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Woolly Thoughts
pattern storeeBooks available as Ravelry Downloads
eBook :
12 patterns
Twelve more mathematical designs for cushions. Nine are knitted and three are crochet. Many are smaller versions of Woolly Thoughts afghans.
eBook :
6 patterns
Six afghan-size traditional board games. Patterns are also available individually.
eBook :
12 patterns
Twelve mathematical designs for cushions. Ten are knitted and two are crochet. Many are smaller versions of Woolly Thoughts afghans.
eBook :
4 patterns
Illusion designs for the four floral emblems of UK.
eBook :
4 patterns
Four ‘cushions’ that can all be twisted and turned in some way. They are called cushions but they are really meant to be decorative, or for their novelty interest. It is perfectly safe to sit, or lean, on them but they will not be particularly comfortable.
eBook :
3 patterns
Here Be Dragons is available as one PDF via the Ravelry download on this page. It contains three booklets:
eBook :
6 patterns
Three knit and three crochet hyperbolic hat designs.
eBook :
4 patterns
Four afghan mazes and a cushion. Patterns are also available individually.
eBook :
11 patterns
A collection of ten shawls and scarves with a mathematical flavour.
eBook :
11 patterns
Eleven knit and crochet toilet roll covers based on mathematical concepts. The ebook also has a section that will help you to design your own covers.
eBook :
1 pattern
The sequel to Woolly Thoughts. Includes a variation of the instructions for Cushion Conglomeration Caper.
eBook :
3 patterns
The ebook contains the three linked patterns but also includes a great deal of information about knitting circles. It explains how to knit a perfect circle using your own yarn needles and stitch pattern. It is intended to help you create your own circular designs.
eBook :
3 patterns
Three witches: an illusion, a glove puppet and a toilet roll cover.
Patterns available as Ravelry Downloads
Knitting: Shawl / Wrap
The design on this shawl will only be of interest to the ladies of Amersham A Cappella, as it was created especially for them. However, the striped fringe is not something I usually add to my shawls so that feature might be useful to others.
Knitting: Baby Blanket
It has been a long time since I designed a new baby blanket and people keep asking for more so here is a cute little puppy.
Knitting: Wall Hanging, Blanket - Other
The illusion is based on a work by Russian artist Lodygin Sergey Pavlovich, (1893 - 1961). There is very little information about him. In his early years he drew for magazines and advertisements and seems to have been involved in political drawings at the time of the Russian Revolution. Later he had his own graphic studio and was also a theatre...
Knitting: Slippers
I suddenly realised that all feet have very similar proportions, regardless of size. That led to this pattern for simple slippers. You only need to know the (approximate) size of a person’s foot and you can make slippers in any yarn, using any needles, without making a tension square.
Knitting: Hanging Ornament, Ball
You can hang these baubles on your tree or just use them to hide a small gift. They are quick and easy to make from three small strips of knitting. The gift can be removed without damaging the bauble.
Knitting: Toys and Hobbies - Other
An anamorphic image is one that appears normal only when seen from some particular perspective or when viewed through something such as a mirror.
Knitting: Toys and Hobbies - Other
You could use this pattern to knit a straightforward garter stitch semi-circle, or join two of them together to make a circle.
Knitting: Toys and Hobbies - Other
Our previous anamorphic pattern was a rainbow reflected in a mirror to give a rectangle with horizontal stripes. This one is what you need to knit if you want to see vertical stripes in the mirror.
Knitting: Component (stitch, edge) - Other
I got addicted to knitting semicircles and then decided to go a little further and make these modular circles. The photos show circles in three sizes. The pattern has instructions for five.
Crochet: Toys and Hobbies - Other
These squiggly things have no practical use but they are very tactile objects. They are fun to make and even more fun to play with. They can be twisted and turned and it is very difficult to put them down once you pick them up.
Knitting: Throw, Baby Blanket
Most people have heard of Fibonacci Numbers but Lucas Numbers are not so well known, which is rather strange as Edouard Lucas was the first to give a name to the Fibonacci Numbers.
Knitting: Pillow / Cushion, Wall Hanging
This is not a pipe. This is not even a picture of a pipe. It is an illusion of a picture of a pipe.
Knitting: Wall Hanging
The winged (or feathered) serpent occurs in the mythology of many different civilisations going back thousands of years. This one is not based on any particular serpent.
Knitting: Wall Hanging
The illusion is based on a painting of Sappho by Auguste Charles Mengin. It was painted in 1877 and is now in Manchester Art Gallery. Sappho was a Greek poet who lived around 600BC. She threw herself into the sea because of unrequited love, still holding her lyre.
Knitting: Blocks
At Christmas I was playing with a complicated paper construction I came across online. There was no chance of knitting it because it would simply have tried to deform to be a sphere. It is in the nature of knitting, and crochet, that all regular 3D shapes try to form themselves into spheres.
Knitting: Wall Hanging
Ada Lovelace (1815 - 1852) was the only legitimate child of the poet Lord Byron. She is regarded by many as the first computer programmer.
Knitting: Wall Hanging
The banner shown in the photos is about 110 cm (44”) long and 15 cm (6”) wide. You can easily add extra to each end if you would like it to be scarf length. It was made using DK yarns but the illusion will work using any thickness of yarn.
