For those who can't face knitting something the size of an afghan, we have a large collection of cushion patterns. Tilting at Windmills is particularly good for using up oddments of yarn. It is knitted entirely in garter stitch so is very easy to make. The cushion in the photos was made with Aran yarn but any other yarns could be used. This pattern is also available in our Cushy Numbers ebook. We also have an afghan version of Tilting at Windmills. Designed by mathekniticians Pat Ashforth and Steve Plummer.

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. The design is to be found on the walls of many UK schools as a poster, published by Tarquin Publications. The afghan came first. It shows fractions from 1 - 12. The first square has one piece, the second square has two pieces, etc. Tarquin were so impressed by the simplicity and clarity of the idea they asked to use it for a poster, about ten years ago. It is still in print and just as popular as it has always been. This is a very easy afghan to make. It is entirely in garter stitch and is worked in blocks which are then stitched together. This makes it a very portable project. The original was made with Aran weight yarns but you can use any yarn of your choice. The booklet includes a colouring sheet so you can try out your own colour choices. The wrinkles you can see in the photos are because the afghan is pinned to a backing and has been hanging for many years. It is best not to use a backing.

or buy at LoveCrafts An afghan or wall-hanging based on the Fibonacci Sequence. It is worked in garter stitch, in any yarn of your choice, and is much less complicated than it looks. Perhaps it is not ideal for a brand new knitter but anyone with just a little experience would be able to make it. The original is approximately 90 cm (36 inches) square without the border and 110 cm (44 inches) including the border. It is made in strips which are stitched together. Only one yarn is used at a time. It was made with two strands of DK yarn but can easily be changed, to other yarns. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. We have two other Fibonacci designs: Fibo-optic afghan Fibre-nacci cushion

I guess this is only of interest to Mathematicians. Who else would care about its peculiarities? The design consists of 14 different rectangles, all with the same area. The total area of the rectangles is equal to the total area of the background. The original used Aran yarns and is approximately 140 cm by 115 cm (55 inches by 45 inches). It is made in one piece but only one yarn is used at a time. Other yarns could be used but this would change the overall dimensions of the afghan as it is not possible to change the size of any of the rectangles. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. We also have a cushion version of Wreck Tangled.

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. Buy the pattern on its own or in Cushy Numbers - a book of 12 patterns We also have an afghan version of Best of Both Whirls. Designed by mathekniticians Pat Ashforth and Steve Plummer.

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. You do not have to use two strands. Any yarn will work. The afghan/rug may be larger or smaller, according to the yarn you have chosen but instructions are included for changing the overall size, if necessary. It is worked in garter stitch, so always lies flat. It is made entirely from triangles. The curves are an optical illuion.

or buy at Payhip or LoveCrafts This is another one for those who like unusual constructions. The technique is very like making mitred squares but these shapes are kites. It is one of those designs that looks different from every direction. The effects can be dramatically changed by the choice of colours. Mathematically, the shapes are all the same. They are identical four-sided shapes, which fit together. From a knitter’s point of view they are not all the same because there are two very different methods of construction which cause the lines of knitting to go in different directions to create a more complex colour pattern. Pros This is an infinitely variable design. You can use as many, or as few, colours as you want. There are colouring-in sheets for you to plan designs with solid-coloured kites or using two or three stripes in each kite. You only use one colour at a time. The maximum number of stitches on the needles is 72 and the number is always reducing. You can use any yarn, in any thickness. You can add more shapes to make the afghan bigger. Instructions are included for changing the size of the shapes. No sewing. Cons You have to pick up stitches for every shape (but it is easy picking-up because each stitch is from the end of a garter ridge). There are a lot of ends to darn in. (If you make the shapes in single colours you reduce the number of ends.) Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The afghan shown measures approximately 100 cm (40”) by 130 cm (52”). Each individual shape measures approximately 20 cm (8”) by 16.25 cm (6.5”) It was made in 5 shades of Stylecraft Special DK and used approximately 450 metres (500 yards) of each colour.

