You could also see the original math problem turning up 6.5 as a solution, not a problem.
If you think of it as not 1 stitch being increased among 6.5, but 2 stitches increased among 13, you could do this:
x x x x x x x x x x x x O x O x x x x x x x x x x x x O x O...
By grouping your increases (or decreases) into groups of two, you allow the math to come out and I think it would look pretty nice, too.
I think this idea can scale, but you will need to figure out a few things:
1) How big do I want to make my groups?
2) How many stitches will go between groups?
If you want to keep 1-stitch divisions between increases (or decreases), you need to take the number of increases (or decreases) in your group (let's call this g) and subtract one. You can see the reason for this by holding out one of your hands. If you have five fingers, you will have 4 spaces in-between your fingers.
Revisiting the questions:
Multiply your increase factor (your original # / the # you want to increase by) by whole, prime numbers until your result equals a whole number (which I will call n). A good list of primes is here. The number you have to multiply by is the number of increases or decreases in your group (g). N is the number of stitches you have, total, in a given set of stitches for your increases or decreases. In the first example, above, n = 13 and the prime needed is 2. That makes g = 2.
To find out what you really need to do to make it work, you have one more step. To find out how many stitches should go in-between your groups of increases or decreases, take n - (g - 1). In the first example, that would be 13 - (2 - 1) = 12.
This seems complex and wordy, although it's really not, so I might make a worksheet for it. What do you think?
Saturday, September 27, 2008
Yaay! Comments!
Comments make this little blogger very happy.
Response to one: Sarah-Marie's Klein Bottle is here. She even has a klein bottle as a hat, and a photo of someone wearing it. Neat!
To sum up from my last post: what we were ultimately dealing with was a remainder. You don't have to break out in hives to deal with having last heard (or read) that word in the third grade. Just divide, say, 13 by 4 to find 3.25. Now, find that 3 * 4 = 12, so 13 = (3 * 4) + 1. Your remainder is 1. If you were increasing (or decreasing) by 4 stitches across 13, you would add or subtract stitches every 3 stitches and have on "extra" stitch to deal with however your heart desires. Numbers can be bigger or smaller, but they can all be tackled in this general way:
x = original number of stitches
y = number of stitches that need to be increased or decreased
r = remainder = "extra" stitches that need to be dealt with
x / y = either whole number or number in the form of a.bbbb. There could be many b's or not.
No b's? That means you have a whole number. On your way. Your math work is done. Simply increase or decrease every a number of stitches. Remember that, if you are decreasing, you will have to take into account the fact that the decreases use some of the a stitches. For example, if you need to decrease by 4 over 12 stitches, your a = 3. You will actually work 1 stitch then ssk or k2t four times, rather than work 3 and then k2t, because both a ssk and a k2t require two stitches to be worked.
If fraction, use x - (y * a) = r to find remainder.
Response to one: Sarah-Marie's Klein Bottle is here. She even has a klein bottle as a hat, and a photo of someone wearing it. Neat!
To sum up from my last post: what we were ultimately dealing with was a remainder. You don't have to break out in hives to deal with having last heard (or read) that word in the third grade. Just divide, say, 13 by 4 to find 3.25. Now, find that 3 * 4 = 12, so 13 = (3 * 4) + 1. Your remainder is 1. If you were increasing (or decreasing) by 4 stitches across 13, you would add or subtract stitches every 3 stitches and have on "extra" stitch to deal with however your heart desires. Numbers can be bigger or smaller, but they can all be tackled in this general way:
x = original number of stitches
y = number of stitches that need to be increased or decreased
r = remainder = "extra" stitches that need to be dealt with
x / y = either whole number or number in the form of a.bbbb. There could be many b's or not.
No b's? That means you have a whole number. On your way. Your math work is done. Simply increase or decrease every a number of stitches. Remember that, if you are decreasing, you will have to take into account the fact that the decreases use some of the a stitches. For example, if you need to decrease by 4 over 12 stitches, your a = 3. You will actually work 1 stitch then ssk or k2t four times, rather than work 3 and then k2t, because both a ssk and a k2t require two stitches to be worked.
If fraction, use x - (y * a) = r to find remainder.
Thursday, September 25, 2008
Sticky Problem and a Super-Math-Rich Post
I just moderated a comment from a listener that said she had to put 41 yarn-overs into 267 stitches evenly. She fudged it. I'm going to say she would have to - it averages to one yarn-over about every 6.5 stitches. This is nearly impossible, really. If I were working some other increase, say, a lifted increase, I would say, just do an *increase, work 6 stitches, increase, work 7 stitches* repeat, and it should even out. I think that would drive me nuts when making eyelets, since my switching between 6 and 7 stitches apart would be obvious, to me, at least.
