe mine is *really* sloppy looking at this stage.

Make clean it upward, and at that place yous go. Mine nevertheless looks pretty crude. This is nearly 3 times the size I usually do a twist in… hmmm… maybe the teacher needs more than practice too!

At present for the fun part. Let'south bend it around a circumvolve.

Just like you did for the braid, draw a center line, pick a midpoint, measure up two" and depict a circle 4" in diameter. Now make a tic marking 1/2" from that circumvolve, moving dorsum toward the midpoint. Draw in another circle using the tic marking & the same midpoint. This ane should be iii" in diameter.

Now with the protractor, marker effectually at 20 degree intervals. Using your ruler, make tic marks to guide you.

And then now that you've had practice doing a twist in a straight line, apply the same steps to going around the circle. I've re-discovered that at this scale, I'g much neater if I draw in both edges of the bands at the same time. Do any works best for you lot, just make sure your weave blueprint is constant.

So those of you who aren't math challenged have probably realized that this is 2 bands of interlace (twist = two curves for a full repeat; 360 degrees in 20 degree segments = 18 segments. An even number of curves keeps this 2 bands). The question is: is that what we desire? Let's pretend the answer is no. In that location's a bunch of ways to address/fix it:

#1 Figure it out earlier hand. Nosotros need an odd number of curves, but desire to keep them relatively the aforementioned size equally nosotros have hither. If we make it 19 segments, instead of the 18 we've washed, we'd brand a tic mark at *almost* every 19 degrees on the protractor (360 / nineteen = 18.94736etc) . Or we could make it 17 curves. That would be a tic mark *about* every 21 degrees (360 / 17 = 21.17647etc). Or we could cede size and make it 15 curves, with tic marks every 24 degrees (360 / xv = 24). Oy. Makes my head injure…

#2 Pause the pattern & join the bands in some way (just once!) like these:

#3 Rob Peter to pay Paul, then to speak. Pick an area & rework the curves, sneaking an extra 1 in (my preferred method if I didn't think of it before I started the whole affair & I don't want to break the pattern). This is essentially the same as fix #1, except yous don't make yourself crazy counting little lines on a protractor!

Withal with me? Next, some rules for working with braids & plaits.

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/color]
[FONT="Book Antiqua"]How does she do that??? Notice out here:[/colour] Celtic Fine art 101

Do not meddle in the affairs of Dragons, for you are crunchy and proficient with ketchup.[/left]

December 29, 2006 at 12:31 pm #1079362

MATH ALERT!
These are the rules for braids & plaits when working in a circumvolve:

Twists – 2 bands
Whatever number of curves divisible by ii = 2 bands (even numbers)
Any number of curves not divisible past 2 = 1 band (odd numbers)

Braids – iii bands
Whatsoever number of curves divisible by 3 = iii bands
Any number of curves non divisible by 3 = 1

4 band plait
whatever number of curves divisible by 4 = 4 bands (8, 12, twenty, etc.)
whatever number not divisible by four but divisible by ii = 2 (14, 18, 22, etc)
whatsoever number divisible by four plus *or* minus 1 = ane (seems like the long way to say that, but it'll make sense in a sec.) So 15 curves = i ring. 17 curves = 1 ring.

5 band plait
any number divisible by 5 = five bands
whatever number non divisible by five = 1

6 band plait
any number of curves divisible past 6 = 6
any number non divisible past 6 but divisible by 2 = 2
any number not divisible by 6 but divisible by iii = 3
any # divisible past 6 + *or* – 1 = 1 So 17 or 19 curves = 1 band

See a pattern emerging? These rules concord true when working a border around a frame, too. Which is why symmetry is *not* your friend if you're trying to make it all one ring! When you're working in a circumvolve, it's piece of cake to sneak an actress bend in or remove one. The human eye doesn't notice information technology very well. In a straight line, information technology'll bound out.

Everyone care to guess what the rules for 8's and 9's are? And everyone find the, um, easiness of the prime number numbers (1,2,3,5,vii,11,thirteen,17, etc.)? And now I could get *really* esoteric and dense on you and launch into a discussion about sacred geometry… But I won't. Although it's tempting…

Questions? Lets encounter how y'all're doing!

Next part will exist knotwork around the circle (brush up on your triangles & pretzels!). I promise I'll have it up in the next few days.

Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/color]
[FONT="Volume Antiqua"]How does she do that??? Find out here:[/colour] Celtic Art 101

Practise non meddle in the diplomacy of Dragons, for y'all are crunchy and proficient with ketchup.[/left]

Jan v, 2007 at 8:50 am #1079363

Hopefully, y'all aren't completely tangled in bending a running border around a circle!