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. It seemed an ideal candidate for translating to knitting. 12 identical shapes make the small dodecagon; 24 shapes make the larger version. Some of the shapes have to be reflected but this doesn’t matter in garter stitch as both sides look the same. It is an interesting shape but limited in its usefulness as any tessellation beyond the 24 shapes creates a pattern with very jagged edges. 12, or 24, shapes can be used for a cushion or afghan. We are publishing it as a free pattern in the hope that someone can see potential for using it more imaginatively. The shapes can be made to any size from very simple instructions. Some interesting optical effects can be created by the positioning of the colours. Photos 1 and 2 show the two sides of the completed cushion. Photos 3, 4 and 5 show different arrangements of the 24 pieces. Picture 6 shows some colour combinations. The final photo shows the paper version which was originally used to demonstrate the proof. (The photos are not to scale.)

This has been the most popular Woolly Thoughts pattern for the past twenty years. That it is probably because it is so versatile. The grey photo shows nine different variations - and that's before you start adding any colours to it.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.The yarn you choose will affect the overall size and the pattern gives other ways to change the size.The pattern includes a colouring-in sheet so you can try out your own colours.

This chart is particularly 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. You could use it as a washcloth or as a block for an afghan.The example shown was made in chunky yarn but any smooth(ish) yarn can be used for illusions.Size given below is for a square made in DK weight. A suggested DK weight yarn is shown below.

Lovely pattern for a pillow, a wall hanging and more! The possibilities are infinite ... Get the pattern via Etsy, it's called Squares That Look Round, designed by Steve Plummer and Pat Ashforth Woolly Thoughts. Made by LanArta. Get the pattern, it's called Squares That Look Round, designed by Steve Plummer and Pat Ashforth Woolly

January 2013 - Knitted version added The pattern now contains three variations Crochet hexaflexagon Crochet hexaflexacube Knitted hexaflexagon There are six photos of each cushion A hexaflexagon is a curiosity, usually made in paper. Version 1 The original hexaflexagon was one of the items made for events we attended during MathsYear2000. It is a crochet version of the paper hexaflexagons we have made with hundreds of kids over the years. It isn’t the most comfortable cushion in the world but it is great fun. I can absolutely predict what will happen when it is presented to a group of kids (or adults!). First, it is used as a frisbee (It is quite aerodynamic.) One person will put it on their head and it isn’t long before someone discovers that a slight tug will pull it over the head and it will sit snuggly round the neck, like a ruff. Eventually they investigate its strange properties and discover that this flat cushion has six faces. The cushion with the black hexagons is the one I made in 2000 and I have re-photographed it to show how well it has stood up to this treatment. It has been handled by thousands of people. In addition to the main yarn you will need small amounts of 9 noticeably different yarns. You can use any yarns of your choice though they should all be the same thickness. The crochet is very basic so you may wish to make the pieces in a different way. It is padded with triangles cut from a sheet of polyester wadding. The original was made with inexpensive acrylic DK yarns. Version 2 The Hexaflexacube was added in September 2008. Although the construction is different, there are still six different faces, each intended to look like a cube. There are obviously three different colour combinations but, if you look carefully, you will see that the positions of the colours change. Version 3 The knitted hexaflexagon is similar to the original crochet version. The coloured triangles are larger so you will need slightly more yarn in each of the nine colours. Three of the colours never reach the centre, regardless of how you flex the cushion. The patterns for all three versions are included in a single Ravelry download by following the link at the top of the page. YouTube video showing folding of Hexaflexagon and Hexaflexacube.

or buy at Payhip or LoveCrafts A very effective, easy-to-make, optical illusion. It can be knitted using any type of yarn, in three colours. The original was knitted in Aran weight in variegated blue and two solid blues. You do not have to work to a particular gauge. You work with small units and only have a large piece when you assemble it at the end. Use the basic ideas to make it any size from baby blanket to king-size bed. Included is a sheet that can be used to try out your own colourways before you begin. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. We also have a cushion version of Cubism, available as an individual pattern, or in the Cushy Numbers book