Knitting: Wall Hanging
The title comes from the poem And did those feet in ancient time by William Blake. It is now very well-known, in UK, as the anthem Jerusalem. ‘Green and pleasant land’ really refers to just England but the map includes the whole of UK and Ireland.
Knitting: Wall Hanging
It would be nice to knit an illusion of the whole of the Statue of Liberty but, to show the amount of detail needed, it would be enormous so I settled for just representing the head.
Knitting: Wall Hanging
When you look straight at the knitting you only see stripes; when you look from an angle you can see that it says LIBERTY.
Knitting: Washcloth / Dishcloth, Wall Hanging
Two small illusion hearts - one to be viewed from the bottom, the other from the side.
Knitting: Scarf, Shawl / Wrap
In recent years there has been a trend towards asymmetric shawls where you start knitting at a point and keep increasing until you get to the size you want.
Knitting: Wall Hanging
At Easter 2016, I went to visit the Lady Lever Art Gallery at Port Sunlight (UK), which had just undergone a huge renovation. The gallery describes itself as A beautiful building housing one of the UK’s finest collections of fine and decorative art
Knitting: Throw
This is another one for those who like unusual constructions. The technique is very like making mitred squares but these shapes are kites.
Knitting: Throw
If you like unconventional construction this could be the blanket for you. If you don’t like picking up stitches then you should stop reading now.
Knitting: Wall Hanging
When you look straight at the knitting you see only stripes; when you look from the side you see an illusion of Vincent Van Gogh’s Self-Portrait with Grey Felt Hat. The portrait was painted in 1887 and is in the Van Gogh Museum, Amsterdam.
Knitting: Pillow / Cushion
When you look directly at this cushion you see only narrow stripes; when you look from an angle you see the heart and lettering.
Crochet: Blanket - Other
This design is based on a page from a mathematical colouring book Snowflake, Seashell, Star : Colouring Adventures in Numberland by Alex Bellos and Edmund Harriss. It represents three superimposed Sudoku solutions where numbers have been replaced by colours.
Knitting: Throw
This design is based on a page from a mathematical colouring book Snowflake, Seashell, Star : Colouring Adventures in Numberland by Alex Bellos and Edmund Harriss.
Knitting: Wall Hanging
A Menger Sponge is a 3D fractal. Theoretically it has an infinite surface and zero volume.
Knitting: Wall Hanging
Home is where the heart is hidden in the illusion.
Knitting: Pillow / Cushion, Wall Hanging
Two simple heart designs for a 25th wedding anniversary, which can be hung on the wall or used for small cushions.
Knitting: Wall Hanging
This flying eagle illusion can be used for a shawl, as shown in the photographs, or it could be adapted to be a rectangular wall-hanging.
Knitting: Wall Hanging
This may not be to everyone’s taste but if you fancy a tarantula walking across your wall or back, this could be just the thing for you.
Knitting: Wall Hanging
Triskelion Alpha is one of three illusion triskelions. When you look straight at the knitting you see only narrow stripes. The image is revealed when you look from the side. You could use these symbols individually as wall-hangings or cushions, or you could use them as squares to make an afghan.
Knitting: Wall Hanging
Triskelion Beta is one of three illusion triskelions. When you look straight at the knitting you see only narrow stripes. The image is revealed when you look from the side. You could use these symbols individually as wall-hangings or cushions, or you could use them as squares to make an afghan.
Knitting: Wall Hanging
Triskelion Gamma is one of three illusion triskelions. When you look straight at the knitting you see only narrow stripes. The image is revealed when you look from the side. You could use these symbols individually as wall-hangings or cushions, or you could use them as squares to make an afghan.
Knitting: Wall Hanging
Ringed Trefoil is one of four illusion ‘knots’. When you look at it from directly in front you see only stripes. You see the knot when you look from the side.
Knitting: Wall Hanging
Trefoil Knot is one of four illusion ‘knots’. When you look at it from directly in front you see only stripes. You see the knot when you look from the side.
Knitting: Wall Hanging
Yin and Yang (sometimes known as Yin-Yang) is a very well-known symbol. It has many interpretations and is used to represent several different types of ‘opposites’, such as light and dark or male and female.
Knitting: Wall Hanging
This is the head from my Lady with an Ermine. It is about 35 cm (14”) square so could be used for a small pillow.
Knitting: Wall Hanging
This is a large piece of knitting. That doesn’t mean it is difficult to knit. It is just big and takes a long time. It has 300 stitches and 249 ridges (498 rows) of knitting.
Knitting: Bathroom
A regal addition to your bathroom. This little lady is queen of the toilet roll.
Knitting: Bathroom
It is reported that Albert Einstein once said
Knitting: Wall Hanging
What could be more magical than a wizard who disappears!
Knitting: Wall Hanging
Every little girl needs a fairy - and this fairy is particularly magical because she disappears when you look straight at her.
Crochet: Animal Toy
This is the simplest crochet duck pattern ever. It doesn’t have the refinements of some other ducks you might find but it is quick, easy, and suitable for beginners.
Crochet: Puppet
This pattern has been created as part of The Little Yellow Duck Project, which aims to raise awareness of the need for blood, stem cell, organ, and tissue donors.
Knitting: Wall Hanging
This map is not much use for planning your holiday but it is fun to have hanging on the wall. When you look straight at the knitting you see only stripes. When you move to the side the map magically appears.
