Available as an eBook from the Woolly Thoughts Ravelry Shop. The individual patterns are also available from my Ravelry store.

Available as an eBook through Woolly Thoughts Ravelry Shop.

Available as an eBook from the Woolly Thoughts Ravelry Shop.

One PDF containing:

Available as an eBook through Woolly Thoughts Ravelry Shop.

A collection of shawls and scarves with a mathematical flavour.

Available from Woolly Thoughts Ravelry shop

This afghan was inspired by a shape of constant width, which is a mathematical curiosity with a lot of practical uses.

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.

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.

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.

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.

Conjoined Möbius (aka Klein Bottle) Hat

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.

Knit or crochet afghan or wall-hanging with variations for a cushion or 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.

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...

Mitred squares

Square Deal Redux is an arrangement of 21 different size squares to make a large square.

Use up all your oddments and make a feature of the knots … or make a smart plain version with new yarn.

An optical illusion using illusion knit techniques.

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.

A mixture of knitting and crochet.

This anamorphic design can be used as a shawl or afghan.

This is an anamorphic representation of our Long and Winding Road afghan.

Knit or crochet.

Do you see holes between two twisting ribbons? What colour are the holes? Or are there three ribbons?

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.

Despite what your eyes may tell you, there are no curves here.

Accessories with a twist - or several twists!

Large-scale tactile dominoes for young children (and older people too).

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.

The Diabolical Cube isn’t really at all diabolical. It is easy to make the pieces and the puzzle is easy to solve.

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, ...

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.

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.

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.

An optical illusion afghan or wall-hanging.

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!

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 underlyin...

The Soma Cube was invented by Piet Hein in 1936 while he was listening to a lecture on quantum mechanics!

There are six hats in the HyperHat Collection. The patterns are available individually or as a collection.

A crochet hat with hyperbolic frills.

A knitted hat with hyperbolic frills.

A knitted hat with hyperbolic frills.

A knitted hat with hyperbolic frills.

A crochet hat with hyperbolic frills.

A crochet hat with spiral hyperbolic frill.

Ten different spirals:

A fun and easy top that can be made to fit anyone in any yarn.

This afghan measures exactly one square metre. It is the size of an A0 piece of paper.

This unusual shaped afghan is based on the Golden Mean and the Fibonacci Sequence.

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.

One booklet with two patterns.

One happy clown, one sad clown!

Two puppets especially for Christmas.

A circle but not a circle! This two-colour spiral only becomes a circle when you get to the end.

This pattern is to raise funds in two ways:

Data Log is a log cabin design with a mathematical purpose.

Challenge your mind! The rings represent the dials of a combination lock. Rotating some of the rings would create a large X-shape in one colour across the afghan.

Maybe this should be called Evolution as it has evolved from Curve of Pursuit.

Two fearsome creatures from Greek myth

Two more puppets with mathematical fronts! They demonstrate Triangular Numbers and Square Numbers.

The ideas behind this project can be found in more detail in the Conglomerations chapter of Second Thoughts.

This serene lady has a secret.

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.

Here is a Pretty Lady to safeguard your jewellery.

A doll with a dark secret.

Stand this little lady by your basin and she will hold your rings, on her tray, while you wash your hands.

These two are really very friendly, once you get to know them.

Meet our mathematical friends: Mr Pythagoras and Mr Fibonacci.

They’re not really that terrible. In fact they’re rather cute.

A spellbinding couple!

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.

Now available as a Ravelry download. Buy using the link at the top of this page.

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.

Meet Roland - another of our Paper People toilet roll covers. He is dressed in pants, hoodie and beanie.

Meet Toilet Trainer - another in our collection of Paper People toilet roll covers.

Make this evil witch to guard your toilet roll.

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 colum...

This must be the easiest scarf in the world to make but the effect is quite dramatic.

A three-in-one shawl/poncho/wrap.

This is a combination of knit and crochet squares.

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.

Here Be Dragons is available as one PDF via the Ravelry download on this page. It contains three booklets:

A collection of ten mathematical shawls, wraps and scarves, along with some more ideas for designing your own.

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 diff...

Each of these three scarves represents a mathematical curiosity known as a Dragon Curve.

This shawl pattern includes knit and crochet versions.

Pentominoes are shapes made from 5 squares. There are 12 different possible shapes and they are all included in this pretty scarf.

Point to Point is a rather strange, yet intriguing, thing.