A possible solution: factor your numbers out and look for common factors. The major issue of this is that 41 is a prime number, which means that we would have to add or subtract somewhere to make this work.
267 is not a prime number, so we can take it apart and see what we have. Unfortunately, we don't have far to go.
267 = 89 * 3
89 is a prime number. Luckily, 3 * 14 = 42. So, we could round 41 to 42 by deciding that one more increase in the mix is better than the crazy-making idea above.
We can mentally, and with stitch markers, divide our work by three - so we're facing putting 14 eyelets into 89 stitches. 14 * 6 = 84, which leaves us with 5 extra stitches for each "wedge" of 89, if we increase every six stitches.
Speaking of which, to increase every six stitches *really* evenly, we would do this:
(x = stitch, o = increase)
(stitch marker) xxx o xxxxxx o xxxxxx o xxxxxx o xxxxxx o xxx...
I'm not going to do it 14 times, but you get the idea.
What do we do about those extra 5 stitches? We could put them in-between wedges, so that at some point, our work will look like this:
o xxxxxx o xxxxxx o xxxxxxxx(stitch marker)xxx o xxxxxx o xxxxxx
Which is to say, that, around our stitch markers, we would have 5 + 6 = 11 stitches as spacers. You could, and I would, decide that this is a design feature and only have to decide where they should lie - it doesn't even have to be 100% evenly, but I would probably put two of them under the arms of a sweater and the third in the middle of the back or front.
Design Feature Solution #2:
Break the set of 42 increases into 3 sets of 14 stitches.
267 / 14 = just over 19.
So, the first set of eyelets will be an increase every 19 stitches.
Total stitches = 281
281 / 14 = just over 20.
The second set could be every 20 stitches.
Total stitches = 295 stitches
295 / 14 = just over 21
The second set could be every 21 stitches.
Total stitches = 309 stitches
So, by adding one total stitch, and I'm not going to try to draw it for you, you could have a perfectly neat little leaning line of yarn-overs, in either 3 rows or 6, depending on how you do it. You could even stagger them by as much as you like, by making your first increase sooner than you would, and letting the stitches fall where they will.
I recorded my show on grafting, but have not knit, grafted, or photographed it, so it is still in the works, so to speak. I may talk about the above math in my next show, because I don't think a lot of you read this blog. Am I wrong? Leave me a comment to prove it. :)
A possible solution: factor your numbers out and look for common factors. The major issue of this is that 41 is a prime number, which means that we would have to add or subtract somewhere to make this work.
267 is not a prime number, so we can take it apart and see what we have. Unfortunately, we don't have far to go.
267 = 89 * 3
89 is a prime number. Luckily, 3 * 14 = 42. So, we could round 41 to 42 by deciding that one more increase in the mix is better than the crazy-making idea above.
We can mentally, and with stitch markers, divide our work by three - so we're facing putting 14 eyelets into 89 stitches. 14 * 6 = 84, which leaves us with 5 extra stitches for each "wedge" of 89, if we increase every six stitches.
Speaking of which, to increase every six stitches *really* evenly, we would do this:
(x = stitch, o = increase)
(stitch marker) xxx o xxxxxx o xxxxxx o xxxxxx o xxxxxx o xxx...
I'm not going to do it 14 times, but you get the idea.
What do we do about those extra 5 stitches? We could put them in-between wedges, so that at some point, our work will look like this:
o xxxxxx o xxxxxx o xxxxxxxx(stitch marker)xxx o xxxxxx o xxxxxx
Which is to say, that, around our stitch markers, we would have 5 + 6 = 11 stitches as spacers. You could, and I would, decide that this is a design feature and only have to decide where they should lie - it doesn't even have to be 100% evenly, but I would probably put two of them under the arms of a sweater and the third in the middle of the back or front.
Design Feature Solution #2:
Break the set of 42 increases into 3 sets of 14 stitches.
267 / 14 = just over 19.
So, the first set of eyelets will be an increase every 19 stitches.
Total stitches = 281
281 / 14 = just over 20.
The second set could be every 20 stitches.
Total stitches = 295 stitches
295 / 14 = just over 21
The second set could be every 21 stitches.