Knitting: Wall Hanging
Just when you thought illusions couldn’t get more mind-boggling, I present a maze that disappears if you get too close.
Knitting: Throw
This afghan was inspired by a shape of constant width, which is a mathematical curiosity with a lot of practical uses.
Knitting: Wall Hanging
This is my biggest and most complex illusion design to date. That doesn’t mean it is more difficult to knit. It is just big and takes a long time. It has 300 stitches and 247 ridges (494 rows) of knitting.
Knitting: Wall Hanging
I designed this small square with the MG logo for some friends who collect classic MG cars. It is 50 stitches wide and comes out at about 25 cm (10”) square when made in DK yarn. Any yarn can be used but this could change the overall size.
Crochet: Fingerless Gloves
Anyone who has ever met me will know that I have to wear gloves every day of the year. The gloves I wear most often are fingerless crochet gloves (or mittens, wristwarmers or whatever else you want to call them). They are simple, practical and quick to make though they can easily be embellished to make them more fancy.
Knitting: Blocks
These two cubes form a perpetual calendar. You can turn them around until you find the date you want. The numbers you need nicely fill all the faces on two cubes - which you might find a little surprising if you have never thought of it before.
Knitting: Ball, Blocks
About eighteen months ago I was given a set of Grime Dice and it has taken me that long to have the idea to make a knitted set.
Knitting: Scarf, Wall Hanging
This scarf was designed to help promote awareness of the Organ Donor Register. It says GIVE THE GIFT OF LIFE on one side and REGISTER AS AN ORGAN DONOR on the other.
Knitting: Shawl / Wrap
Illustriation appears to have several shades of grey but only uses four different yarns. Anyone looking straight at the shawl will see wide bands of colour which are made up of narrow stripes. As the wearer turns a checkerboard effect comes in and out of view. The viewer will see something different from every angle.
Knitting: Throw
Double Vision has always been one of our most popular designs so we thought the time had come to combine it with our love of illusion kniting (also known as shadow knitting) to create Double Vision Squared. It can be used as an afghan or wall-hanging.
Crochet: Throw, Wall Hanging
Knit or crochet afghan or wall-hanging with variations for a cushion or baby blanket.
Knitting: Wall Hanging
The Heraldic Lion Illusion knit is now available alone and as part of our Royal Standard of Scotland Illusion knit wall hanging pattern. It is approximately 16” (40cm) square and could be used individually or sewn together with other of our similar sized illusion knit designs to create items such as cushion covers, wall hangings or bed covers.
Knitting: Throw, Pillow / Cushion, Baby Blanket
A few months ago we went to a Maths convention and were intrigued by a simple proof that showed how the area of a dodecagon could be doubled to create a larger dodecagon.
Knitting: Cardigan, Pullover
Baby sweaters don’t get simpler than this. If you can do the knit stitch you can make a sweater any size you want without having to follow conventional pattern instructions. The instructions include step-by-step illustrations for everything you need to know. It is also a good pattern for experienced knitters as it gives you the flexibility to b...
Knitting: Shawl / Wrap
People have often asked whether variegated yarns can be used for illusion knits so we decided to experiment with two such yarns. Our conclusion was that when your brain can perceive enough of the design to be able recognise it the yarns can be solid or variegated.
Knitting: Pillow / Cushion
The American Football Helmet Illusion Knit is the latest addition to the sport related series of illusion knits that, so far, includes a soccer ball, an American football and a volleyball. All of the pieces in this series are the same size as each other, approximately 16” (40cm) square, so can be used individually or sewn together with other of...
Knitting: Wall Hanging
The Volleyball Illusion Knit is the latest addition to the sport related series of illusion knits that, so far, includes a soccer ball and an American football. All of the pieces in this series are the same size as each other, approximately 16” (40cm) square, so can be used individually or sewn together with other of the designs to create items...
Knitting: Wall Hanging
This American Football illusion knit is the second in an intended series of sport related illusion knit panels, the first being the Soccer Ball illusion knit. Like the soccer ball it is approximately 16” (40cm) and uses 140metres in each of two contrasting colours when knitted using 3mm needles.
Knitting: Pillow / Cushion
The Fleur-de-Lis illusion knit design measures approximately 16 inches (40cm) square when using DK yarn and 3mm needles. It is designed to be viewed from the side so is ideal for use as an emblem on a garment, as a front/back for a cushion or as the centre piece for a wall hanging or bed cover.
Knitting: Pillow / Cushion
This Daffodil Illusion is one of four national emblem cushions I originally designed for the Woolsack project as part of the Cultural Olympiad for London2012. The others are:
Knitting: Pillow / Cushion
This Rose Illusion is one of four national emblem cushions I originally designed for the Woolsack project as part of the Cultural Olympiad for London2012. The others are:
Knitting: Pillow / Cushion
This Shamrock Illusion is one of four national emblem cushions I originally designed for the Woolsack project as part of the Cultural Olympiad for London2012. The others are:
Knitting: Pillow / Cushion
This Thistle Illusion is one of four national emblem cushions I originally designed for the Woolsack project as part of the Cultural Olympiad for London2012. The others are:
Knitting: Shawl / Wrap
Some weeks ago we took part in a Stitched Science Event at the London Science Museum. We were talking about creating patterns from geometric shapes, how to create illusion knits and why illusion knitting works. This shawl came about as part of that. I wanted a piece of illusion knitting that would show the process and demonstrate how and why it...
