Return to circles, knit “pies” 3

Elizabeth Zimmermann provided guidelines for circular shawls in her books and publications, including “Knitting Workshop”. For a basic pi shawl (p. 112, Schoolhouse Press, 1984) the assumption is that each section is twice as deep as the previous section and has twice as many stitches. Below CO row represents cast on stitches if the work is to begin from the center out, Column A the row count on which the increases take place, column B the number of rows knit just prior to increase row (A-1), and C the number of rows available for any planned repeat (A-2), thse are constants. The columns directly below each cast on (CO) number (orange) counts represent the number of stitches when increases are complete. The stitch count doubles when the number of rounds has doubled.Mary Thomas’s Book of Knitting Patterns, Dover 1972, p.p. 245-247 provides guidelines for circular medallions. She calls her first a “disc” medallion. In executing it the aim is to scatter increases so they are less visible and do not form spokes. Four stitches are cast on, with 4 stitches increased in the total count every other row. The number of stitches between M1s increases by one on every other row. My chart happens to read from left to right. As with any knitting in the round, the process may be reversed, starting at the circumference and moving toward center. I personally like charts to help visualize results, and have revised her counts in the illustration below so increases are at the same rate, but placed a bit differently within the rows. On rows with even numbers between decreases, start row with half that number of knit stitches before the first increase. Because one is knitting in the round, with knit side facing, all rows are knit. If the work were knit on 2 needles, knitting every row would produce garter stitch.what happens if increases “line up”For her circular “radiant” medallion after the first 2 rows increases are made every 4th round. My chart is renumbered excluding the first 2 rows, so the increase rounds would occur on numbers divisible by 4, making it easier for tracking them. Each “building” round increases the number of stitches by 16.

In her “target” circular medallion, the building increases are arranged in concentric circles. Each increase row begins with a M1. Once RC 20 is reached, a stitch is added between increases on each increase round. This chart reflects the knitting progress, but not the shape. STS column on right reflects the total number of stitches after increases have been made. Each building round after RC 6 increases the count by 32. Formulas for more, varied geometry based medallions are also offered in the book.  I finally “discovered” actually using formulas in Excel! The video that clearly and quickly helped me learn how to: at the flow in table form for the first 2 medallions

These formulas do not take into account changes in gauge, or stitch type within bands. For similar shapes to be achieved in machine knitting, the number of transfers would be prohibitive. In order to achieve similar shapes one begins with the radius of the finished circle and the shapes in the family may be knit sideways, using holding.

Handknitters can work with 4 double pointed needles, one or 2 (or more) circular needles, and crocheters can follow similar shaping methods. The advantage to long circulars is less bunching up as the work grows, and if you like working flat or want to try the garment on while shaping it, you can use more than one long needle, making the piece or the try on manageable. Working from the top down when knitting such shapes may give one more control over the size of the finished piece i.e.. on length of body and sleeves, height between bands, extending a yoke into a shoulderette or cape. Stitch pattern size and repeats add to the math calculations. Garter stitch is the only hand knit stitch that approaches a square gauge, could be used in combination with patterned bands.

The charted patterns above rely on M1 to increases. Yarn overs may be used for decorative holes at increase points. If preferred, the hole may be diminished by twisting the stitch when picking it up on the next round.

When knitting in stripes, the “jog” at the color change in knitting can be eliminated by slipping the old color purl-wise, and starting to knit the second stitch. TECHknitting provides more alternatives in her posts: For a method using yarn ends and a needle when yarn is cut

For shawl shapes and their geometry using YO increases, see the posts and publications by Holly Chayes.

To start it all from center out: I am used to doing the magic loop cast on with a crochet hook, and then moving on from there, Kitty Falol shows it worked with DPNs.

Return to circles, knit “pies” 2

Just as other knitwear styles have varied in style, ease and fit over the years, round yoke sweaters have also done so. Yokes can be wide or narrow, in patterned or textured stitches, and in varied proximity to the neckline. This is not generally a tailored style. Ease in knits can be calculated on the basis of fashion or personal preference. With some familiarity with slopers measurements may however, be adjusted in this style as in any other sweater. Neckline measurements do not reflect the measurements achieved after adding finishes i.e. turtle or round. Depending on the size of the yoke, shaping can begin at the armhole level bind off (seen in the early hand knitting directions in the 70s), while smaller yoke shaping can begin at whatever point is desired, extending to the neckline, or simply to create a design band. The shaping is created by decreases if the garment is knit from the bottom up, and with increases if worked from the top down. In most styles the same number of rows are worked from the armhole bind off or held section to where yoke sections meet. At that point if hand knitting on circulars the 4 sections: i.e. left sleeve, front yoke, right sleeve, and back yoke may be picked up and joined for completing the yoke. My illustrations have been created using Mac’s Pages lines and shapes.  They are not to scale.