Which way are the columns pointing? Can you see hexagons ... or octagons ... something else? If you can knit garter stitch, you can make this. It is very easy to knit in seven columns which are then joined together, making it a very portable project. Any yarn can be used. The original was Aran weight. If you use a thinner yarn you may need to add extra rows and/or columns. The pattern comes with an outline drawing for you to try out your own colour combinations. Designed by mathekniticians Pat Ashforth and Steve Plummer

or buy at Payhip or LoveCrafts Can anyone resist following the path of a maze? This design is based on a hedge maze at Chevening, Kent, England. It can be knitted using any yarn and needles and can be used as an afghan or wall-hanging. Changing the thickness of the yarn will change the overall size. The version in the photos used two strands of Double Knitting yarn throughout. The maze is knitted in four triangular pieces starting at the centre. You do have to be able to handle several balls of yarn across the row, in some places. For this reason it is the most difficult design we produce but it is still not beyond the skills of anyone but an absolute beginner. The afghan in the photo was made using two strands of Double Knitting yarn held together but any other yarn could be used. It is approximately 125 cm (50 inches) square. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The pattern is also available in Maisie’s Mazes. See other patterns in the book here.

or buy at Payhip or LoveCrafts 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 are five sizes of square, getting ever smaller. The design is like a fractal as the same pattern is repeated at smaller sizes. The afghan can be made in any yarn although the choice of yarn will dictate the finished size. The original was made in Aran weight yarn; the replacement was made using two strands of Double Knitting throughout. The instructions are extremely easy to follow. The afghan is worked entirely in garter stitch with the squares and triangles being knitted first and the background knitted on afterwards. The booklet includes a colouring sheet where you can plan your own colour combination. The original afghan was bought by the Mathematics Collection of the London Science Museum. The two versions are shown in the photos. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. We also have a cushion pattern demonstrating Pythagoras Theorem in a different way

Mitred squares No sewing No blocking One yarn at a time This is our third version of a mathematical curiosity sometimes known as the squared square. It is made up from 21 different sized squares, which is the smallest number of different squares that can be fitted together to make big square. Each square has all the other smaller squares nested inside it. The squares are mitred and each one is made by picking up from existing squares. An easy to follow diagram shows you exactly where to join on the new squares. The afghan in the photos was made in DK yarns and measures 120 cm (48”) square. It could be made in other yarns though this would probably change the overall size. This may look complicated but it is really very easy - and addictive. It is almost a mindless project though not recommended whilst travelling as it is in one piece and there is frequent turning at the end of each square. Designed by mathekniticians Pat Ashforth and Steve Plummer

or buy at Payhip or LoveCrafts This afghan is based on a design sent to us by the famous Oxford mathematician Sir Roger Penrose. It is named in his honour. The first Penrose afghan was the red, yellow and orange version. It was bought by the London Science Museum for their Mathematics Collection. The second was in shades of green to give a very different effect. The instructions are very easy to follow and you can use any yarn you choose, though your choice will affect the overall size of the afghan. It may look complicated but, if you can knit garter stitch, you can make this. You work with one yarn at a time to create eight sections which are then stitched together. You do not have to work to a particular gauge. A colouring sheet is included so that you can try out your own colourways before you begin. The booklet also contains information about the aperiodic tiling that inspired the design. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The pale version of Penrose was made by my mother, who died on July 31, 2008. We are making a donation of £1, to Kidney Research UK, for every copy of the pattern sold. Click here to see why we support this charity. If you would like to start with something smaller, we have a cushion version of Penrose. The cushion pattern is also available in our Cushy Numbers book. June 2017 The original afghan can now be seen in the Science Museum online catalogue.