Crochet: Throw, Blanket - Other
Square Deal Redux is an arrangement of 21 different size squares to make a large square.
Knitting: Throw
This was really designed by Pat (Woolhelmina) but we have added it to my designs to keep all our illusion designs in one place.
Knitting: Throw
I am intending to create a series of illusion designs that centre around various kinds of sport. These designs will take the form of small panels that can be used individually as cushions or as the motif on a sweater or put together to form a wall hanging, throw or bedspread.
Knitting: Chart
A lot of people have asked about lettering for illusion knitting so here are ten alphabets for you to use.
Knitting: Throw
Use up all your oddments and make a feature of the knots … or make a smart plain version with new yarn.
Knitting: Pillow / Cushion
This cushion was really designed and made by Pat (Woolhelmina) but I have added the pattern here to keep all the illusion cushions in one place. (If you are looking for illusion afghans, they are in our Woolly Thoughts designs. Confusing, isn’t it?)
Knitting: Throw, Bedspread, Pillow / Cushion, Baby Blanket
Curve of Pursuit has been our most popular design for many years. Now we have In Pursuit of an Illusion which is a shadow knit version based on the same mathematical concept as the original.
Knitting: Pillow / Cushion
Two illusion cushions based on the work of M C Escher.
Knitting: Coffee / Tea Pot
We were recently asked to make a tea cosy for a local event. At first we declined then decided it would be a good opportunity to try out another way of using illusion knitting.
Knitting: Wall Hanging
Another illusion knitting experiment. It didn’t come out exactly as we thought but is still very interesting and surprising.
Knitting: Pillow / Cushion
Does illusion knitting work in circles?
Knitting: Pillow / Cushion
An illusion - in more ways than one!
Knitting: Pillow / Cushion
Pattern update - July 2012 - to add instructions for wall-hangings.
Knitting: Shawl / Wrap, Throw
This anamorphic design can be used as a shawl or afghan.
Knitting: Tutorial
This design looks more complicated than many of our other samples. It is no more difficult to knit. It was originally intended as a laptop cover. You could make it rectangular, like the one shown, or you could omit the sides of the chart to make it square, making it suitable for a washcloth or afghan block.
Knitting: Washcloth / Dishcloth
This is a very simple pattern and is one of the samples recommended as an introduction to Woolly Thoughts illusions. If you are new to illusion knitting you might like to try this before you embark on one of our bigger pieces.
Knitting: Tutorial
If you want to view illusion knitting from the side, instead of from the bottom, it has to be charted differently. You cannot just turn the chart and knit sideways. The two samples in this pattern are based on the same original photo of a maple leaf and are to be viewed from different directions.
Knitting: Tutorial
This pattern combines illusion knitting with the mitred square technique.
Knitting: Washcloth / Dishcloth
This pattern combines illusion knitting with the mitred square technique.
Knitting: Washcloth / Dishcloth
This square is intended as a practice piece. Woolly Thoughts illusions are different from many others. It will help you understand how to use our charts. It has light and dark stripes, going in different directions, to show some of the effects that can be achieved just by using rows of straightforward knit and purl.
Knitting: Tutorial
The aim of this pattern is to show different effects that can be achieved by using the same two yarns.
Knitting: Washcloth / Dishcloth
This design uses the same two colours as Directional Shadows so they may look similar at first glance. When you look straight at the squares you see only narrow stripes, going in different directions. Looking from an angle reveals a smaller square inside each of the squares. Some of these squares are yellow and some are green.
Knitting: Tutorial
This design is different from our other samples because it uses a small design that can be repeated across the knitting as often as you wish.
Knitting: Washcloth / Dishcloth
This simple striped design is intended as an introduction to Woolly Thoughts illusion patterns. When you look at the square from directly in front you see only narrow ridges of alternating colours. When you look from an angle you see broad stripes of the two colours. The square could be used for an afghan block or a washcloth.
Knitting: Washcloth / Dishcloth
This is intended as an introduction to Woolly Thoughts illusion patterns. It is a simple striped design, where you see two-colour stripes from directly in front but stripes in three colours when you look from an angle even though you only use two colours of yarn. The stripes change position halfway up the square but you could make them continuo...
Knitting: Washcloth / Dishcloth
You can create interesting effects in illusion knitting by making the ridges of knitting to run in different directions.
Knitting: Throw
This is an anamorphic representation of our Long and Winding Road afghan.
Knitting: Wall Hanging
The David Tennant Illusion Knit came about following requests from various Doctor Who fans after the actor had left the series.
Knitting: Throw
Do you see holes between two twisting ribbons? What colour are the holes? Or are there three ribbons?
Knitting: Mittens
By popular request, I have added this booklet as a Ravelry download. It was written over ten years ago and has now been updated (January 2010) to take into account the fashion for fingerless mittens.
Knitting: Throw
Despite what your eyes may tell you, there are no curves here.
Knitting: Toys and Hobbies, Toy Game
Pentominoes are shapes that can be made with five squares. There are 12 different pentominoes. You can see an arrangement of Pentominoes, and their reflections, in our Bunch of Fives afghan, which has often been used as a teaching aid.