Beginning to visualize process: yokes are generally superimposed on raglan shaping

they form part of a flat circle; here is how they might appear in a partially seamed cardigan without front bands. They may be created in varying widths or patterns,

and in a pull over with shaping in back that raises the rear neckline. Some of the early patterns were executed with front/ back and both sleeves sharing equal measurements and slopes

separate the elements: the yoke 

the front and back can be begin to consider shaping at breasts, waist, and those wedges under where the yoke “circle” meets the sweater may be short rowed on each side with the intent of achieving a much better personal fit


Hand knitters are probably familiar with Elizabeth Zimmermann and her daughter, Meg Swansen. Handknitting with Meg Swansen 1995, and Elizabeth Zimmermann’s Knitting workshop 1981, Knitting around 1989, Knitting without tears 1971 are classical references that include information on yoke creation, including these guidelines

Other authors suggest 1/4 of total body and sleeve measurement in stitches (excluding armhole) for a tighter neckline (turtle neck), one third for a more open style (crewneck). Original circumference/ body measurement should include any ease. Though decreases for the yoke: first halfway up 25%(one out of every 4), second 3/4 up 33% (one out of every 3), and last 1/2 inch before full depth is reached 40% (two out of every 5) are the most common, they can be placed and varied to suit your own design.

In drafting your own patterns and partnering with someone, a tape measure or string can be laid on shoulder line, etc. for an idea as to preferred placement and measurement. Necklines finished by bound off stitches whether machine or hand knit, do not stretch, so measuring your head with something that does not as well gives you a guideline. Yokes end in open stitches, so the thing to consider there is what method is used to finish the neckline, and its own stretch factor after bind off. Hand knitters have the added benefit of splitting the work on 2 circulars and trying on the sweater or its pieces on while in progress to double check fit.

Japanese designers began to publish patterns that often included yokes that were constructed on the top of the drop shoulder line, with the back yoke placed higher than on the front. Such yokes also began to be represented in stepped figures showing decreases. In the round calculations are gauge based, not relying on the pi formula.

modified raglan for higher placement of yoke on back of body

full pattern with traditional full cap sleeve

pieces meeting at dropped shoulder line: dotted line represents back collar placement, note difference in height between back panel on lower back, and front panel on lower right

a sample diagram from a Japanese magazine 

Yoke shaping may be indicated in stacked format. The final count and frequency of decreases is shown, publishers may vary in language. On the first row here 4 sts – 2X means there is a group of 4 stitches followed by a decrease 2 times, then 5 stitches followed by a decrease 23 times, etc.

Two online calculators are available to help with DIY:  1. the Yoke-U-Lator, and 2. for Lopi, Icelandic styles. The image below is a screenshot from the latter website, indicating a sample possible result.

Jessica Tromp offers free circular knitting patterns with round yoke, dimensions in inches and ounces.

There are endless possibilities for combining math formulas, gauge, and pi. There are many ways to do decreases. With planning so that much more frequent intervals happen between decrease rounds, the decreases themselves can be fabricated to line up in line, and the resulting texture creates the interest in the sweater as opposed to any color patterning (i.e. along white lines)

“pie wedges” may be placed on neckline, yokes, sweater parts, various silhouettes and garment pieces, or full shapes (red dots outline possible dolman sleeve)from a Japanese magazine a hint of detail that must be calculatedand the pie may be oriented in different locations on any one piece 

from a Japanese knitting magazine, an idea for long sleeve and side details merging with and becoming part of a circular yokeFor some of the math  calculations please see:

“Decreases” in rib sometimes can be achieved through changes in needle size if hand knitting, or tension changes on the machine. The yoke in machine knitting would need to be split in 2 parts or knit sideways. Plain colored rows between bands of FI may appear noticeably lighter in weight, so using a 1X1 one color FI pattern or double strand of one of the pattern colors may improve the look.

