Two Kinds of Magic

Illusion knitting seems like magic. Things appear and disappear. A Kind of Magic is also the name of the chorus who became National Mixed Chorus Champions 2019 at the British Association of Barbershop Singers Convention. The chorus was an amalgamation of The Cottontown Chorus and Amersham A Cappella. Steve designed a wall-hanging to commemorate this fantastic win.

The video shows how the image in illusion knitting changes as your view changes. Watch the video with your sound turned on as the soundtrack is of the same two choruses singing in eight-part harmony at a rehearsal of It’s a Kind of Magic.

Both choruses are multi-medal winners in their own right. A couple of years ago they sang two songs together in eight-part harmony. For such talented groups that was comparatively easy because they were able to learn the two halves separately with one combined rehearsal at the last minute. The two songs were The Climb and It’s a Kind of Magic.

Their competition pieces were much more difficult. The rules for competition Barbershop are quite strict. Only four parts are allowed. Generally speaking this means that many of the men have to sing lower parts than they usually do and many of the women have to move upwards. It was quite challenging and made even more so because the two groups are 200 miles apart and they only had one real-life rehearsal. (For more info, and to watch the two competition songs, go to this previous post.)

In the bar, in the evening after the win, one of the Amersham ladies said, ‘Are you the person who was knitting at the rehearsal?’ It suddenly seemed a good idea to make something specially for the chorus so, as soon as we got home, Steve set about designing a shawl/wall-hanging, incorporating the Amersham logo and the words A Kind of Magic.

Finding the right yarn was tricky. We wanted purple and white (because these are Amersham’s colours) – with sparkles. We went on a journey and managed to find Woolcraft Diamonds. Amazingly, today, we went into our local branch of Poundstretcher and they had some yarn. There must have been less than 100 balls in total. Two were white and sparkly, two were purple and sparkly! (For those who don’t know, Poundstretcher is a cheap British store that sells a very odd mixture of things.)

Small block letters are quite easy to do in illusion knitting. Fancy writing is more tricky. It has to be big to be able to show the small details of the font. There was just enough room to fit the lettering onto a shawl. Although it can be worn as a shawl, it is much more impressive when it is seen flat. When someone wears the shawl you only see flashes of some of the lettering. It has a channel at the top so it can be hung on a pole.

We do not often add a fringe to a shawl but it seemed a nice finishing touch this time. There are as many pieces of fringe as there are stripes. The strands line up with the stripes.

Whenever Amersham go on stage in a competition they take a Barbie doll dressed to match their stage costume. I don’t usually make doll clothes but thought it was only right that Barbie should have a shawl. She looked a bit strange with just a shawl so she also got a dress, hat and boots.

Barbie is too small to show any kind of illusion but the dress and shawl use illusion techniques to make the purple appear more prominent in the shawl and the white more noticeable in the dress.

Barbie wouldn’t stand up to have her photograph taken. Steve downloaded a file from Thingiverse to 3D print a stand for her. It had a support that went round her waist so it spoiled the effect of the stripes in her dress. He used the base of the original stand with a shorter piece for her to lean against.

The pattern for the Amersham shawl will be of little interest to anyone other than Amersham members but it is available for anyone to download from Ravelry.
The Barbie pattern is also available as a free download.

Flatland Lock

About ten years ago we came across a puzzle called Bank Raid, in Leonardo’s Mirror & Other Puzzles by Ivan Moscovich.

The puzzle itself was inspired by the 2- dimensional world of Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott.

At the time we made a crochet blanket. Obviously it was not possible to physically move the pieces so it was just a reasoning puzzle.

I have now gone back to it to make a version where you can actually move the pieces.

The complete puzzle.

The lid is fixed to the base at the four corners. The sides of the frame are open for the pieces to slide out.

The four pieces of the lock can move up, down, left and right.

How do you remove all the pieces?

One of the photos below shows the complete shapes of the four pieces; the other shows what you see when the lid is not in place.

The four pieces
What you see when the lid is not fixed on

The files for making the puzzle can be downloaded from Thingiverse or Pinshape.

There are six pieces in total
The studs on the back allow the pieces to move along the grooves in the base

The video shows the solution

You can download the afghan pattern from Ravelry

More Needle Gauges (4)

This is my last board of gauges. They tend to be oddments that didn’t quite fit with anything else. Most are plastic. Many were given away with various magazines.

Inox Calculator + Counting Frame
This is quite complex. The holes are metric sizes from 1.5 mm to 10 mm. In the photo all the smaller sizes are under the red pointer so very few holes are easily accessible. All of the instructions are in English, French and German so it is very crowded. There are 10 cm rulers for rows and stitches, and another 14 cm ruler. On the pointer it says Take reading of stitches or rows and it is numbered from 1 to 10, then in tens up to 100. It points at numbers from 8 to 49. The instructions say:

  • Example
  • counted: 24 stitches at 10 cm
  • adjust: pointer to 24
  • required: number of stitches at 55 cm
  • take at 50 cm = 120 stitches
  • reading: at 5 cm = 12 stitches
  • result: at 55 cm = 132 stitches

I think this assumes that you already know the width of the piece of knitting you want to make. You then count the number of stitches you knit in a 10 cm square and it calculates how many stitches you need in total.