Knitting: Toys and Hobbies, Toy Game
The Diabolical Cube isn’t really at all diabolical. It is easy to make the pieces and the puzzle is easy to solve.
Knitting: Toy Game, Blocks
Knit a set of Napier’s Bones (also known as Napier’s Rods) as a fun way to learn multiplication. Children love them. The knitted bones are far more tactile than the wooden versions you might find elsewhere. They have a thin foam filling to make them flexible and almost indestructible. You can stiffen them with card or plastic strip, if you pref...
Knitting: Toy Game
The Tower of Hanoi is a mathematical game or puzzle, which can also be used as a simple stacking toy for a young child. The pattern includes knit and crochet versions.
Knitting: Toys and Hobbies, Toy Game
You will have seen wooden versions of this toy before. We call it Octopush (and sometimes Octocube ). It is made up from eight cubes joined in a special way so that you can fold and unfold the large cube continuously to reveal several different faces.
Knitting: Toy Game
The Tangram is a very old puzzle which originated in China. The seven individual pieces are known as tans. They are traditionally coloured black. The aim of the puzzle is to assemble the pieces into various shapes such as people, animals and geometric figures.
Knitting: Pillow / Cushion
To accompany our impossible triangle afghan we have an impossible square represented on a cushion. It is the square that is impossible, not the cushion!
Knitting: Throw
Rule of Three is a representation of the Penrose Triangle (which is sometimes referred to as a Tribar). Although it was first created by the Swedish artist Oscar Reutersvärd in 1934, Sir Roger Penrose and his father, Lionel, independently devised this and other impossible figures in the 1950s. Their discoveries are known to many as the underlyi...
Knitting: Hats - Other
There are six hats in the HyperHat Collection. The patterns are available individually or as a collection.
Knitting: Shrug / Bolero, Sleeveless Top
A fun and easy top that can be made to fit anyone in any yarn.
Crochet: Throw
This unusual shaped afghan is based on the Golden Mean and the Fibonacci Sequence.
Crochet: Throw
If you are the sort of person who likes popping the bubbles in bubble wrap, you will love this. The undulating surface is good to look at but you can also pop all the little points to the back, then turn the whole thing over and pop them back again.
Knitting: Throw
A circle but not a circle! This two-colour spiral only becomes a circle when you get to the end.
Knitting: Throw
Maybe this should be called Evolution as it has evolved from Curve of Pursuit.
Knitting: Doll, Puppet
Two more puppets with mathematical fronts! They demonstrate Triangular Numbers and Square Numbers.
Knitting: Tutorial
The ideas behind this project can be found in more detail in the Conglomerations chapter of Second Thoughts.
Knitting: Containers, Toys and Hobbies, Doll, Decorative - Other
This serene lady has a secret.
Knitting: Containers, Decorative Ornament, Doll, Decorative - Other
The Old Bag Lady will guard your possessions and nobody will even suspect what she is doing. She has a hidden secret. She can hide your rings, earrings and necklaces in her bags and, in addition to this, you can make her with a large hidden compartment to store more of your jewelry.
Knitting: Containers, Toys and Hobbies, Doll, Decorative - Other
Here is a Pretty Lady to safeguard your jewellery.
Knitting: Containers, Toys and Hobbies, Doll, Decorative - Other
Stand this little lady by your basin and she will hold your rings, on her tray, while you wash your hands.
Knitting: Doll, Puppet
These two are really very friendly, once you get to know them.
Knitting: Puppet
Meet our mathematical friends: Mr Pythagoras and Mr Fibonacci.
Knitting: Puppet
They’re not really that terrible. In fact they’re rather cute.
Knitting: Throw, Wall Hanging, Baby Blanket
This pattern is suitable for hand or machine knitting, or crochet, using any yarn and needles. Make it any size from baby blanket to king-size bed. It can be made in two or six colours.
Knitting:
Now available as a Ravelry download. Buy using the link at the top of this page.
Knitting: Bathroom, Doll
Meet Lulu - a toilet roll cover to add fun to any bathroom. Dress her in colours to suit your bathroom or make her as a mascot doll for your favourite cheerleader.
Knitting: Bathroom, Doll
Meet Roland - another of our Paper People toilet roll covers. He is dressed in pants, hoodie and beanie.
Knitting: Bathroom
Make this evil witch to guard your toilet roll.
Knitting: Bathroom, Doll
Meet Toilet Trainer - another in our collection of Paper People toilet roll covers.
Crochet: Throw, Wall Hanging
Under Orders represents a pack of ten cards being shuffled. Each card is represented by a colour. The first column shows the cards in their starting places. The second column shows the positions after one perfect shuffle so that the cards which were in the bottom half of column one alternate with those which were in the top half. The third colu...
Crochet: Scarf
This is a very simple lightweight scarf. If you can make chains you can do this.
Crochet: Pillow / Cushion
It is perfectly possible to knit or crochet Platonic solids that keep their shape. They need to be worked very tightly or to be stiffened in some other way. When they are not stiffened, all knitted or crocheted objects try to turn themselves into spheres. This is because a sphere has the smallest surface area for any given volume.
Crochet: Scarf
This is one of four scarves from Neck and Neck … and Neck and Neck. They are all just about as easy as scarves can get.
Knitting: Poncho
There are hundreds of variations for this pattern. It can be made to any size, using any yarn. You can even use different weights of yarn in every square, if you wish. The photographs and diagrams will give you a few ideas to start your imagination working. The final choice is yours.