Before transferring stitches on the machine in the single color rows, make your transfers. The lace carriage may be used after selecting appropriate needles and putting them in position. Knit the following row before removing knitting on waste yarn or garter bar. If stitches are tight for garter bar use sometimes the row after transfers may be knit at a looser tension to facilitate the process, and the difference may not be noticeable when knitting at “normal tension” is resumed. The carriage should be set to plain knit for row prior to and after transfers. It may be easier to work toward the center from each side when returning stitches to the needle bed. In order to match the pattern at the shoulder seams or when motifs need to stack in position on separate bands, the stitches need to be rehung at specific positions on the needle bed that take into consideration the size of the repeat and its location within the stitch count. Also, take into account the seam allowance. One stitch extra on each of the meeting seam sides will allow the end needle selection stitch or an extra patterning needle to be hidden within a full stitch join. Working on machines that preselect needles or pushers makes tracking a bit easier. It is possible to combine knitting pieces in both directions. For example, knit yoke up toward neck, join shoulders, and then pick up appropriate stitches to knit body and sleeves from the top down. Top down makes any adjustments in length easier prior to finishing the sweater. Short rowing in garment segments underneath the yokes makes for a better fit at bust line and upper back.

Calculators to help with all that math: online

for purchase:

Going low tech: if gauge works out to whole numbers, shapes can be plotted out on square grid graph graph paper (or grid created within software to suit) where each square represents one stitch, one row. Draw connecting lines, follow outline, filling in squares (or removing them) as the edge moves a whole unit (k2 tog). Here the goal is to go from 39 stitches to 5 over 60 rows. Color bands could be added and planned between decreases, which should occur on single color rows. Once a gauge is obtained, charting on graph paper or within programs can be boiled down to connecting dots and following outlines as above. Some simple breakdowns for outlines of garment pieces/ shapes 

Illusion DIY patterns in crochet

I previously posted on illusion knitting, and on one approach to designing simple patterns using the technique. The first 3 images below are of the swatch illustrating one of my hand knit patterns. 

Since I am now involved in a group interested chiefly in crochet, I got curious about executing the fabric in crochet. Part of the problem is that enough texture needs to be created to be able to read the “shadows”. I tried crocheting in different parts of the chain, around the posts in the row below, and ultimately went back to afghan stitch. I had not used the latter since making blankets first for my son, and then for my grandchildren.

the tunisian aka afghan stitch fabric as it looks head on tilted up to its side and its rear view

Those of you new to the technique can find some instruction at the Red Heart website , and in a beginning how to video from Crochetcrowd. I used Tunisian simple and Reverse Tunisian simple stitches to create my pattern. In this technique, chart texture rows are read right to left. The return rows are not illustrated. It takes 2 passes of color one, followed by 2 passes of color 2 to complete one pattern row. Yarn is carried up the side, color is changed in the same manner as in any crochet stitch. In my test swatch, no border stitches were planned for or included. It is always wise to test the repeat in repeat before working the fabric.

 two passes are needed with each color, so here is the repeat double length 

columns    A: color used   B: forward and backward pass for each color   C: number of passes to complete a single repeat. The highlighted box at bottom indicates a completed single design row. Only 2 colors are in use in the swatch. I found it easier to track my work and the edges where the textures need to meet by using an additional pair of colors in the chart itself. Rather than use the crochet terminology I marked my first stitches with F and B for each color, referencing the front/ forward, and rear/ back vertical loops/ posts respectively. As one moves across the row from right to left, when the color/ texture change is reached, the yarn is brought to the front or the back as needed, and the next color/ texture is worked in the reverse post/ loop.

working in back loop only of the starting chain produces a firmer edge at the bottom of the piece return pass every other row, not represented in chart changing color Front, vertical loop Back, vertical loopH: horizontal, V: vertical red indicates hook entrance through front, green for through back vertical bars respectively, prior to working the next stitch

Both swatches were made using similar weight yarns. The crochet version required more passes back and forth than in knitting, where the work may be turned over and the texture reversed on each knit row. The knit repeat measured approximately 5.5 inches L by approximately 4W, isolating my best guess stitch number equivalent to the crochet one. The crochet swatch measures 7 inches L by 6W.

Return to circles, knit and crochet “pies” 1

I began a series of posts on miters and spirals created on the knitting machine back in 2011. The oldest posts, 12, and 3 begin to address creating flat circles in machine knitting using holding techniques.