Total stitches = 309 stitches
So, by adding one total stitch, and I'm not going to try to draw it for you, you could have a perfectly neat little leaning line of yarn-overs, in either 3 rows or 6, depending on how you do it. You could even stagger them by as much as you like, by making your first increase sooner than you would, and letting the stitches fall where they will.
I recorded my show on grafting, but have not knit, grafted, or photographed it, so it is still in the works, so to speak. I may talk about the above math in my next show, because I don't think a lot of you read this blog. Am I wrong? Leave me a comment to prove it. :)
Sunday, August 17, 2008
Episode 39
Download Episode 39.
I had the idea for these shows because I made a golf-club cover for someone a while ago (not my dad, he actually framed the covers I gave him because he's afraid of messing them up) and he said it sprung holes almost right away. It could have been a split stitch, I guess, but it really looks like an act of a cat to me.
When darning, first stabilize the patient. I like to use small needles and/or dental floss to thread through the live stitches, starting with the lowest row that has a loose stitch. The dental floss is more flexible, but, to me, the small needles make it easier to hold the structure. On the other hand, a whole lot of dental floss can fit in your knitting bag and it's much cheaper than having extra needles around all of the time.
If that loose stitch has ladders over it (stitches that have slipped in the same way as if you dropped a stitch off the needle), I pull the stitches up with a crochet hook.
Now, I have brought up the loose stitch and isolated the lowest place in the knitting that is a full row without a hole in it. So, I take my darning needle and some matching yarn and a start a row of darning two stitches from the edge of my hole (leaving a tail to be darned in, too, in its time).
The stripes in this example are a good thing for us. It makes it easier to see that, while it looks like I'm actually darning one row up from where I should (or that I'm too close to the row of black) you have to remember that the "loose" stitches are a row, so be sure that you are working the correct row. If you're not, you can always jump rows when you get to the live stitches. So, I only have to darn one row of gold before I get to black.
You can see, above, that I screwed up. I accidentally darned in the wrong direction and made a purl stitch instead of a knit stitch. This is ok, because if you're paying attention, you can notice that, simply undo it, and learn more about how to do it properly.
So, we see that this hole can be fixed with one row of darning, although it seemed much worse before, because of a dropped stitch. So, it probably was just a single stitch that went south. Just goes to show - one stitch can sometimes cost nine darn photos.
This is the same idea, in two rows of white:
Now, a little bit of slight-of-hand. I darned this hole, but then found a mistake in one of the stitches - I had twisted it when I made the darn. Instead of picking it out, I darned over it again, strengthening my join and hiding my mistake.
I had the idea for these shows because I made a golf-club cover for someone a while ago (not my dad, he actually framed the covers I gave him because he's afraid of messing them up) and he said it sprung holes almost right away. It could have been a split stitch, I guess, but it really looks like an act of a cat to me.
When darning, first stabilize the patient. I like to use small needles and/or dental floss to thread through the live stitches, starting with the lowest row that has a loose stitch. The dental floss is more flexible, but, to me, the small needles make it easier to hold the structure. On the other hand, a whole lot of dental floss can fit in your knitting bag and it's much cheaper than having extra needles around all of the time.
If that loose stitch has ladders over it (stitches that have slipped in the same way as if you dropped a stitch off the needle), I pull the stitches up with a crochet hook.
Now, I have brought up the loose stitch and isolated the lowest place in the knitting that is a full row without a hole in it. So, I take my darning needle and some matching yarn and a start a row of darning two stitches from the edge of my hole (leaving a tail to be darned in, too, in its time).
The stripes in this example are a good thing for us. It makes it easier to see that, while it looks like I'm actually darning one row up from where I should (or that I'm too close to the row of black) you have to remember that the "loose" stitches are a row, so be sure that you are working the correct row. If you're not, you can always jump rows when you get to the live stitches. So, I only have to darn one row of gold before I get to black.
You can see, above, that I screwed up. I accidentally darned in the wrong direction and made a purl stitch instead of a knit stitch. This is ok, because if you're paying attention, you can notice that, simply undo it, and learn more about how to do it properly.
So, we see that this hole can be fixed with one row of darning, although it seemed much worse before, because of a dropped stitch. So, it probably was just a single stitch that went south. Just goes to show - one stitch can sometimes cost nine darn photos.
This is the same idea, in two rows of white:
Now, a little bit of slight-of-hand. I darned this hole, but then found a mistake in one of the stitches - I had twisted it when I made the darn. Instead of picking it out, I darned over it again, strengthening my join and hiding my mistake.
Rerun of Episode 30: The MD Sheep and Wool Festival Trip, 2007
I'm just running Episode 30 over again without a new podcast attached, because it is already almost an hour long.