A simple square with a 10 cm measuring square and holes from 2 mm to 10 mm.

Woman’s Own (Small square inside Addi)
Free with magazine. Slot for needle sizes is marked with UK sizes 1 to 17. On the back the metric sizes are 1½, 2, 2½, 3, 3½, 4, 4½, 5, 6, and 7. These don’t correspond to UK sizes and would be very difficult to use with any accuracy.
It also has a 1-inch/2.5 cm square and three sliders, with no labels. One is marked 0 to 4, the others 0 to 9.

  • Zero – safe for washing all woollens (I have never heard of Zero)
  • Woman’s Day Knitting Know-all
  • Woman’s Realm Home Sewing and Knitting (Two alike in slightly different colours)

These four are very similar. They were all given free. The information is the same on all. The slots are UK 6 to 14.There is a 1-inch hole and a 3-inch ruler. The tables are for No. of Needle, 2-Ply Stitches and Rows, 3-Ply Stitches and Rows, on one side, and for 4-Ply and DK on the back. The DK column for needle sizes 13 and 14 is blank.

The first five are bobbins for winding small amounts of yarn onto – which would make them tricky for measuring needles. The blue ones are called My Home Busy Bobbin and have needle sizes 5 and 13, 7 and 11, and 9 and 10. I don’t know whether there were more to complete a set. The others are alike, with no name. The sizes are 8 to 13.

The curved yellow one is called Reetidi. I do not know how it was intended to be used, or what the protruding clip is for. It says Presented free with My Home & Family Patent applied for No 35858/66 The hole sizes are 6 to 14.

The yellow rectangle is from Woman’s Weekly. The holes are sizes 000 to 14, with metric equivalents. The 10 cm slot has small pointers at each cm.

Blue rectangle is Patons (with a small picture of a beehive). It has 2-inch measuring slits. The holes are metric sizes 2 mm to 10 mm, and also numbered with US sizes for needles, and letters for hooks.

The hat shape is Clover, from Japan. The sizes are US and metric, from 2 mm to 15 mm.

The two little I needle u people are alike. The holes sizes, which are randomly arranged are from 2 mm to 6 mm.

The sock shape is made of wood, which seems to have become a trend since the advent of laser cutting machines. It is by Blue Willow Enterprises of Idaho. It says Knitting products designed and tested by a Knitter. The holes are in metric and US sizes, from 2 mm to 9 mm. It is a little strange as it gives both 3.0 mm and 3.25 mm as being US size 3.

The metal sheep is Goose Pond 2004. It has metric and US sizes from 1.25 mm to 10 mm. It has 2-inch measuring slots.

The transparent rectangle is from Woman. It is probably intended to slide over a pattern to mark your place. It seems to have something missing from the circular ring of numbers, which go from 1 to 12. On one edge there are holes are numbered with metric and English sizes from 2 mm to 7½ mm, and a 6-inch ruler. Along the other edge it has the comparative sizes of new and old crochet hooks, and a 12 cm ruler.
The strangely shaped corner looks as though it could also have something missing. It also has a triangle marked with the part to the cut-out as 1″ and the uncut part as 3 cm.

The two white gauges are very similar. One is called Turbo Needlegauge Skacel Collection, the other is Handwerken zonder grenzen. They both have a blade that slides out of a channel on the back. Handwerken is marked with metric sizes; Turbo has metric and US sizes. Both are from 1.5 mm to 10 mm, but Turbo has one more hole. Interestingly Turbo says approx against its needle sizes. I have not seen this on any other gauge.
The measure at the top is in millimetres on the Handwerken and inches and millimetres on the Turbo.

All of these were given away with magazines but are not all named. From the top down:

Regd. Design – Pat. Applied for – Made in England. It looks as though it originally had a piece to slide over a pattern. The dial on the end counts rows from 1 to 16. Hole sizes are 1 to 14. It has a 6-inch ruler.

The next two are alike, but different colours. One has a piece missing. The curves at the top are for measuring English Sizes crochet hooks from 1 to 12, on the front, with metric sizes on the back. The large slot at the bottom is for needles from 1 to 12. Unfortunately, on the pale blue version, the 1 is missing from 12 so it says 2. It has rulers on both sides and is also labelled as a Tassel Frame.

My Home Row Counter, with no measuring gauges.

Holes from 1 to 18 with a 1-inch measuring slot.

New Crochet Sizes 2.5 mm to 5.5 mm.