Hand knitting in circular format and crochet share some similarities. There are 2 methods of constructing circular work in crochet. 1: in rounds, (akin to knit miters in shape) where the end of each circular row is joined up to its own beginning to form a ring. A new starting chain (s) is formed to take the row up to the proper height for the next row to remain constant. Depending on the pattern, one has the option of continuing by turning the work or not at the end of each row. Doing so allows the opportunity of altering textures and working in the fronts or backs of stitches. 2: in spirals. Rather than joining the ring, one continues on by going into the tops of the posts in the previous row.

With spirals it is useful to mark the beginning of each round. Knitting markers shaped like safety pins are handy for that purpose. A line of contrasting color can also be created using a separate strand of yarn and alternating carrying it back or to the front prior to forming the first stitch in the new row.

As with knitting, crocheted circles are not true circles, but rather, they are polygons. The way to make shapes more circular is to scramble the increase points, putting them in different starting positions in each round (always spacing them equally and keeping the formula). Within limits one may make the starting number of stitches in the first round a multiple of the number of segments in the finished shape.

With the creation of a flat circle in mind, the number of stitches needed depends on the height of the stitch. The taller the stitch, the greater the number of stitches required. If the stitch stays the same throughout, the number of stitches added on each round is constant. Test work regularly at intervals as the work grows by placing it on a firm, flat surface, to see if working only one stitch into each stitch is required / enough at that point to maintain the shape. The more segments, the smoother the circumference.

Unlike in hand knitting, the first loop on the hook does not count as a stitch until you make it into something.

Spirals or miters knit on the machine begin with their radius; one possible construction method may be inferred from these images

Spreadsheet programs such as Excel and Numbers have pie charts and other tools that can help visualize or even plan the work with symbols. Unlike machine knitting, both crochet and hand knitting may begin and grow from the center out or from the outside in. Calculated shaping with increases or decreases along circumferences at different points on the pie create the desired shape. For the purposes of this discussion I will address stitches in US terms. There are various published guidelines with some variations. Fiber content and matching gauge (if required) may need editing of the numbers, but, as starting points:
Single Crochet [sc] : Start with 6 sc and increase 6 sc in each round so that the total stitch count in each round is a multiple of 6
Half Double Crochet [hdc] : multiple of 8
Double Crochet [dc] : Multiple of 12
Treble [tr]: multiple of 16

Some symbols and number of stitches required in base rows in table form, for working from center out:
the more wedges in the pie, the smoother the circumference no matter what the method. Single crochet is worked in 6 wedgesdouble crochet in 12 wedgeswedges may be reduced to simple line segments rounds may also be created to log in and track more details adding wedge outlines before filling in symbols

single crochet worked with slip stitch at the end of each row will produce  points similar to those seen in miters in machine knitting

spirals produce a rounder shape double crochet echoes the forms 

Building your own charts requires vector programs to allow for rotation of symbols around an axis. My chart was quickly produced in Inkscape, which is free to download for both Mac and PC users. Mac users in addition will also need to download XQuartz to run the program. I created the chart with my own symbols and freeform laid them down while viewing the grid. It turned out however, that there are 2 published videos on how to use the program for charting crochet stitches, part 1 and part 2 by

Two YouTube videos on topic:  using Illustrator CS 5.1, Marnie Mac Lean’s video, and using StitchWorksSoftware. An online generator by Stitch Fiddle, and its associated video.

if donuts are the goal: find your round 

An example: in single crochet, if round 3 had been completed, there would be 18 completed stitches. Chain 18, either slip stitch or continue in spiral to match count at that point. For round 4: increase every 4th, round 5: every fifth, round 6: every 6th, round 7: every 7th stitch.

A few sites to see for crochet tutorials:
magic ring start : no chain stitches, no center hole
working in spirals
a nice ending
crocheting a flat circle in single crochet: note the start “magic circle”
changing colors

I tend to swatch in easy to see colors, “friendly” yarn, and use tools that allow moving in and out of stitches easily until I have techniques sorted out. When knitting circles in the round, things get a bit more complex, particularly if one begins to introduce items such as round yokes with patterns into garments where gauge matters significantly.