Small items using surface crochet Dragon Curves.

The photos do not do justice to this undulating surface.

This is just what you need to use up all those oddments - and there is no need to worry about darning in the ends!

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.

Unless you are a mathematician, you may not be interested in the special properties of Double Shuffle.

Faultless does not mean this cushion is without errors. This is more like the kind of fault in the earth’s crust.

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.

All the different quadrilaterals on one cushion!

Quadrille has an openwork grid with a pattern applied in surface crochet.

Square Deal represents the smallest number of different squares which can be fitted together to make a larger square.

How many squares are here? You make sixteen squares but probably se link at thee only five (plus a few triangles).

Do you remember those Stereogram books from a few years ago? This is the cushion version.

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.

Haven’t you always wanted to prove Pythagoras’ Theorem with a cushion? Now you can.

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.

Mathematically, this is an Archimedean Spiral. That means it moves out from the centre by the same distance on each rotation.

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.

12 Pillows of Wisdom is now available as a Ravelry download. Buy using the link at the top of this page.

Starting at brick number one, and always moving forwards, how many different paths can you take to reach the brick at the bottom?

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.

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, mathematical...

Every time you look at this optical illusion afghan you will see something different!

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.

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.

For those who love our Double Vision afghan but can’t face knitting 100 squares, here we have the cushion version.

This cushion cover is based on a maze built by Sir Gilbert Scott in Ely Cathedral. It was specially designed for the cathedral and was considered to be different from ‘traditional’ mazes.

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.

January 2013 - Knitted version added

This octagonal cushion is part of a Penrose tiling. This small section of the design does not demonstrate the unique properties of these tilings, which are non-repeating patterns.

Roundabouts is a square made from four triangles. So why do we say ‘follow the path round and round’?

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.

For those who don’t want a big project, this is the cushion version of From Square To Eternity.

For those who can’t face knitting something the size of an afghan, we have a large collection of cushion patterns.

Curve of Pursuit’s baby brother!

Cushy Numbers is available as a Ravelry download. Buy using the link at the top of this page.

Maisie’s Mazes is now available as a Ravelry download. Buy using the link at the top of this page.

Make this mind-boggling afghan from our booklet of instructions.

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.

This afghan, or wall-hanging is a representation of a Roman labyrinth discovered in Wales (UK).

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 physic...

The instructions for making the jacket should be considered a guide to recreating the design. They are not as definitive as a conventional pattern.

A square in a square in a square …… Keep going and make it as big as you want.

An afghan that can also be used as a floor game! Make this for your favourite backgammon player.

Checkmate is another of our Afghan Games. Use it as an afghan or put it on the floor and play the game. You don’t have to make it in these vivid colours!

Afghan Games is available as a Ravelry download. Buy using the link at the top of this page.

In UK we call this game Draughts. You may know it by other names.

In UK we call this game Ludo. It has alternative names in other countries.

In UK we call this game Noughts and Crosses but it is known all over the world.

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 ...

You might see this as just an interesting design. It is also a crochet representation of square numbers and triangular numbers.

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.

Can anyone resist following the path of a maze?

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.

Double Vision is a stunning afghan. It appears to have 55 different shades though it only uses 10 ordinary, easily available colours.

Second Thoughts is now available as a Ravelry download. Buy using the link at the top of this page. You can also buy as a softback book from Lulu.com

An afghan or wall-hanging based on the Fibonacci Sequence.

Just a simple octagon? Or is it? How many other shapes can you find?

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.

This is a very light and airy afghan, which could also be used as a hanging or doubled over and used as a shawl.

This is a very light and airy afghan, which could also be used as a hanging or doubled over and used as a shawl.

Have you ever wondered how many different ways you could combine five colours?

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.

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.

I guess this is only of interest to Mathematicians. Who else would care about its peculiarities?

Do you see purple on orange? Or orange on purple?

Twelve pentominoes and their reflections.

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 differ...

A very effective, easy-to-make, optical illusion.

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.

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.

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.

Have you ever wondered how many different ways can you arrange four colours?

Which way are the columns pointing?

This afghan is based on a design sent to us by the famous Oxford mathematican Sir Roger Penrose. It is named in his honour.

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.

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...

This is one of our earliest designs but still very popular.

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.

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.

One of my students said she felt she was in New York, looking down on tall buildings - hence the name Tower Blocks.

I see this as rows of ten windows in ten coloured columns. Others see it differently.