The original notes from the show are above, and if you want to see where we shopped and vendors we talked about, scroll down a bit, it is on the same page.
I don't normally listen to myself in old podcasts, but I listened today, because I love hearing my sister talk and I miss living nearer to her. I love you, sisser.
The original notes from the show are above, and if you want to see where we shopped and vendors we talked about, scroll down a bit, it is on the same page.
I don't normally listen to myself in old podcasts, but I listened today, because I love hearing my sister talk and I miss living nearer to her. I love you, sisser.
Wednesday, August 06, 2008
I am not slacking, I swear
I'm not able to podcast this week because I'm using my mic for actual work. At my job. Now my intern, who is on her last week with us, is using it, too. It's way, way too much fun.
Monday, July 07, 2008
Episode 38: Part 1 of 3 (darn that hole)
Today, I talk about swiss darning, otherwise known as duplicate stitch, and how it lays the path for darning holes and grafting or kitchener-stitching live stitches.
The rerun for this show is episode 29. Notes for that show are here.
There are a LOT of photos for this, so I'm going to break it into three posts: stockinette, garter stitch and ribbing.
Download Episode 38.
The rerun for this show is episode 29. Notes for that show are here.
There are a LOT of photos for this, so I'm going to break it into three posts: stockinette, garter stitch and ribbing.
Download Episode 38.
Friday, July 04, 2008
Darn That Hole
This isn't really about math, but I'm working on my next show about darning holes. This is something a lot of knitters avoid, but the skills involved can also be used to seamlessly complete garments using kitchener stitch, which is basically one long row of darning, or add color details by darning on top of existing knit fabric (sometimes called swiss darning or duplicate stitch). If you want to follow along, dig up or create a gauge swatch that includes garter stitch, ribbing and stockinette stitch and have a good darning needle (I prefer curved ones) and yarn of the same weight, but different color, handy.
Tuesday, May 27, 2008
Things I've Been Doing @ Work Lately
Work has been crazy, to say the least. So, no podcast recently. But, soon, I hope.
Thursday, May 22, 2008
New Episodes problem
Some people have told me (and not told me, I suppose) that they are having trouble with my feed in iTunes.
I think we have found a solution.
Just unsubscribing and re-subscribing doesn't seem to work.
"What worked in the end was actually deleting the feeds in iTunes and then subscribing with the link you provided, easy and quick."
-M. Wergeland of Matthew's Thread Work
The link is: http://www.laraneel.com/podcast/Math4Knitters.xml
I hope it works. Let me know. The problem on my end is, no matter how many computers I try, I can't get the problem to happen to me. It's possible this is because I am working with machines that are starting from scratch and something is going on with the old feed. Or maybe the other old feed. Who knows?
I am cooking up a new show. I'm just waiting for my work schedule to cool down a bit. Things have been strange and busy around here, to say the least.
I think we have found a solution.
Just unsubscribing and re-subscribing doesn't seem to work.
"What worked in the end was actually deleting the feeds in iTunes and then subscribing with the link you provided, easy and quick."
-M. Wergeland of Matthew's Thread Work
The link is: http://www.laraneel.com/podcast/Math4Knitters.xml
I hope it works. Let me know. The problem on my end is, no matter how many computers I try, I can't get the problem to happen to me. It's possible this is because I am working with machines that are starting from scratch and something is going on with the old feed. Or maybe the other old feed. Who knows?
I am cooking up a new show. I'm just waiting for my work schedule to cool down a bit. Things have been strange and busy around here, to say the least.
Wednesday, May 07, 2008
Episode 37: Gauge Swatches and Experiments
Elizabeth Zimmerman called it "unventing", I call it "experimenting". I think she didn't like the image of the white lab coat, but I always loved knitting in my white lab coat. You know, back when I was a scientist, getting chalk dust on my knitting.
On this week's show, I answer questions from two Ravelry users who have messaged me. I really appreciate their questions, because otherwise I would just blather on about my sweaters and my cats. That's all well and good, but sometimes I have to talk about other things.
I didn't do a podcast last week because I lost my voice. Nearly a 100% loss. This has never happened to me before. I think it was a combination of teaching at a conference/workshop for three days, then talking with an old friend for about 6 hours straight. During hour 5, I was already feeling a bit croaky. By that night, I was down for the count, voice-wise. It has taken a while to recover and my spring allergies are still keeping me a little rough.