Some of the same principles may be used in hand knitting. For magic loop start with circular needles: KNITFreedom, and on DPs Webs yarn

MK ladders, and a bit of crochet

I have recently been thinking about collars and edgings again, this time adding crochet detailing to help cut the edge curl and add interest. In a previous post I showed an edging done in drop stitch (double bed lace). Here to simplify things, I decided to work with ladder spaces to create the fabric. If a large width of this fabric is required, multiple bands would need to be joined to achieve it, crochet is then applied in turn to the the finished knit piece. Seam as you knit can make the joining nearly invisible. Using excel, I tried to also create crochet symbols using its shapes menu. The number of rows knit in open pattern or all knit prior to binding off are at your discretion, depending on your needs and planned final product. For my sample I began knitting with COR, and to end with COR for bind off row, I chose to work with even numbered groups of rows. Consider fiber content if the intent is to permanently block as flat as possible, or not.

my chart symbols symbols_70


needle set up, waste yarn cast on, knit for desired length  setup_62img_4095bring one empty needle into worktransfer_63img_4096knit one row, bring remaining empty needle into work plain-knit_64img_4097knit one row img_4099knit rows desired for top bandimg_4100transfer eon from L to rightallk-transfer_65img_4101latch tool bind off around gate pegs for all needles/stitches img_4102

img_4103do not cut yarn, lift work off machine; turn work over (knit side facing)
chain 5, slip stitch into eyelet created by transfers, repeat across the knit, end with slip stitch into last eyelet space detail_4121turn work over (purl side facing once again), chain 3, 2 double crochet, slip stitch into center of chain 5 space, repeat across the knit, end with slip stitch into last chain 5 space detail_4120unblocked trim, 2/15 acrylic yarn img_4104

img_4105detail after steaming, the trim is side leaning img_4119


To use: rehang open stitches on every needle (or other arrangement) eliminating ladder spaces and bind off,  join to another piece of knit, etc.

A bit of holding 5: intarsia and more 2

So you have some shapes you love and know: wanting to go large, mixing them up, requires thinking things through. Testing on small swatches will help determine holding sequences and whether the results are predictable or even liked. I no longer have access to Adobe photoshop or illustrator, so some of my image editing is now achieved in gimp. Labeling below is with Skitch, and charting is with Excel.

A starting freehand swatch experiment and some observations: shape variations in red areas occur by altering sequence for knitting first and last 2 shapes in hold



Planning possible sequences out in charting can be confusing. The image direction will be reversed on the knit side. Approaching the technique like intarsia with individual yarns or bobbins eliminates the need for some of the concerns where 2 row sequences or specific starting sides are necessary to keep yarns continuous or for execution of the desired shape. Trying to imagine the shapes that create the larger one together in a simple 2D drawing can get one started, but  then shapes need to be rearranged. I usually began by “playing”, trying to figure out steps needed, and follow that by trying to produce an executable chart. Making the process as easy as possible to track is always a consideration.

screenshot_09possible stitch counts and adding a center line “stem”/ stripescreenshot_10its knitting sequence tulip_numbereda resulting swatch, stitch counts not consistent with chart


In the chart below the design is worked with 2 needles brought out to work or pushed back into work at any one time, making tracking changing numbers in hold unnecessary. Pink rows indicate starting and ending knit rows, orange “stitches” are cast on and bound off in turn, creating a shape extending out from the edge of the knit. Arrows indicate where shapes meet to create forms.


Holding sequence for each shape may be worked begin with carriage on either side; with experience this may be planned at times to eliminate some of those cut yarn ends that later must be woven in. Getting back to arrows indicating carriage moves, using the center shape for illustration purposes and beginning with COR

directionif beginning with COL, simply flip the image horizontally direction flip


The yarns used were “throw away acrylics” in white and red. The green is a rayon chenille, which required a looser tension, resulting in the other colors looser than I would want in a final fabric

idea for a larger image in the process of being editedscreenshot_07

A possible sequence in knitting if it is to be executed as shown. The arrow marks rows that knit all needles across the width of the piece. The piece segments are  numbered to create a starting line for later joining.
numbered1If the goal is knitting as close to a flat circle as possible, eliminating rows will create a smaller center hole as well after the form is completed and seamed. Knitting segments 1-6 should be adequatecircle2In larger pieces ie shawls, adding knit rows without adding stitches can be done by altering #8, 1, 6, 7. Red line indicates changing angles. Blue and green lines below indicate increasing rows knit at center of shapes as a result. exteded

Knitting and cast on sequences flow around left purl edge, straight or diagonal edges on a chart such as above may become foundation rows that are later seamed. Sort out your sequence and preferences on smaller swatches, keeping notes as you go. Additional shaping can happen along the edges of any plain knit rows between shapes by increasing or decreasing on either or both sides to create crescent shapes  or triangle variants.