Knit’n Sew Time Saver Designed by Woman and Home. It has UK needle holes 1 to 16, a 4-inch ruler, a 1-inch square and various cut-outs for measuring scallops, seam allowances, button spacing, etc.

The crochet sizer above is part of one of these. The long pointed part at the bottom is labelled as 45° Mitre. It also has three holes marked as Button Markers. The functions of the other pieces can only be guessed at.

At the top are two metal miniature gauges. The flat one says Miniature Knitting & Rug Supplies and is from an address in Lancashire, UK. The holes are UK, US and metric. The metric sizes are from 0.50 mm to 2 mm. The heavy circular one is numbered 16 to 24.

Ganute (? script is difficult to read) – small triangle. Hole sizes numbered 1 to 15.

Polysew – large triangle. UK (000 to 14) on one side, metric on the other.

Owl shape (no name). Metric & US Hook Sizes. The labelling is quite complicated. Some holes have just a number; others have a number and letter e.g. 20&S; others have number, letter and number e.g. 6.5&K/10.5.

Woman. There are six slots labelled Tricot No.3, 2.50 + 2.00, 3.50 + 3.00, 4.50 + 4.00, 5.50 + 5.00, 7.00 + 6.00.

Stratnoid Made in England Pat. Pending. This was made in the 1950s and is unusual for that time as it has UK and metric labels.The slot measures from 1 to 16. It is different from other gauges with slots like this as it has notches for the needle sizes.

“MP” Handy Guide For Knitting & Crochet. British Made. Reg No 813814. People often think these are rare, perhaps because they are bigger and more elaborate than most gauges. In fact they turn up quite often in charity shops and car boot sales. They have lasted well because they are so substantial. They also came in a bronze colour.
The columns are headed Rows, Increase, Times. Instructions are on the back. The hole sizes are 6 to 12.

Addi circular needle card has a measuring slot for needles from 2 mm to 8 mm. I imagine this would soon get distorted if used.

Hjertegarn Made in Denmark. The holes are UK and metric from 2 mm to 10 mm. I do not know the purpose of the sliders, or why it has a hanging loop at the end.

These are the last of my knitting needle gauges. Click here to see all the others.

World Wide Knit in Public Day

Next Saturday (June 8th) is World Wide Knit in Public Day. It is an annual event that takes place every year on the second Saturday in June. The aim is to promote knitting, and other fibrecrafts, and to help dispel some of the old preconceptions. Knitters are not little old ladies making bedsocks. There are many types of knitters of all genders, ages, nationalities, etc. and some of them do very unexpected things.

The day takes several different forms. In some places there are large-scale organised community projects. It is entirely down to individuals, or groups, as to how they show their craft. Some groups also promote the therapeutic benefits of a relaxing craft.

World Wide Knit in Public Day became ‘a thing’ in 2005 but that isn’t where it began. In 2002 the Knitting and Crochet Guild, in UK, organised Knitting at Noon when all guild members were encouraged to knit, at mid-day, in their local communities. It was a forerunner of the world-wide event. There may have been others.

Steve drew this cartoon, in 2002, for the Guild to promote the event.

A Kind of Magic

Steve has been pursuing his other passion – Barbershop singing. He belongs to Cottontown Chorus, from Bolton, who have been National Chorus Champions seven times, most recently in 2018.

Last weekend they had to relinquish their crown at the annual convention of the British Association of Barbershop Singers (BABS).

As retiring champions they were barred from the competition but it was still a very busy weekend. On Friday evening they performed in a show. On Saturday they were up for breakfast at 6.15 to start rehearsing ready to open the chorus competition at 10. Then they were able to relax a little and listen to some of the other choruses, before being whisked off again at 3 to prepare for the closing ceremony at 6. From a field of 35 choruses the new champions were Hallmark of Harmony, from Sheffield.

In a normal year the ten songs they had sung would have been the end but this year was very different from usual. As with so many other organisations BABS (previously only for men) has been making moves to include women so there is now a Mixed Chorus competition. (LABBS, and Sweet Adelines Region 31 are long-established separate organisations for women.)

Cottontown Chorus joined forces with Amersham A Cappella to form a new chorus called A Kind of Magic. It wasn’t easy because usually, when two choruses meet, they sing in eight-part harmony but this had to be pure barbershop four-part harmony. Many people had to learn a part they don’t normally sing. It was made even more difficult as the two choruses are based 200 miles apart and only had one rehearsal until the day of the competition.

The preparation was a closely guarded secret. I was at the rehearsal day, in March, when it was obviously going to be good but still a long way from being a polished performance. A great deal of time, dedication, and effort, would be needed to pull it all together.

The next two months of rehearsals were done in the two halves. Thank goodness for social media. Facebook and YouTube were kept in business, with videos constantly going backwards and forwards.