or buy at Payhip or LoveCrafts 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. The background is made first and the walls added later. It can be made using any yarn and hook. The yarn chosen will determine the finished size. Walls of Troy is based on a drawing from Mazes by Adrian Fisher and Diana Kingham The caption to the drawing says ‘Walls of Troy in Holderness, Humberside, was an unusually shaped maze some 40 feet (12 metres) in diameter. It was destroyed after 1815.’ It has 12 sides. The same book explains that mazes are of pagan origin but were adopted and adapted by the Christian church. It says The earliest surviving full-sized example is the ‘Chemin de Jerusalem’ pavement maze in the nave of Chartres Cathedral, France, built in 1235 …. They represented the path of life and reflected the recent journeys of the Crusaders; reaching the centre symbolised reaching both Jerusalem and salvation. The Chartres Cathedral Maze is so similar to the Walls of Troy that the variation is included in the booklet. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The pattern is also included in our Maisie’s Mazes book.

or buy at Payhip or LoveCrafts An optical illusion afghan or wall-hanging. The original (green and brown) version you see in the photos is only about one metre square. If you want to make it bigger, the pattern gives instructions for changing the overall size in a variety of ways. There are also several variations of the design given, including one that will allow you to use up lots of oddments of yarn. You can use any yarn of your choice though smooth, plain yarns are recommended. As with all our patterns, there is a colouring-in sheet so you can plan your own colour combinations. The name comes from a quote by Albert Einstein The mere formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. August 2016 The pattern now includes an extra file with pages for several variations that you can colour in to plan your design. You can also download this file from the Afghan Colouring page of the Woolly Thoughts website.

An optical illusion using illusion knit techniques. When you look straight at the afghan you see stripes in squares and zigzags. When you look at it from other angles you start to see steps and cubes, sometimes with light tops and sometimes with dark. Step Up can be made to any size you want, using any yarn. The one shown in the photos was made in DK yarn and measures about 86 cm by 96 cm (34 inches by 38 inches). There are never more than 20 stitches on the needles at any time but, because the sections are small, the work has to be turned often. Most of the joining is done as you go but there are a few small seams left to be stitched. You also need to be familiar with 3-needle bind off. There are a lot of ends to be darned in. The instructions begin by leading you stage-by-stage. Once you have learned the method, you can decide for yourself which direction to work and how big to make the afghan. Although this design is very simple to make it is not recommended for beginners.

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. Some 3D illusions don’t work when you change the scale. This one does. The technique used for the cushion guarantees that the shades will blend together to give the 3D effect. This pattern is also available in our Cushy Numbers ebook and we have an afghan version of Cubism

or buy at Payhip or LoveCrafts 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. The background is made first and the walls added later. It can be made using any yarn and hook. The yarn chosen will determine the finished size. Walls of Troy is based on a drawing from Mazes by Adrian Fisher and Diana Kingham The caption to the drawing says ‘Walls of Troy in Holderness, Humberside, was an unusually shaped maze some 40 feet (12 metres) in diameter. It was destroyed after 1815.’ It has 12 sides. The same book explains that mazes are of pagan origin but were adopted and adapted by the Christian church. It says The earliest surviving full-sized example is the ‘Chemin de Jerusalem’ pavement maze in the nave of Chartres Cathedral, France, built in 1235 …. They represented the path of life and reflected the recent journeys of the Crusaders; reaching the centre symbolised reaching both Jerusalem and salvation. The Chartres Cathedral Maze is so similar to the Walls of Troy that the variation is included in the booklet. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The pattern is also included in our Maisie’s Mazes book.

or buy at Payhip or LoveCrafts 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. You can make more, or fewer, rows of cables, as you wish. The original afghan was made using Chunky (Bulky) weight yarn but the instructions explain how to make it in any yarn of your choice. This is not a conventional knitting pattern. If you can knit garter stitch you can make this. It is suitable for beginners and experienced knitters, or even for two, or more, people working together. You do not have to work to a particular gauge. A sheet is included where you can plan your own colourways before you begin. Read the story of this afghan on Ravelry or on Woolly Thoughts web site.