Now a quandary if gauge matters: knit stitches are not square. One option is to generate a grid appropriate graph paper. In holding sequences happen in 2 row sequences. Graph paper cells may be created at twice the height desired. Each rectangle will represent a single stitch, 2 row sequence. To create your own knitting graph paper in excel please see post as a place to start. A common knit ratio is 4W X 6H. An editable workbook in 2W X 6H ratio that takes into account following outline in 2 row holding sequences: landscape2X6. Links for designing knit graph papers online:

Using the 4X6 model reduced to 2X3 this is a sample generated using excel, with borders in a 2X6 ratio, so in execution, each single cell represents one stitch and 2 rows knit. The shape is one from the shape menu in the program, easily resized. The yellow bars show the gradations in holding. These cells are too small for adding text within the program itself. The math can be double checked: there are 70 stitches, 34 rows in the rectangle at the center of the shape. Holding happens over 5 chart units (10 rows actual knitting) at the top and bottom of the center shape; 70/5 = 14 X5, matching the drawing shape on grid

the accompanying, editable workbook Excel 2008  landscape2X6

So the goal is a shawl or garment, graph paper is becoming impractical to follow? Time to pull out your knit leader. Draw out each wedge or piece full size, number  segments breaking sections into knitting sequences, and let the KL guide you. For consistency, if the same shape is to be repeated many times and accuracy matters, it may be worth “air knitting” it while noting shaping as you go, keeping a row by row flow chart. An editable workbook to help track holding patterns, increases, decreases, etc. as a starting point for your own preferences: tracking knit.

Gauge or shape do not matter? time to scrumble it all and be surprised!



Revisiting miters, spirals, going square, round, and more

I am working on updating my flickr photostream albums, including “all things holding” and will be revisiting posts on this topic over  the next few weeks, possibly adding edits.

There are times in knitting when math becomes a necessity. With online libraries, tools, and fairly intuitive software, drafting angles and shapes is now much easier. I will be teaching a class that includes miters and spirals at a seminar next month, leading me to revisiting the topic. Most published pattern instructions will give starting carriage locations, but shapes may be constructed counter clockwise or clockwise depending on preference. With understanding of how the shapes are formed and stacked, they may in turn be automated (depending on their size and the type of km) using the slip stitch setting. Stitches that are to be knit on each row are programmed as pixels, black squares, or punched holes.

Miter shaping may occur on side or in center of each triangular shape; a minimum of 2 knit rows usually occur at designated spots. Adding more knit rows and playing with angles of triangles will create ruffling effects, other angular shapes, pleats, and more. I have returned to using  Mac Numbers, their shapes and charts to generate most of the images below. Here the colored areas represent knit stitches, white negative (white) spaces stitches in hold. Red lines represent all knit row(s)/ spots for seaming at top and bottom of sequences. Seaming is easiest when done by joining all knit rows. Stitches are always brought into hold opposite the carriage side, returned to work on carriage side. In shaping guide, COL= carriage on left, COR= carriage on right.

knitting each segment

COR                                   COLwedges

Yellow triangle segment: bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work. Green triangle segment: with all the needles in work, begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold.

If seaming is desired in miter shaping with resulting eyelets at sides of triangle, the full wedge is split between the top (yellow segment) and the bottom of the piece (green segment). Knitting always starts with at least one or 2 rows of knitting (depending on whether the finished shape is to have a grafted seam.  For the full wedge: * yellow segment, bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work. Reverse shaping with green segment: with all the needles in work, begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold. End with knit rows (red line) across all stitches*. Repeat  from * to * for desired number of full segments, end at top with a yellow segment if needed, followed with knit row(s) (red line) before binding off or seaming.

shaping with resulting eyelets at sides of triangle: the final shape COReyelet at sidethe knitting sequence with top/bottom 1/2 triangle segments shown

COR                                   COLfinal at sides

For miter with shaping and resulting eyelets at center of triangle: begin with all knit row(s) (red line) at the start. To shape full wedge: *green segment is worked bringing stitches into hold opposite the carriage at the determined rate until all the needles are in hold. Shaping is next reversed with yellow segment, pushing needles back at the determined rate until all needles are returned to work. End with all knit rows (red line) *. The sides of this miter are all knit rows, an easier place to seam/ graft joins if needed.

shaping with resulting eyelets at center of triangle: the final shape COReyelet at center2the knitting sequence