The ladies were fortunate to get a token man at one of their rehearsals:

Ash was playing the part of twelve men:

On the day of the competition they started rehearsing at 8.30 ready to be on stage at 12.20, singing fifth in a line-up of ten. I was able to listen to all the performances and particularly liked Endeavour, who came second. I was also impressed by MUBS (a young chorus from Manchester University), who came fourth.

Most of the choruses were fairly small. A Kind of Magic had 107 and it took forever for them to get onto the risers but it was very slick and everyone knew exactly where they had to be to fit on. The size of the chorus made them very different from all the others but it was the atmosphere they created, not the size, that made them really impressive. After they had performed their two songs the audience erupted, almost everyone in the auditorium was on their feet, and it was obvious that we had just seen a gold medal performance.

It was definitely some kind of magic. You can judge for yourself:

At the end of the competition the two musical directors, Neil Firth and Helen Lappert, were presented with the trophy.

Later, behind the scenes, each member of the chorus was presented with a medal, as it would have taken far too long to give them out on stage.

Then they had to do it all again in the evening on the Champions Show along with two other songs in eight-part harmony, one of them being “A Kind of Magic”.

If you would like to view other convention weekend performances, of choruses and quartets, go to the On Demand Service pages. Cottontown Chorus are first and last on this page.

There are Barbershop choruses across the country and all welcome new members at any time.

The Great Pyramid

Almost nine years ago Steve designed, and knitted, an illusion of the Great Pyramid and Sphinx. He constantly looks for new challenges and this was a very early one. At the time he wrote:

“I’ve been looking, for a while, for a recognisable landscape or place to try as an illusion knit. The Great Pyramid and Sphinx seemed a good idea as it is a view known to many.

The illusion has been designed to be viewed from the side so is intended to be a wall hanging but could easily be incorporated into a design for a bedspread or table runner.”

He was pleased with the result. Photographs never do justice to illusion knitting. They have to be seen in real-life to appreciate how much they change as you move past them. For a better impression view an animation on our web site. (The animation is not on this page because some people do not like moving images.)

This is what you see from directly in front.

About four years ago the original piece was acquired by Ripley’s Believe It Or Not! Then, a few weeks ago, they asked for another (I don’t know why they need two copies of the same illusion.)

Steve knitted the original, I knitted the second. I calculated that it took about 70 hours to knit. The finished piece measures approximately 89 cm x 58 cm (35” x 23”). Eventually we may find out where this can be seen.

The pattern is available on Ravelry.

More Needle Gauges (3)

Many of these gauges are relatively modern. The organisation is not always completely logical as there are so many different ways the gauges could be grouped together. 

This board has my two favourite gauges. I love them because they are so wrong. Can you spot them?

Part of the reason I originally started collecting gauges was that they are not always as reliable as you might hope. As a mathematician, I want things to be precise. As a knitter, I want things to work out properly. Needle gauges, whether they are accurate or not, can only give you a size for the needles. They do not automatically help create the right size stitches to make a garment come out at the correct size.

Six of these are alike. Only the colours are different. I believe they are French. They have metric sizes from 1.5 mm to 9 mm on one side, and corresponding English sizes on the other, leaving unmarked holes where there is no English equivalent. They are like giant paperclips so you could use them to mark your place on the pattern.

The centre gauge says HD-100 Made in Taiwan. It has English sizes 00 to 14.

These are my favourites! How can anything designed for measuring ‘accurately’ be so wrong?

They are called M-P Knitting Needle Gauge Glove and Sock Measure.

If you only had one of these you would probably believe all that it was telling you. It is obvious in the photo that they are not the same length. They claim to be 12″ long. One is about 11½”, the other is slightly over 12″. They are in three sections and can be folded. This is not the cause of the discrepancy.

Trying to match the holes shows that those in the white one are smaller than those in the brown though the numbers are the same. If you move them along one place the holes match. Size 1 on the white measure is size 2 on the brown.

This kind of inaccuracy is not unusual but it is much more obvious in this case because these both come from the same manufacturer. The only sure-fire way of knowing the actual size of a needle is to use calipers. This is not just a problem with old gauges and needles. You will probably find that if you check your expensive new needles with calipers they are not what they say they are.

These five gauges are exactly alike in size and shape but not as similar as they might appear. Four are plastic, one metal.