To start with, we'll utilize a pretzel knot & a triangle knot. And nosotros'll keep it uncomplicated. If you lot're aiming to brand a edge or a ring of a circle all one line, an easy brusque-cut is to create a repeat that uses only 1 band to begin with. Like a pretzel knot. Or opening a triangle knot (simply once!) in some way. To testify what I mean, here's the pretzel knot we'll be using. All I've done is replace the lesser curve of the pretzel with a twist.

And here's the slightly modified triangle knot. In this case, I bankrupt one of the curves & turned them into straight bands.

Now, the nice thing well-nigh this is that no thing how many of either of those you lot connect upwardly, it'll nonetheless exist all i band as long as yous're using those open ends. If I go likewise fast or skip over something you'd similar in more detail, definitely allow me know!

Prepare?

For this i, nosotros'll exist doing a 9-pointed star ringed by a 4band plait. So just similar for the previous section, nosotros'll starting time drawing in some concentric circles. Draw in your center line, choice your midpoint, & describe in a circle that'due south 5" in diameter, then 4", and finally 2". With your protractor, brand tic marks every 20 degrees. Going around the circle, draw in a solid line from your first tic mark to the midpoint. At the adjacent tic marking, just make little marks across the lines for your circles to the midpoint. One time you've gone around, erase the midline that'south breaking the design. You lot should have something that looks like this:

At present from the tic marking on the outside edge of your 2d ring, depict a directly line to the side by side solid line on the inner edge. From the same tic mark, draw in a straight line to the other solid line. After you've gone around the circle, you should have this:

So in your center band, depict in the pretzel knot using the solid lines & your tic marks to help y'all get the spacing correct. Pretty bully, eh?

Moving to the middle band, flip the pretzel knot so the twist portion is pointing outward. Now, for this one, I won't be joining the rings of knots. *Only* if you want to, in social club to keep your weave consequent, this 2nd ring volition need to run the contrary management as the centre ring (it'due south because these knots are only 1 ring). So the center in my example is rotating clockwise. The 2nd ring rotates counter-clockwise.

Side by side comes the triangle knot. Work 2 of them in the spaces between the points similar this:

Afterwards you lot've gone around the circle, you lot should take something that looks similar this:

And final pace, put a 4-band plait in that outside ring. For this example I'm not all that concerned most trying for all one line. And so 'cause its like shooting fish in a barrel I'yard doing two curves on the outside per section. And out of addiction, I've got them pulling clockwise. If I wanted to connect the middle band to the outside, the plait would need to pull counterclockwise. Use the tic marks to help yous get the spacing right. I've done it here every bit a progression.

And here information technology is completed:

Thanks to a fiddling photoshopping, here's what it would look like if we had the middle ring rotating clockwise, too.

The difference between the two is very subtle, but information technology is there in how the viewer's centre moves around the circle. This is something to continue in mind when you're composing a larger piece. Sometimes, y'all need to run things in an opposite direction. Information technology helps to hold the slice still for the viewer.

Set to move on?

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/colour]
[FONT="Book Antiqua"]How does she do that??? Find out here:[/color] Celtic Art 101

Do non meddle in the affairs of Dragons, for yous are crunchy and good with ketchup.[/left]

Jan 5, 2007 at viii:55 am #1079364

For this adjacent 1, lets use the same knots, just in a slightly different layout and order.

Again, we'll do 3 concentric circles. First 1 is 5" in diameter, then iii", and lastly 2". And in the interest of not completely redoing the layout, tic marks at 20 degrees. So but like before, divide the smallest ring into 9 pie pieces. Leave the middle ring open (the plait will go here). In the outer ring, describe in the points of the star, and then the fatty end of the triangles line up with the ones on the very inside circle. Here's what mine looks like:

Simply like the previous instance, piece of work the pretzel knot in the middle.

Adjacent, work the four band plait. I've done 2 curves per department, assuasive it to pull clockwise.

This time, I'll put the triangle knot in the "points", and work 2 of the pretzel knots in the spaces between.

And here information technology is completed.

If you look at them side by side, even though they use the exact same elements used in a slightly unlike social club, they expect *very* different. So hopefully by at present y'all're getting some ideas of different ways you lot can have some really basic elements and make them look *hugely* complicated.

Ready to take in upwards a notch? I should take the next part posted subsequently today. And please! If I'thou going too fast or you need me to explicate something, feel complimentary to post or pm me.

Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/colour]
[FONT="Book Antiqua"]How does she exercise that??? Detect out here:[/color] Celtic Art 101

Do not meddle in the affairs of Dragons, for you are crunchy and good with ketchup.[/left]

January 5, 2007 at ix:28 am #1079400

Tess, This is awesome! Looks like a challenge. I'd better observe a protractor and get hopping (or knotting every bit the case may be). Nifty offset for the new year!! – Chris

January 5, 2007 at 2:17 pm #1079365

Great to take you along, Chris!

Buckle your seat chugalug, 'crusade this side by side one's a doozy!

Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/color]
[FONT="Volume Antiqua"]How does she do that??? Find out hither:[/color] Celtic Art 101

Do not meddle in the affairs of Dragons, for you are crunchy and good with ketchup.[/left]

Jan five, 2007 at two:30 pm #1079366

Ok, on this one, nosotros're going to shoot the moon. Past the time we're done, it *will* exist all one band. We'll be using iv chief elements. A braid in that outside band, then 3 unlike knots. 2 of the knots are variations of the same triangle knot. Hither are the knots:

Knot A should be fairly familiar from the pretzels & triangles thread. Now, notice that B and C are essentially the same, except instead of a point at the bottom, I've substituted a curve. That'll make sense in a sec. If you want to see a stride-by-pace of how to draw these, let me know.

So lets start drawing in our circles. Merely like before, describe your midline & selection your midpoint. We'll be drawing 3 concentric circles again (did I mention I accept a thing about threes?). Exterior circle will be 6" in diameter, and so v", and lastly three". With your protractor, make tic marks every 10 degrees. We'll start by dividing our circles into 12 pie pieces. And then starting at your midline, skip the next 2 tic marks & draw a line at the 3rd mark (30 degrees) that passes through the midpoint to the other side. Make tic marks for the other caste points across your circle lines (10 & 20 degrees). Here'south what mine looks like:

In that centre ring, start at your midline. Draw a line from the inner edge of the ring to the adjacent tic marking on the outer border of the ring. Echo on the other side of your midline. Now do the same around the circle at *all* of the solid lines. You'll end up with something that looks like a bunch of chicken feet like this:

And then starting with your center ring, depict in knot B. As usual, I've done mine pulling clockwise.

In the eye band, work knot C with the bend snugged up to the outer edge of the ring. Make sure information technology's pulling the same direction equally the center band. Once again, mine is going clockwise.

Now work knot A in the triangle spaces you take left. Unlike the previous examples, we don't need to practice two of them. If the line that divides that triangle in half is confusing you, become ahead & erase it. I similar to exit information technology 'crusade it helps me go the points right. Just practise what works for you. In case you haven't guessed information technology yet, this is our repeat unit.

Now for the complect in the outer band. This is the tricky function. Getting information technology to line upwards correctly with the heart band is crucial. Then instead of starting to draw your curves for the bands on the outer border of the ring (like usual), offset on the inner border. Nosotros need a curve to run side by side to that middle curve of knot A and the curve of knot C. So first with those (ignore the erased bits… got a fiddling ahead of myself).

Now make full in the other curves yous need on that inner edge like this:

Now do the outer border. Recollect that for a braid the curves don't mirror each other. And so for this I've got 4 curves on the exterior edge of the ring similar this:

Ok, because I'm neater if I do the whole affair at in one case, I'll go ahead and make full in the braid the rest of the way around. If you lot desire to go section by department, that's just fine. Just make sure all of your "overs" are pulling the same fashion. Looking at the exterior edge of the braid, mine are going *counter-clockwise*. This is of *huge* importance a bit later when we offset joining the divide knots together.

So now that I've got the braid finished, I'll echo knots A, B, & C around the circumvolve like this:

Here they are, all filled in:

Whew. Next, let's connect them.

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/color]
[FONT="Book Antiqua"]How does she exercise that??? Find out hither:[/color] Celtic Art 101

Practise non meddle in the affairs of Dragons, for you are crunchy and good with ketchup.[/left]

January 5, 2007 at 2:39 pm #1079367

Alright, permit'southward figure out how to join the knots!

Before nosotros intermission & bring together anything, let's effigy out what's going on… some of you may have already realized that the braid on the outside ring is iii strands (360 / 12 sections = 48; 48 / four (# of curves on our outside edge per segment) = 12. Which is evenly divisible by three.). Remember the possible ways to "fix" the trouble? In this instance, because of where we need those inside curves to exist, we tin't sneak in an actress curve & I *really* don't want to alter the layout. So we'll need to break & re-join the braid in some way. Outset thinking nearly it. We'll come back to it.

Now the plan is to bring together knots B (from the center ring) to knots C in the center ring. And then join our new BC knot to the braid. And because we don't want it to feel left out, we'll also join knot A to the braid. Once we've done that, we'll be left with 3 bands. Here information technology is in color so you can meet a little better what'southward going to happen.