The rerun this week is episode 28. We are almost through them all. I considered running Episode 30 this week to go with the Maryland Sheep and Wool Festival, but I thought that would confuse things. The original notes for that show are here.
Download Episode 37.
On this week's show, I answer questions from two Ravelry users who have messaged me. I really appreciate their questions, because otherwise I would just blather on about my sweaters and my cats. That's all well and good, but sometimes I have to talk about other things.
I didn't do a podcast last week because I lost my voice. Nearly a 100% loss. This has never happened to me before. I think it was a combination of teaching at a conference/workshop for three days, then talking with an old friend for about 6 hours straight. During hour 5, I was already feeling a bit croaky. By that night, I was down for the count, voice-wise. It has taken a while to recover and my spring allergies are still keeping me a little rough.
The rerun this week is episode 28. We are almost through them all. I considered running Episode 30 this week to go with the Maryland Sheep and Wool Festival, but I thought that would confuse things. The original notes for that show are here.
Download Episode 37.
Monday, April 28, 2008
NOT podfading
I am not fading out, I just have a very sore throat and can't really talk right now. I expect a full recovery and another show out soon.
Monday, April 14, 2008
Episode 36: Notes and Mistakes
Today, I talk about my latest "design feature", we get another visit from my co-host, Boomer, so I hope you like cat hair, and I talk about Black Purl Magazine and Knitting Step by Step.
The rerun with this show is episode 27. The original notes for that show are here.
Download Episode 36.
The rerun with this show is episode 27. The original notes for that show are here.
Download Episode 36.
Tuesday, March 25, 2008
Episode 35: Letting Go
After all of my yammering about taking control of your knitting, I decide it's ok to let go a little sometimes.
I also talk, way way too fast, about my current sweater and the sweater I made a year ago.
The yarn I'm using is from Brooks Farm Yarn. The label says Macero Mas-Acero and it's gold heathered with black.
My two design "bibles" are Barbara Walker's Second Treasury of Knitting Patterns and Barbara Walker's Knitting From the Top.
Today's rerun is Episode 26. The notes for that show are here.
Download Episode 35.
I also talk, way way too fast, about my current sweater and the sweater I made a year ago.
The yarn I'm using is from Brooks Farm Yarn. The label says Macero Mas-Acero and it's gold heathered with black.
My two design "bibles" are Barbara Walker's Second Treasury of Knitting Patterns and Barbara Walker's Knitting From the Top.
Today's rerun is Episode 26. The notes for that show are here.
Download Episode 35.
Monday, March 17, 2008
Episode 34: Overcoming Fear
This week I talk about overcoming fear in knitting.
I started (and finished) 10 copies of the same project - Wreath Earrings (although I'm not using them for earrings) from Twist and Loop by Annie Modesitt.
There is also a great article about knitting with wire from The Anticraft.
Download Episode 34.
The rerun is episode 25. The original notes for that show are here.
I started (and finished) 10 copies of the same project - Wreath Earrings (although I'm not using them for earrings) from Twist and Loop by Annie Modesitt.
There is also a great article about knitting with wire from The Anticraft.
Download Episode 34.
The rerun is episode 25. The original notes for that show are here.
Saturday, March 01, 2008
Episode 33: All Praise the Gauge Swatch
This week, I ramble about gauge swatches, yarn, and my cats.
I also play a promo for a new, prolific podcaster. Do I mention her just because she mentions me and Elizabeth Zimmermann in the same breath? Perish the thought!
And, a rerun of episode 24.
The original notes for that show are here.
The book I am talking about is Favorite Mittens.
I also just started a group on Ravelry for people who listen to the show. So, come visit if you want to send along show ideas, questions or stash-busting tips.
Download Episode 33.
I also play a promo for a new, prolific podcaster. Do I mention her just because she mentions me and Elizabeth Zimmermann in the same breath? Perish the thought!
And, a rerun of episode 24.
The original notes for that show are here.
The book I am talking about is Favorite Mittens.
I also just started a group on Ravelry for people who listen to the show. So, come visit if you want to send along show ideas, questions or stash-busting tips.
Download Episode 33.
Monday, February 18, 2008
I was going to podcast today...
But I have discovered something about ravelry. I put some stash up for sale/trade over a week ago. Nothing, except for a book that got snapped up in hours. Today, I uploaded some photos of the yarn and BAM, instant interest.
So, I may spend some time rollicking around ravelry today, instead of podcasting. Maybe I will do it in the morning.
So, I may spend some time rollicking around ravelry today, instead of podcasting. Maybe I will do it in the morning.
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