  • Clover (in packet with Oriental writing). The holes are named as No. and mm. The millimetre sizes do not correspond to sizes used on Western gauges. They begin with 2.1, 2.4, 2.7. The only whole number sizes are 3, 6, 7 and 8 (which is the hole the gauge is hanging from). The other numbers go from 0 to 15.
  • Tailorform. Knitting Gauge – Jauge a Tricoter Made in Canada No 699. This is some form of lightweight metal alloy. On the front the holes are numbered in metric (2 mm to 10 mm), on the back they are American (0 to 15) and Canadian (000 to 14). It has 150 mm rulers on both sides of the front and 6 inch rulers on the back.
  • Unnamed. There are 19 holes marked as Metric (2 mm to 10 mm) and Imperial (000 to 14). On the back it has a 12 cm ruler and a 5 inch ruler.
  • Unnamed. 17 holes which are Metric and Imperial but there are no labels to say so. 12 cm and 5 inch rulers on the back.
  • Lion Brand Yarns. 19 holes. On the front the holes are labelled as Metric and US sizes. On the back they are only labelled as US. The start and end sizes are the same as the previous gauges but it includes 2.5 mm and 3.5 mm.

These ten gauges are basically alike. Eight are plastic, two are metal. One is unusual as it has Braille markings. They all have 19 holes.

  • Milward. Henry Milward & Sons, Studley, Warwickshire, England B80 7AS. Sizes given as mm. There are also numbers for Imperial sizes but it does not say so. The back has nothing but a barcode.
  • As above but with Braille markings. The Imperial sizes have raised dots on the front. US sizes are on the back, with Braille.
  • Called Inox on one side, Prym on the other. From Germany. Metric sizes on the front. On the back the sizes are US and BWG. Imperial sizes were originally defined by the Birmingham Wire Gauge. This later became the Standard Wire Gauge (SWG) but has rarely been labelled as such on gauges. It is now also known as the British Wire Gauge (BWG).
  • Inox on one side, Rump & Prym on the other. Otherwise very similar to previous gauge.
  • Wendy Wools. Very similar to first gauge but it has nothing on the back.
  • Milward (metal). Front says metric and mm. On the back it has Imperial numbers but does not say what they are. In addition to the usual Knitting Pin Gauge, which also appears in French and German on most of these gauges, this one also has Dutch.
  • Milward. Similar to Wendy Wools, with the same red printing, but named in English, French and German.
  • Named as Inox on both sides. US and BWG on one side, mm on the other.
  • Similar to Milward metal. Named as Prym on both sides.
  • Winfield (metal). Metric and Imperial. This does not seem to have been very well made as the numbers are wearing off.

These are all from US. Most are metal.

  • Marcia Lynn. The holes are U.S. Standard Sizes and are marked with numbers for needle sizes (1 to 16) and letters for crochet hook sizes (B to N). Stitch’n Needle 5 in 1 Gauge – Stitches to the inch gauge – Rows to the inch gauge – Knitting needle and crochet hook gauge – 6-inch ruler. It also has detailed instructions for checking your stitch gauge.
  • Susan Bates “Knit-Check”. Very similar to previous gauge. Needle Gauge Stitch Measure Ruler. World’s finest knitting needles. ‘Checking your stitch gauge’ is identical to above.
  • Susan Bates. Identical to Marcia Lynn apart from colour, company name and address.
  • Susan Bates (rectangle). Has all the same information as previous gauge. Only the shape is different.
  • The Boye Needle Company (plastic). US sizes (1 to 15). Knitting Gauge 6″ Ruler 2″ Stitch Measure. It also has detailed instructions to check your gauge.
  • Boye Count 10 Plus. US sizes (0 to 17). It has a slider that ‘calculates’ the number of stitches per inch. The only instruction is Set points at 10 stitches.
  • Boye. World’s Standard of Quality Knitting Pins and Crochet Hooks. The Boye Needle Company New York Chicago San Francisco. Holes 0 to 10½. 3 inch ruler.
  • Two Sears, different only in colour. Original US Standard Knitting Needle Gauge. Sears Roebuck and Co. Made in USA. Holes 0 to 15. 6 inch ruler and Two inch stitch Measure.
  • Two Lacis, different only in colour. They are made from very thin, flexible, plastic. Berkeley, CA (This is the first gauge I have with a website mentioned). Knitting Needle & Crochet Hook Gauge. These have the largest range of sizes that I have ever seen. There are 28 holes. They are for needles and hooks so have letters and numbers in the US sizes. They are also in Metric. The metric sizes are from 0.5 to 20 mm.
  • Unnamed. Knitting Needle Gauge. This is made from discoloured clear plastic. I don’t know how old it is, or where it originated, but it is like the very old clear plastic that used to turn a strange shade of brown.
    It looks almost as though it might have been attached to something else, with two rounded corners at the top and a slightly rough, straight, bottom edge. Holes are, presumably, UK 1 to 17.
  • Inox. US and BWG (000 to 14) on one side, Metric on the other. Very similar to the Inox gauges above, apart from the shape.
  • Unnamed. This is plastic made to resemble bone, with transfers of flowers that are beginning to wear off. The only printing is for the hole sizes, which are rather unusual. The smallest is ½, then they go up to 10 in whole numbers, with 11 above the flowers.
  • Perlac. Sizes 2 – 10 (Metric). 20 cm ruler.
  • Ariel Atan. 11 holes (Metric), sizes 2 to 9.
  • Good Shepherd Fingering Yarns. This is made of the same material, and has the same numbers, as the gauge with the flowers.