The fob is going to be connecting the red strand to the yellow strand. And and then connecting the blueish to the red. And then the yellow one to the blue… hmmm…

Ok, commencement things get-go. Allow's bring together upwardly the knots in the inner two rings. Think of the tic marks where nosotros drew the solid lines creating the "pie" pieces as numbers on a clock… This'll make the side by side part easier. Because I like how it looks with all of those points coming together at the "12 o'clock" line, we'll leave those & join them on the other edge (circled in cerise). And to maintain residue, nosotros'll mirror that when we join the next pairs (circled in blue). And permit's non forget connecting to the outer braid (circled in yellow)

So take the points & change them into curves on knots B & C. And supersede the curves on the outer border & the braid with an "X". Here is a particular view of how to do it:

And here's the full view:

This is all the same 3 bands. So… Here's how to break & rejoin the braid into one band. Downward at the 6 o'clock position, change the 2 curves on the outer edge into spade corners. Do the aforementioned matter at 2 o'clock & 10 o'clock.

See what happened? At 10 o'clock, the bluish & red bands are connected, assuasive the yellow to pass by. At 2 o'clock, the red & the yellow are joined & the blue slips through. 6 o'clock is where the magic happens… This is where the blue & the yellow go doubled back on themselves & get continued.

And now nosotros take 1 band! There are other ways to do it. Simply I'll let y'all figure them out on your own.!

Whatsoever questions? Allow's run across how you're doing!

I'one thousand off to start getting the demos ready for the spirals…
Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/colour]
[FONT="Book Antiqua"]How does she do that??? Find out here:[/color] Celtic Art 101

Do not meddle in the affairs of Dragons, for you lot are crunchy and good with ketchup.[/left]

January 5, 2007 at vii:20 pm #1079368

Ok, I have *no* thought what happened, but it'south been brought to my attention that these two layout images I posted are *not* correct for the simpler pretzel/triangle circumvolve demo. They are correct for the monster-brand-it-all-one-line demo. I'll attempt to post the correct ones later tonight. So then pitiful if I've confused anyone!

[/QUOTE]

Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/color]
[FONT="Volume Antiqua"]How does she do that??? Find out hither:[/color] Celtic Art 101

Practice not meddle in the affairs of Dragons, for you are crunchy and good with ketchup.[/left]

January five, 2007 at nine:50 pm #1079369

Ok, these are the right layouts for that first pretzel/triangle circle:

It was as well pointed out to me (thank Husband who was reading over my shoulder) that this:

(360 / 12 sections = 48; 48 / 4 (# of curves on our outside edge per segment) = 12. Which is evenly divisible past 3.)

is full gibberish. :o Clearly, math challenged. What I meant is:

360 / 12 sections, four curves per section = 48 curves. Which is evenly divided by 3 (16, btw.)

And so. I *think* that takes care of the corrections. So sorry if I befuddled y'all!
Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/color]
[FONT="Book Antiqua"]How does she do that??? Observe out hither:[/color] Celtic Art 101

Do not meddle in the affairs of Dragons, for you are crunchy and good with ketchup.[/left]

Jan vi, 2007 at 9:24 pm #1079401

Tess, I take whiplash from post-obit the curves and spirals. I'm getting me a protractor tomorrow (Eyeballing information technology doesn't work well). – Chris

January 7, 2007 at 7:42 am #1079370

Tess, I take whiplash from following the curves and spirals. I'thou getting me a protractor tomorrow (Eyeballing it doesn't work well). – Chris

no no no…. no injury! Yep, protractors are your friends…

Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/color]
[FONT="Book Antiqua"]How does she do that??? Detect out hither:[/color] Celtic Art 101

Practise not meddle in the affairs of Dragons, for you are crunchy and skillful with ketchup.[/left]

Jan 8, 2007 at 5:58 am #1079411

this makes my head injure!

[FONT=Book Antiqua]you don't quit laughing when you grow quondam.y'all grow old when y'all quit laughing!

ancientcityinkworks.com

January eight, 2007 at half dozen:37 am #1079371

Ok, and so far I've given Chris whiplash & mud'south head is going to explode…

anyone else going to try?

Postal service or PM if you need me to, um, put crash pads on this thread…
Tess

[FONT="Palatino Linotype"]Rosemary (aka Tess) - [/colour]
[FONT="Volume Antiqua"]How does she do that??? Find out here:[/colour] Celtic Art 101

Practice not meddle in the affairs of Dragons, for you lot are crunchy and expert with ketchup.[/left]
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