Crochet: Throw, Wall Hanging
This is a combination of knit and crochet squares.
Crochet: Scarf
There are 24 different ways of placing four colours in a square - or sitting four people round a table. 12 of these can be seen by looking at one side of the scarf. The other 12, which are reflections of the first set, can be seen by turning the scarf over. Folding the scarf in half might lead you to believe that there are only 6 completely dif...
Knitting: Shawl / Wrap
This triangular shawl is worked in one piece using one colour at a time. It starts with one large square and progressively smaller triangles are added, according to the rules of Pythagoras Theorem. It measures 150 cm (60”) across and 75 cm (30”) high but can easily be adjusted to other sizes.
Crochet: Wall Hanging
It may be difficult to see that this wall-hanging is closely related to our Scaled Up afghan as one is all twists and turns, the other is all straight lines.
Crochet: Scarf
Each of these three scarves represents a mathematical curiosity known as a Dragon Curve.
Crochet: Shawl / Wrap
This shawl is made from simple granny squares. It is the combination of yarns that create the subtle shading effect.
Knitting: Shawl / Wrap
This shawl is knitted in L shapes to create simple garter stitch squares. It is the combination of yarns that create the subtle shading effect.
Crochet: Scarf, Shawl / Wrap
Dragon curves are complex space-filling curves with a very simple origin. Fold a strip of paper in half, fold in half again, and again. Unfold the paper and you have a dragon curve. The dragons on this crochet wrap are what you get when you fold the paper 2, 4 or 7 times. They fit together to cover the surface.
Knitting: Scarf, Shawl / Wrap
A collection of ten mathematical shawls, wraps and scarves, along with some more ideas for designing your own.
Crochet: Scarf
The Fibonacci Sequence (or series) is a pattern of numbers which recurs frequently in Maths and Nature. It is closely related to the Golden Section. This simple crochet scarf is a representation of the numbers in the sequence.
Knitting: Shawl / Wrap
This is based on one of our favourite designs called From Square to Eternity. This is only half of that design so becomes Halfway to Paradise.
Crochet: Shawl / Wrap
This is a very simple shawl worked in exactly the same way as half a granny square. Seven bands of colour represent the first seven numbers in the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13.
Crochet: Throw, Wall Hanging
Point to Point is a rather strange, yet intriguing, thing.
Crochet: Scarf
Pentominoes are shapes made from 5 squares. There are 12 different possible shapes and they are all included in this pretty scarf.
Crochet: Scarf
This simple filet crochet scarf hides a secret message. When you hold it up to the light, or place it on a contrasting background, the message is revealed. Mine says Mufflermatics, which is the title of the book it comes from. I used the word twice, once in each direction with the ends of the words towards the centre.
Crochet: Throw, Wall Hanging
The photos do not do justice to this undulating surface.
Knitting: Throw, Bedspread
This is just what you need to use up all those oddments - and there is no need to worry about darning in the ends!
Knitting: Throw, Wall Hanging
This dramatic design would be very impressive hanging on your wall or for use as an afghan. I always think it looks like giant knitted cables. Others see the shapes as spirals.
Crochet: Pillow / Cushion
Unless you are a mathematician, you may not be interested in the special properties of Double Shuffle.
Knitting: Pillow / Cushion
Faultless does not mean this cushion is without errors. This is more like the kind of fault in the earth’s crust.
Knitting: Pillow / Cushion
Named after Leonardo Fibonacci (Leonardo of Pisa) who lived around 800 years ago, this sequence is closely related to the Golden Section, which is much used by artists and architects. This pattern of numbers has been found to occur frequently in nature Each term is found by adding together the two previous terms.
Knitting: Pillow / Cushion
All the different quadrilaterals on one cushion!
Crochet: Pillow / Cushion
Quadrille has an openwork grid with a pattern applied in surface crochet.
Knitting: Pillow / Cushion
Square Deal represents the smallest number of different squares which can be fitted together to make a larger square.
Knitting: Pillow / Cushion
How many squares are here? You make sixteen squares but probably see only five (plus a few triangles).
Knitting: Pillow / Cushion
Do you remember those Stereogram books from a few years ago? This is the cushion version.
Knitting: Pillow / Cushion
A tangram is a traditional Chinese puzzle. The pieces should be cut apart (Not recommended for your cushion!) and used to construct a multitude of patterns and figures.
Knitting: Pillow / Cushion
Haven’t you always wanted to prove Pythagoras’ Theorem with a cushion? Now you can.
Knitting: Pillow / Cushion
Thirty-six squares - one in the first colour, two in the second, three in the third, etc. Adding these numbers together gives the sequence of Triangular Numbers. When you get to 8 the whole shape forms a 6 x 6 square - a Square Number and a Triangular Number coincide.
Crochet: Pillow / Cushion
Mathematically, this is an Archimedean Spiral. That means it moves out from the centre by the same distance on each rotation.
Knitting: Pillow / Cushion
Wreck Tangled has 7 rectangles; 3 on one side; 3 on the other; 1 that spreads on both sides. Each rectangle has the same area. In knitting terms, that means they all have the same number of stitches.