Klein Bottles

You have probably heard of Klein bottles before but may not know that a Klein bottle is like two opposite Möbius strips joined together.

A few years ago we made a knitted Klein bottle hat, in two colours to make it obvious how the pieces joined.


I wanted to make a 3D printed Klein bottle in a similar way.

It was trial and error. My first attempt was very messy. I used white supports for blue filament so a lot of white was left on the finished model. The channels on the ‘inside’ of the bottle were too narrow. The walls were too thin so the walls were uneven.

For my second attempt I used supports that matched the model so, when they were broken off, it wasn’t so obvious where they had been. The walls were still too thin.

Perhaps the way to go was to make a model that didn’t need supports. This is much easier to do with a gently sloping surface rather than curved edges.

It worked but the shape was not how you would expect a Klein bottle to be.

I needed a complete change of plan to get a rounded shape. Instead of building the pieces from the bottom up, I started from the flat edge where the pieces would eventually be joined together. The advantage of this was that all the supports would be on the inside so would not really show if they did not break away cleanly.

I could make thicker walls because they were well-supported. I also made wider channels.

Squiggly Things

A few months ago I made some ‘Squiggly Things’. They don’t have a proper name but they are a form of hyperbolic crochet and great fun to make. They are nice toys for children or for stress-relief. They are very tactile and can be twisted and turned without getting damaged.

This week someone asked me a question that made me go back and look at them again. (See below)

My squiggles were colour-coded. The first were made with orange edges. Every stitch is increased to make two stitches. Some were started with chains, some with circles. Adding more rows of crochet makes the shapes curl and become more densely packed.

The question that was asked was ‘How do you work out the area of a squiggle?’ We assumed that this meant what would the area be if you could measure the surface of one side of all the twists in the squiggle.

Interestingly, after the first few rounds of crochet, the overall shape of a round squiggle doesn’t change much. The ‘ball’ just become more and more tightly packed but there is clearly much more surface inside.

The best attempt at calculating the area can only be an approximation as there are strange factors to be taken into account. It is easy to work out the number of stitches. If the squiggle begins with 6 stitches and an increase is made in each stitch, the number of stitches doubles on each round.

  • Round 1 = 6 stitches
  • Round 2 = 12 stitches. Total = 6 + 12 = 18
  • Round 3 = 24 stitches. Total = 6 + 12 + 24 = 42
  • Round 4 = 48 stitches. Total = 6 + 12 + 24 + 48 = 90
  • Round 5 = 96 stitches. Total = 6 + 12 + 24 + 48 + 96 = 186
  • Round 6 = 192 stitches. Total = 6 + 12 + 24 + 48 + 96 + 192 = 378

If you know the area of each stitch you can then calculate the total area worked so far.

Or can you?

All of the stitches are worked into the top of existing stitches but what happens to the tops of the stitches on the top row? Do the stitches on the top row have a greater area than the rest because they are not sharing any space with other stitches?

Wool is squashy. The bottoms of the stitches are squashed together and the tops are more spread out. Does this mean they have more volume but no more area? Does volume matter at all if we are calculating the surface area?

I don’t think there can be an accurate answer to the question.

After pondering these questions, I moved on to thinking about the squiggles I made with different rates of increase. When I made them I was very surprised by how a seemingly small change made a dramatic difference. Then we made a video to try to show what happens. The three-section squiggle shows the changes and the table shows the maths behind it.

My favourite squiggles are the rainbows in this video

I made lots of squiggles. In my Ravelry projects you can see photos and find information such as the amount of yarn needed for each:
1 2 3 4 5 6

If you want to know about the maths of hyperbolic crochet, look up the work of Daina Taimina. She is the expert.

The problem of calculating the area is closely related to the Coastline Paradox and the Wheat and Chessboard Problem.

Download the free pattern

More Needle Gauges (2)

Another board full of gauges. Again the order is not always logical. There are gauges on other boards that have close links to some of these. (Click knitting tools in the tags, or categories, to see posts about other gauges.)

Left-hand Column
The gauges are all the same size and shape with a one-inch measuring slot and holes from 1 to 16. They also have a six-inch ruler along one edge. Emu and WB (William Briggs) are identical apart from the printing so were probably made by the same manufacturer. The other four are all alike and may all be of Canadian origin – Rayolith, unnamed, Magic Baking Powder, Nabob Irradiated Coffee.

These celluloid gauges were cheap to make and were probably all given as free gifts. They are flexible and difficult to break but they have the disadvantage that the writing sometimes wears off.

Right-hand Column
The three gauges at the top are from Canada. They have American and Canadian sizes. They are very similar in format.