COR                             COLfinal at center

a tiny test

shaping at side                              shaping at center



In the following images the red or blue lines indicate seams or joins

segments composing a square shape 
adding squares or rectangles to alter the square
squarextra_seamsadding triangular segments: hexagonpentagon_seamexpanding it with rectangles, shaping at sides
dodecadon extra_seams2shaping at centerhexagon extra_seamsgoing 3D: triangular pocket with point at center 3dmiter

combining shapes: this one is often seen in tams (hats); bottom shaping is on only one side, at the top it occurs on both sides


tam2adding rectangles or squares to alter shape


bringing needles out to hold opposite carriage

Spiral stack 1/ green full triangle : knit row (s), *with all the needles in work begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold, end with all knit row(s) (red line).

COR                                   COLspiral stack1 cor

Spiral stack 2yellow full triangle:  knit row (s), *bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work, end with all knit row(s) (red line).

COR                                   COLfull stack 2

3D spiral 3Dspiral

If the object is to construct a circular shape, the greater the number of panels, the smoother the outer edge of the piece . Some of the pie-bilities: so many pies

In all instances above the radius and therefore 2 sides of each wedge remain equal in size, and therefore are composed of the same number of stitches. The triangle knit to achieve these shapes are isosceles triangles, where 2 of 3 sides are equal in length and in this case, number of stitches. The 2 equal sides are usually referred as legs, the remaining one as the base. The 2 base angles are equal as well. The remaining angle is the vertex one. In knitting, this will be the pivot point for the wedges, the center point of the “pie” shape. In the illustrations below the vertex angles are marked by blue dots. Its angle value is the first represented in the numbers immediately below each shape, with the other 2 numbers indicating the remaining, equal 2 angles. The sum of all 3 should equal 180 degrees.all anglesTaking it to a shape: octagon (half the total # of wedges shown). In colored shapes spiral, stacking equal triangles is shown on left; full triangle, divided into 2 segment shaping for miter on right.octagon col

Oh, yes, the math! The desired shape may be drawn to scale using any number of tools. Wedges may in turn be shaped following the scale drawing on any charting device such as knit-leaders, or stitches and rows required may be calculated on actual full drawing measurements. In knitting, the equal sides (AC, AB) of the triangles are formed by stitches, the height of the triangle (CB) by rows. If finished size matters, accurate gauge is required. One approach to calculating the base (CB) is to think of the whole shape as a complete circle, in this case divided into 8 “pie” wedges, with congruent sides (radius) measuring 10 inches each. To find the circumference of the circle, multiply the diameter (20) inches by pi 3.14 = the total in this case, of 62.8, rounded off to 63. Divide that number by the number of sections (8) = 7.85, rounded off to 8 inches (rows). If stitch gauge is 6 stitches and 8 rows per inch, each triangle would be 60 stitches wide, 64 rows high. Holding happens every other row, opposite the carriage, so total number of rows is divided by 2 = 32 for knitting a spiral. The stitches are distributed along one edge over the total 64 rows in height. The goal is to reduce shape down to the next to last group, followed by two rows knit over all the stitches at the end of each section. This will cause a small hole at the center of each completed pie due to extra rows knit. For a miter 2 triangular shapes are required for each wedge, so holding sequences are recalculated with shaping now occurring over 16 rows for knitting a miter. screenshot_09 color

An online calculator is available to help calculate the number of stitches brought into hold opposite the carriage or into work on carriage side, sequence preference should be tested on swatches where gauge is significant

  spiral screenshot_02miter Miter online

Magic formula (X represents times)magic formula

In the photo below I chose to start with all the needles out to hold,  pushing them back into work across the knit for the spiral. For the miter again, I began with all needles in hold, pushing back the required needles into work; for the top half of each wedge needles were returned to hold opposite the carriage at the same rate, forming the upper half of the “pie slice”. The swatch is not worked at the same rate as shapes calculated above. It is shown on its purl side with color changes to highlight the intersections where wedges begin to repeat. The yarns used are random acrylics, in different weights. photo miter spiral

A previous post on short row knitting from with links to other online sources A category search in my blog roll for miters and spirals will link to blog posts including pies:  breaking and mixing up pie wedges: . A garter bar short row trim: Charting shapes: using Gimp and Mac Numbers:  . Executable charts, shapes, automating with slip stitch:

Cellular automata charts for knitting, etc.