In UK we call this game Ludo. It has alternative names in other countries. As you might guess Granny’s Ludo is basically made of crochet granny squares. It can be used as an afghan or floor game. It is one of six Afghan Games. You can see them all here. These games are surprisingly popular with teenagers as well as with young children. Some of our favourite photos of all time were taken at a Maths Festival in July 2000 when a young girl with very limited mobility and co-ordination spent nearly two hours playing on this game with her father and sister. She loved the game because she could sit on it and it was at a scale she could manage. The bottom photos, of other people, were taken in a shopping centre in Birmingham. The pattern is available on its own or in Afghan Games. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. Yarn quantities using DK. These amounts are approximate. Other thicknesses can be used Red, blue, green, yellow: 400 metres (440 yards) of each Neutral: 700 metres (770 yards) Black (for border, if required): 300 metres (330 yards)

or buy at Payhip or LoveCrafts An optical illusion using illusion knit techniques. When you look straight at the afghan you see stripes in squares and zigzags. When you look at it from other angles you start to see steps and cubes, sometimes with light tops and sometimes with dark. Step Up can be made to any size you want, using any yarn. The one shown in the photos was made in DK yarn and measures about 86 cm by 96 cm (34 inches by 38 inches). There are never more than 20 stitches on the needles at any time but, because the sections are small, the work has to be turned often. Most of the joining is done as you go but there are a few small seams left to be stitched. You also need to be familiar with 3-needle bind off. There are a lot of ends to be darned in. The instructions begin by leading you stage-by-stage. Once you have learned the method, you can decide for yourself which direction to work and how big to make the afghan. Although this design is very simple to make it is not recommended for beginners.

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. We have revisited the ideas we had for the afghan to create a set of pieces that can be assembled as a puzzle. Pentominoes have some interesting properties. Amongst other things, a set of 12 can be arranged in rectangles with the proportions of 6 x 10, 5 x 12, 4 x 15 or 3 x 20 (The afghan shows a solution for 6 x 10) If Pentominoes are turned into 3D shapes, with a height the same as the size of the squares, they become Pentacubes. Pentacubes can be fitted into rectangular boxes of 2 x 5 x 6, 3 x 4 x 5 or 2 x 3 x 10. The pattern includes two separate sets of instructions. One of these is very easy although it does require a lot of sewing; the other has each shape knitted as a single piece with just one edge to be stitched at the end. There are instructions for Pentominoes (flat shapes) and Pentacubes (3D shapes). The photograph with the four Ws shows four versions, varying the techniques slightly. None of the examples in the photo is the completely flat shape. It would be very easy to convert the shapes to crochet. Crochet instructions are not included. Note: These pieces are very tactile and fun to play with but they cannot be as accurate as solid shapes. Some versions of the puzzle distort more easily than others so might not be suitable for very small children who might simply distort the shapes to make them fit together.

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 column shows what happens when the cards in the second column are shuffled again, and so on. After ten perfect shuffles, the cards have returned to their original order, shown in the last column. A crochet afghan is shown here but the instruction booklet describes how to make an afghan of this design using knitting or crochet. Read the story of this afghan on Ravelry or on Woolly Thoughts web site.

or buy at Payhip or LoveCrafts This is another one for those who like unusual constructions. The technique is very like making mitred squares but these shapes are kites. It is one of those designs that looks different from every direction. The effects can be dramatically changed by the choice of colours. Mathematically, the shapes are all the same. They are identical four-sided shapes, which fit together. From a knitter’s point of view they are not all the same because there are two very different methods of construction which cause the lines of knitting to go in different directions to create a more complex colour pattern. Pros This is an infinitely variable design. You can use as many, or as few, colours as you want. There are colouring-in sheets for you to plan designs with solid-coloured kites or using two or three stripes in each kite. You only use one colour at a time. The maximum number of stitches on the needles is 72 and the number is always reducing. You can use any yarn, in any thickness. You can add more shapes to make the afghan bigger. Instructions are included for changing the size of the shapes. No sewing. Cons You have to pick up stitches for every shape (but it is easy picking-up because each stitch is from the end of a garter ridge). There are a lot of ends to darn in. (If you make the shapes in single colours you reduce the number of ends.) Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The afghan shown measures approximately 100 cm (40”) by 130 cm (52”). Each individual shape measures approximately 20 cm (8”) by 16.25 cm (6.5”) It was made in 5 shades of Stylecraft Special DK and used approximately 450 metres (500 yards) of each colour.