  • Elgin Group of Hotels. It has pictures of the Lord Elgin Hotel, Ottawa and the Laurentien Hotel, Montreal. Lord Elgin was built in 1941 and Laurentien in 1947 so the gauge probably dates from the late 1940s. It seems a strange gift for a hotel to give.
  • Bouquet by Dominion Woollens. This company went into receivership in 1959 so the gauge is probably earlier than that.
  • PK Mothproof Wools.

Two metal gauges

  • The first has a badge which says MV Devonshire. I have been able to find information about this ship but have no idea why there should be a souvenir needle gauge.
  • The other says Use Monarch Yarns For Best Results.

Plastic gauges in the form of rulers are very common. They were given as free gifts and the plastic is very strong so they have survived well.

Left-hand Column

  • The top two are Canadian with Canadian sizes (which are the same as British) on one side, and metric on the other. There is no indication where they came from.
  • The white one was given by People’s Friend (which celebrates its 150th anniversary this year). In addition to the ruler and measuring holes, it has a slider and numbers so that you can count rows. It pre-dates metric sizing. The holes are from 3 to 14.
  • Unnamed with metric and UK sizes.
  • Betterwear. These came in many colours. Make Betterwear The Rule. Betterwear Knitting Needle Gauge. Free Gift. Hole sizes 7 to 14.

Right-hand Column

  • Betterwear gauges. The name is not immediately obvious as it is printed on the cut-out part that is meant to act as a bookmark or pattern marker. It says Betterwear Free Gift. On the back it says Knitting Needle Gauges. Hole sizes 7 to 14.

All these are made of cardboard.
  • Knitter’s Companion. Thick card. There are two rotating pointers in the centre. One is labelled Register of Times (1 to 15). The other is Register of Increases or Decreases (1 to 20). The outer circle has numbers from 1 to 50 but no caption. The hole sizes are 6 to 12 and there is a 4 inch ruler.
  • woolmeter Registered Design. One side has UK sizes, a 6 inch ruler and a 2 inch ruler. The holes are the same size as the cut-outs along the edge. The other side (white background with black bars) has metric sizes and ruler. I think it was primarily a metric gauge but there are some anomalies. The UK side has one hole labelled 12/13 and another labelled 9/10. The metric side has no 3.25, which is commonly used in UK but it does have 3.5, which is not standard UK. It also has letters A to O, which are not used in UK. The holes are not stamped accurately within the stripes.
  • Nomotta. Gauge and Interchangeability of Nomotta Yarns. The holes appear to be American sizes. They are from 1 to 9. On the back it says Printed in U.S. Zone of Germany. It could date from about 1949. There is a great deal of information, on the back, about washing, rinsing, blocking, etc.
  • Bear Brand Yarns – Glossilla – Bucilla Yarns and Cottons. This is probably from US. It has three different gauges, which are (1) Actual Sizes of Celluloid Bone and Wood Crochet Hooks and Knitting Needles (2) Actual Sizes of Steel Circular, Steel and Aluminum Knitting Needles. Also Aluminum Crochet Hooks (3) Actual Sizes of Double Pointed Steel Needles. It also lists the sizes all their needles are made in. Both sides are covered in information including helpful advice like To Obtain Best Results Use Only “BUCILLA” Crochet Hooks and Knitting Needles. By Following the Directions Exactly You Will Insure the Correctness Of Your Work
  • English and French versions (with red cross). Compliments of The Yellow Pages of Your Telephone Directory. These seem to be UK sizes 1 to 14 so the gauges probably come from Canada.
  • Compliments of Your Super Yarn & Markets, Inc. On the back it has addresses of seven US stores. US sizes 0 to 15. The first rule for happy knitting is to check your stitch gauge. Knit a swatch and adjust your needle size to give you the correct gauge.
  • Lux Won’t Shrink Woollens. English Gauge. 6 inch ruler. Holes 1 to 16.
  • Doesn’t Your Sweater Need a Dip in Lux Tonight? Very similar to the gauge above but narrower.
  • Betterwear. Very flimsy card with lines drawn on the back. To check the size of your knitting needles lay them on this accurate needle gauge. Sizes are from 1 to 24. This suggests it pre-dates any of the plastic Betterwear gauges. On the front it says Increase your leisure! – use Betterwear The Better Polish. Manufactured only by Betterwear Products Ltd., Romford, Essex.
  • “AT – A – GLANCE” Knitting Counter and Needle Gauge. Very thick card with two rotating discs. Registers any number from 1 to 99. Revolve the discs to show the number required. A “Lazy Rainbow” Product. Patent Applied For. Made in England. It has a 3 inch ruler and holes from 2 to 16.
Five are cardboard. Vogue is plastic
  • The two on the left are exactly alike. They are called Knitting Register. The first two columns are for counting rows (1 – 50); the third column says Increase or Decrease (1 – 20 with some blank spaces at the bottom); the fourth column says Times (1 – 25). The cardboard sliders can be pushed up and down the columns. There is a 5 inch ruler. The holes are from 6 – 12.