Knitting: Pillow / Cushion
12 Pillows of Wisdom is now available as a Ravelry download. Buy using the link at the top of this page.
Crochet: Throw, Wall Hanging, Toy Game
Starting at brick number one, and always moving forwards, how many different paths can you take to reach the brick at the bottom?
Knitting: Throw, Wall Hanging
Believe it or not, this afghan started its life as a worksheet for pupils in a mathematics classroom. Some pupils were having difficulty identifying the properties of four-sided shapes so we devised a colouring-in sheet for them. Every shape in the patchwork has four sides.
Crochet: Throw, Wall Hanging
How often have you folded a strip of paper in half, in half again and so on until you can’t fold it any more? Did you know you were half way to the magical world of Dragon Curves? Unfold the paper, make all the folds right angles, and you get a lovely twisting shape. With the piece of paper you can only make about 6 folds but, mathematically, i...
Knitting: Throw, Wall Hanging
Every time you look at this optical illusion afghan you will see something different!
Knitting: Pillow / Cushion, Afghan block
There are no curves here. The spirals you see are made entirely from straight lines. You can make Best of Both Whirls from 1 large module or 4 small ones. Either way will give you exactly the same size so the back and front could be different.
Knitting: Pillow / Cushion
Many people feel daunted by the thought of knitting something the size of an afghan so we adapted some of our designs to become cushions.
Knitting: Pillow / Cushion
For those who love our Double Vision afghan but can’t face knitting 100 squares, here we have the cushion version.
Crochet: Pillow / Cushion
This cushion cover is based on a labyrinth built by Sir Gilbert Scott in Ely Cathedral. It was specially designed for the cathedral and was considered to be different from ‘traditional’ mazes/labyrinths.
Knitting: Pillow / Cushion
How many different ways can you arrange 4 colours? Have It All Ways gives you the answer. Each block has a different permutation - and there are more on the back.
Knitting: Pillow / Cushion
This octagonal cushion is part of an aperiodic tiling. This small section of the design does not demonstrate the unique properties of these tilings, which are non-repeating patterns.
Knitting: Pillow / Cushion
Roundabouts is a square made from four triangles. So why do we say ‘follow the path round and round’?
Crochet: Pillow / Cushion
The curve on this cushion cover is known as a ‘Hilbert Open Peano Curve’. Theoretically, curves of this type can be made to completely cover a surface.
Knitting: Pillow / Cushion
For those who don’t want a big project, this is the cushion version of From Square To Eternity.
Knitting: Pillow / Cushion
For those who can’t face knitting something the size of an afghan, we have a large collection of cushion patterns.
Knitting: Pillow / Cushion
Cushy Numbers is available as a Ravelry download. Buy using the link at the top of this page.
Knitting: Throw, Pillow / Cushion, Wall Hanging
Maisie’s Mazes is now available as a Ravelry download. Buy using the link at the top of this page.
Knitting: Throw, Wall Hanging
Make this mind-boggling afghan from our booklet of instructions.
Knitting: Throw
This PDF was originally intended for UK schools but the methods are equally useful to any knitters wanting to work together on a project. It was originally produced in booklet form and has been used in many countries around the world. It was written with children in mind and has proved to be equally acceptable to adults.
Crochet: Throw, Wall Hanging, Toy Game
This afghan, or wall-hanging is a representation of a Roman labyrinth discovered in Wales (UK).
Crochet: Pillow / Cushion, Toys and Hobbies, Toy Game
January 2013 - Knitted version added
Knitting: Throw
You might call this Pythagoras Gone Mad. It is a fractal representation of Pythagoras Theorem and was inspired by the work of a young teacher who gave his pupils a diagram of the centre of this design and asked them to complete it. They soon realised it was impossible to complete as they had to add ever smaller pieces and, if they had the physi...
Knitting: Cardigan
The instructions for making the jacket should be considered a guide to recreating the design. They are not as definitive as a conventional pattern.
Knitting: Throw, Wall Hanging
A square in a square in a square …… Keep going and make it as big as you want.
Knitting: Throw, Toy Game
An afghan that can also be used as a floor game! Make this for your favourite backgammon player.
Knitting: Throw, Bedspread, Wall Hanging, Toy Game, Baby Blanket
Afghan Games is available as a Ravelry download. Buy using the link at the top of this page.
Crochet: Throw, Toy Game
In UK we call this game Draughts. You may know it by other names.
Crochet: Throw, Toy Game
In UK we call this game Ludo. It has alternative names in other countries.
Crochet: Throw, Toy Game
In UK we call this game Noughts and Crosses but it is known all over the world.
Knitting: Throw, Toy Game
We made two versions of this afghan/floor game. The first was knitted entirely from oddments of yarn and cost absolutely nothing to make. The bits of yarn were, individually, rather dull and uninteresting but together they create a very harmonious effect. The second was made on a knitting machine with a garter carriage, using a single colour as...
Crochet: Throw, Wall Hanging
You might see this as just an interesting design. It is also a crochet representation of square numbers and triangular numbers.
Crochet: Throw
This is a booklet of instructions for making the two afghans that can be seen in the photos. It is not a conventional pattern. If you can make granny squares you can make this.
Knitting: Throw
Basketweave is made up from small squares and rectangles. The placement of the pieces gives the impression of strips weaving under and over each other.
Knitting: Throw, Wall Hanging
Double Vision is a stunning afghan. It appears to have 55 different shades though it only uses 10 ordinary, easily available colours.