I have written before on the fact that since my knitting is done primarily on a Brother 910 and a Brother punchcard models, I am ever curious re and exploring ways to produce charted images that will allow me to knit patterns via mylars or punchcards, with an occasional wincrea download to my Passap via an ancient laptop. My eternal wish list to date has included the option to download to a hacked Brother model I already own, or to my Passap, directly from my Mac (presently Mavericks OS). Mathematical knits via hacked or commercial knitting machine use have been explored by some, including Claire Williams  and Fabienne. With the help of online generators, even with a lack of understanding of the math involved, one can produce charts for knitting or other textile applications.

Wolfram  site is a resource for both Mac and Windows platform users who are interested in math, computation and its visual results. There is a downloadable CDF player that allows exploration of documents and provides for download, CDF format explained, demonstrations projects, search for cellular automata. Below are some samples obtained through browsing the site. In some instances show mesh option will provide a gridded motif, show scale will indicate “stitch counts”


then there is this

screenshot_31an isolated segment
screenshot_30the image  in Photoshop (CS3) photoshop no gridas it appears with program’s self color adjusted grid photoshop gridGIMPGIMP_cellular2creating a colored grid grid for easier countsgimp color grid

see previous blogposts on isolating repeats, drawing additional markings, and other uses for GIMP.

A visual guide to  automata “rules”

Weaving drafts as inspiration for other textile techniques

Weaving drafts can be a source of inspiration for other textile mediums as well. Luminescence is an online weaving program developed by Andrew Glassner. There are ample instructions and help files on site re weaving. My first instinct however, is often to interpret images of all sorts for knits (I abandoned weaving many a year ago). I am sharing some very quick first experiments with the software with that possible intention. The same charts might be used for other counted stitch unit textiles. The first draft I chose to load from the app’s pull down menu was called High Seas. The numbers indicate “Fabric Size”

120High Seas120

Quoting from the help files: “Show grids: This is another cosmetic choice. Turning this on draws the internal grid lines for all 6 grids (warp pattern, warp colors, weft pattern, weft colors, tie-up, and fabric). These let you easily count the cells, which can make it easier to match a published draft. As with Show threads, this checkbox and its effect are disabled if the Fabric size is 100 or more.” “

“To save an image of the fabric, just right-click on it. You should get a pop-up menu that offers you a few options. One of these will be Save Image As… (or something close to that). Choose that, and you’ll get a standard dialog box that lets you put the image where you want it. The image is saved in the standard PNG format, which offers the highest quality. You can change that to JPG or anything else using almost any image editing program.” Safari in Mac Mavericks was problematic with saves, allowing only for a web archive or screen crop/ capture. No issues using Firefox as the browser.

99 Hi seas99easier to see and/ or count units, clear tiling: 60hig seas 60enough to easily sort out repeats: 30hi seas30

your preferred paint program may be used to draw lines that isolate single “knit” repeats; threading and tie up sequence repeats are used as guides, making process fairly straightforward

hi seas30 repeatimagining possible related borders screenshot_51a more complicated draftkiss me you fool 99isolating the much larger repeat kiss me you fool REPEAT

kiss me REPEAT

always double check tiling prior to knitting for accuracy, any “surprises”, and possible pattern placement on knitting machine’s needle bedtile check

got a draft from an online pub? always good to start simplescreenshot_01isolate the repeat (GIMP):  crop tool and size control154crop

in this instance the result is a 154X 154 pixel square image, with 14 X 14 unit desired subdivision, making my grid  preferences setting 11 X 11 pixels

200_11_11gridtiling test: looks like a match!tiled_04

line width, colors, etc. may all be set and changed to suit individual needs and preferences. Please note superimposed grid lines are lost when image is tiled or exported from GIMP, some version of screen grab or snap must be used to capture and save gridded images

an additional draft, same process


second sample



A bit on the charting: after launching the program and loading an image, the GIMP windows options will become available. I leave my toolbox always active. Tool Options give the opportunity for controlling crop size, pencil line width, etc. As you click on/ select any tool, the option windows will change and offer selections for managing that particular tool

windowscropcroppencil brushpencil

notes from a  previous post on charting for straight line drawing on Mac: “first select color and pencil tool. Place a pencil dot where you want the line to start. If you press the shift key, a cross hair will appear, press the command key in turn as well for straight line mode, click where you want the line to end. Consecutive clicks will continue drawing straight lines that originate from the end of the last line. Pressing both the shift and the command one at once after the initial pencil mark will call up the color picker and require a color selection and an OK”