On the back it says Knitting Register (With Needle Gauge and Measure)
A Handy Help For The War-Time Knitter
Number indicated is the one above the guide.
To register “Rows completed”, etc., move Guides with finger or with point of needle. After registering 50, go back to 1.
When casting on or casting off, use Increase or Decrease Guide.
When using fancy patterns, etc., use the Times Guide.
Keep Guides not in use on blank spaces.
WILBEE Seeries No. W2

  • The next gauge is very similar except that it is called “Bestway” Knitting Register and does not say it is for the war-time knitter.
  • Family Circle Knitting Gauge looks as though it was intended to be folded but there is no fold line. It has dotted lines on the top and bottom of the front half saying Cut here. I presume the aim is to cut at the top and bottom of the two 4 inch rulers. It was printed in US in 1972. The holes are US sizes 4 to 11. The other section has detailed instructions about knitting a small sample square and using the cut-out square to count the number of stitches and rows.
  • Card with three orange pointers is Woman’s Weekly Knitting Register.
    It was given away with the UK magazine in 1972. It has a 6 inch ruler and a 10 centimetre ruler. Strangely, on the back, the metric ruler begins with 2 inches and a label saying 2 ins = 5 cm. It does not mark 5 cm on the scale and continues from 6 to 15. One corner of back and front is marked as a tension gauge for stitches and rows. The dials are for Rows (40), Increase or Decrease (24) and Times (24). They have markings spaced all round but are only labelled on the quadrants. Hole sizes are 6 to 14. The back has instructions for use:
    Use large dial for registering rows ; when 40 are completed move ‘Times’ dial to 1 and continue counting on large dial.
    Register increases and decreases on centre dial. If both increases and decreases are worked simultaneously use both centre and ‘Times’ dials.
    Use the ‘Times’ dial for counting pattern repeats.
    Push un-numbered needles through the Needle Gauge holes – they should fit closely.
    For checking tension lay the appropriate corner squarely on the knitting and count stitches one way, rows the other.
    50 gramme ball of yarn equals 1¾ ounces.
  • Vogue Knitting To save time, take time to check stitch gauge. This is made of thin plastic. It has a 5 inch ruler, a 16 centimetre ruler, and a cut-out shape, 2 inches in each direction. There are 21 holes; 16 are marked in US sizes, 19 in metric.
Old and modern versions of Boye

Old Boye
Front has a huge amount of information, including a copyright date 1933.
Two gauges. One is for Double Point Steel Pins Only (Sized in millimetres from 1 to 3¾ and Boye from 8 to 18, 8 being the largest); the other is Standard Gauge For Pins Other Than Double Point Steel (Sized in millimetres from 2 to 6½ and Boye from 0 to 10½, with 10½ being the largest)
The cream-coloured ring lists many different yarns, in very small print.
The rotating black bar has a lot of writing. Against one of the windows it says Corresponding Crochet Hook Sizes (Some of the sizes are numbers, some are letters). Another says Number of Stitches (Some of these give the number of stitches in 1″, others are in 2″). The bigger hole says Materials Used.
The sizes of hooks and the number of stitches are on the two green rings under the black bar.

Back has a 1 inch ruler, information about lengths and sizes of all Single Point Steel, Double Point Steel, Single Point Non-inflammable Composition, and Double Point Non-inflammable Composition Circular, needles. It also has lots of helpful advice.
This gauge is regulated to indicate sizes for even, medium, flat knitting, with sizes of crochet hooks to correspond. A tight worker uses one size larger pin or hook – A loose worker one size smaller than gauge specified.
Dont’s (sic) for Knitters. (1) Never bend a circular pin before starting work. It will take its own curvature as work progresses. (2) Never begin work without first making a 2″ sample square to test work. Wash and block, then measure and compare with Stitch Gauge. In measuring work it should be allowed to hang naturally with pin against top edge of yard stick or tape measure. — Always allow 4″ to 5″ more than natural waist measurement so that garment will slip over body.

After reading all that I am surprised anybody ever managed to knit anything.

Modern Boye
3 in 1 Tool, (1) Gauge Check (2) Needle & Hook Check (3) Yarn & Gauge Recommendations
Holes in millimetres from 2.25 to 10.
One rotating dial with five windows – Needle Size, Gauge in Knit per 4 inches, Yarn Weight, Gauge in Crochet per 4 inches, Hook Size. The yarn weights are also listed on icons with numbers.

Two 4 inch rulers to form the sides of a square.
Instructions To Determine Stitch Gauge and To Determine Row Gauge. These are well laid out and much as you would expect.