Knitting: Throw, Wall Hanging
An afghan or wall-hanging based on the Fibonacci Sequence.
Knitting: Throw
Just a simple octagon? Or is it? How many other shapes can you find?
Knitting: Throw, Wall Hanging
Half Measures was the result of a workshop at a Mathematics Conference in 1998. The delegates were challenged to design a series of eight squares to fit particular criteria.
Knitting: Cardigan, Pullover, Coat / Jacket, Sweater - Other
Second Thoughts is now available as a Ravelry download. Buy using the link at the top of this page.
Knitting: Cape
This circular cape was designed to go with the Simply Circles Skater Skirt. They are both delightfully swishy to wear. The cape stays in place in your shoulders and hangs down in soft folds. There is enough fabric that you can probably also throw the end over your shoulder and pin it in place. It can be fastened with buttons or some other type ...
Knitting: Beret, Tam
This hat is one element of an outfit that was originally designed, and short-listed, for the International Mohair Competition 1997. The patterns have been available, on our website, for a long time but are new to Ravelry.
Knitting: Skirt
This amazingly swirly skirt has a hidden secret that means that the same skirt can fit a variety of people of many different ages and sizes. Make it for yourself but lend it to your mother, daughter, sister, friend … and you can even wear it as a poncho.
Crochet: Throw, Wall Hanging
This is a very light and airy afghan, which could also be used as a hanging or doubled over and used as a shawl.
Crochet: Throw, Wall Hanging
This is a very light and airy afghan, which could also be used as a hanging or doubled over and used as a shawl.
Knitting: Throw
In recent years, The Long and Winding Road has become a very popular pattern. Maybe this is because it has some resemblance to ‘log cabin’ although the method is completely different.
Knitting: Throw, Wall Hanging, Afghan block
This has always been one of our most popular designs. In addition to it being a stunning way to decorate your room, as a wall-hanging or afghan, it is ideal for using up all the oddments of yarn you have accumulated.
Knitting: Throw, Wall Hanging
I guess this is only of interest to Mathematicians. Who else would care about its peculiarities?
Knitting: Throw, Wall Hanging, Afghan block
Do you see purple on orange? Or orange on purple?
Knitting: Throw, Wall Hanging, Toy Game
The finished item can be used as a wall-hanging or afghan. We use ours for education purposes. It is a ‘100 square’. The squares across the top row represent the numbers 1 -10, the second row 11 - 20, and so on. The colours show which numbers, from 1 - 10, divide into the numbers represented by the squares. Each colour shows a different multipl...
Knitting: Throw, Wall Hanging
The easy-to-follow instructions allow you to make an afghan or wall-hanging in any yarn of your choice, to any size. It may look complicated but, if you can knit garter stitch, you can make this.
Knitting: Throw, Wall Hanging
You might want to make this afghan just because it is bold and colourful. You might want to make it, for a child, as a teaching aid.
Knitting: Throw, Wall Hanging
This is one of our earliest afghans - and still one of my favourites. I particularly like it because, apart from the very smallest squares in the centres, the number of stitches is always decreasing and so it seems to go very quickly.
Knitting: Throw, Wall Hanging
Have you ever wondered how many different ways can you arrange four colours?
Knitting: Throw
Do you see stars or octagons? You might think that is a pointless question so try asking a few other people. You may be surprised by their answers.
Knitting: Throw, Wall Hanging
Pythagoras Tree represents Pythagoras Theorem: ‘The square on the hypotenuse is equal to the sum of the squares on the other two sides.’ In this case, the ‘squares on the other two sides’ are equal so, in knitting terms, that means that each small square has exactly half as many stitches to knit as the large square on the same triangle. There a...
Knitting: Throw, Wall Hanging
This is one of our earliest designs but still very popular.
Knitting: Throw, Wall Hanging
This afghan or wall-hanging can be knitted using any yarn and needles. The yarn chosen will change the finished size but it can be made in a large range of sizes, whatever yarn you choose. You can even make it very small, as a cushion or pillow.
Knitting: Throw
Swirl Without End is a good design for using up left over odds and ends in four colour groups. The original was made with two strands of DK; when one strand ran out another was added so the colours blend and there are no obvious stripes.
Knitting: Throw, Wall Hanging
One of my students said she felt she was in New York, looking down on tall buildings - hence the name Tower Blocks.
Knitting: Throw, Wall Hanging
I see this as rows of ten windows in ten coloured columns. Others see it differently.
Knitting: Afghan block
This is one of a set of five patterns that we have been using for about 20 years to give people a few ideas about using simple ‘half-and-half’ squares to create original afghan designs.
Knitting: Afghan block
This is the second in a set of five patterns that we have been using for about 20 years to give people a few ideas about using simple ‘half-and-half’ squares to create original afghan designs.
Knitting: Afghan block
This is the third in a set of five patterns that we have been using for about 20 years to give people a few ideas about using simple ‘half-and-half’ squares to create original afghan designs.
Knitting: Afghan block
This is the fourth in a set of five patterns that we have been using for about 20 years to give people a few ideas about using simple ‘half-and-half’ squares to create original afghan designs.
Knitting: Afghan block
This is the last in a set of five patterns that we have been using for about 20 years to give people a few ideas about using simple ‘half-and-half’ squares to create original afghan designs.