or buy at Payhip or LoveCrafts This afghan is based on a design sent to us by the famous Oxford mathematician Sir Roger Penrose. It is named in his honour. The first Penrose afghan was the red, yellow and orange version. It was bought by the London Science Museum for their Mathematics Collection. The second was in shades of green to give a very different effect. The instructions are very easy to follow and you can use any yarn you choose, though your choice will affect the overall size of the afghan. It may look complicated but, if you can knit garter stitch, you can make this. You work with one yarn at a time to create eight sections which are then stitched together. You do not have to work to a particular gauge. A colouring sheet is included so that you can try out your own colourways before you begin. The booklet also contains information about the aperiodic tiling that inspired the design. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The pale version of Penrose was made by my mother, who died on July 31, 2008. We are making a donation of £1, to Kidney Research UK, for every copy of the pattern sold. Click here to see why we support this charity. If you would like to start with something smaller, we have a cushion version of Penrose. The cushion pattern is also available in our Cushy Numbers book. June 2017 The original afghan can now be seen in the Science Museum online catalogue.

For those who can’t face knitting something the size of an afghan, we have a large collection of cushion patterns. Tilting at Windmills is particularly good for using up oddments of yarn. It is knitted entirely in garter stitch. This pattern is also available in our Cushy Numbers ebook. We have an afghan version of Tilting at Windmills.

or buy at Payhip or LoveCrafts An optical illusion afghan or wall-hanging. The original (green and brown) version you see in the photos is only about one metre square. If you want to make it bigger, the pattern gives instructions for changing the overall size in a variety of ways. There are also several variations of the design given, including one that will allow you to use up lots of oddments of yarn. You can use any yarn of your choice though smooth, plain yarns are recommended. As with all our patterns, there is a colouring-in sheet so you can plan your own colour combinations. The name comes from a quote by Albert Einstein The mere formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. August 2016 The pattern now includes an extra file with pages for several variations that you can colour in to plan your design. You can also download this file from the Afghan Colouring page of the Woolly Thoughts website.

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. We have revisited the ideas we had for the afghan to create a set of pieces that can be assembled as a puzzle. Pentominoes have some interesting properties. Amongst other things, a set of 12 can be arranged in rectangles with the proportions of 6 x 10, 5 x 12, 4 x 15 or 3 x 20 (The afghan shows a solution for 6 x 10) If Pentominoes are turned into 3D shapes, with a height the same as the size of the squares, they become Pentacubes. Pentacubes can be fitted into rectangular boxes of 2 x 5 x 6, 3 x 4 x 5 or 2 x 3 x 10. The pattern includes two separate sets of instructions. One of these is very easy although it does require a lot of sewing; the other has each shape knitted as a single piece with just one edge to be stitched at the end. There are instructions for Pentominoes (flat shapes) and Pentacubes (3D shapes). The photograph with the four Ws shows four versions, varying the techniques slightly. None of the examples in the photo is the completely flat shape. It would be very easy to convert the shapes to crochet. Crochet instructions are not included. Note: These pieces are very tactile and fun to play with but they cannot be as accurate as solid shapes. Some versions of the puzzle distort more easily than others so might not be suitable for very small children who might simply distort the shapes to make them fit together.

or buy at Payhip or LoveCrafts This afghan is based on a design sent to us by the famous Oxford mathematician Sir Roger Penrose. It is named in his honour. The first Penrose afghan was the red, yellow and orange version. It was bought by the London Science Museum for their Mathematics Collection. The second was in shades of green to give a very different effect. The instructions are very easy to follow and you can use any yarn you choose, though your choice will affect the overall size of the afghan. It may look complicated but, if you can knit garter stitch, you can make this. You work with one yarn at a time to create eight sections which are then stitched together. You do not have to work to a particular gauge. A colouring sheet is included so that you can try out your own colourways before you begin. The booklet also contains information about the aperiodic tiling that inspired the design. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. The pale version of Penrose was made by my mother, who died on July 31, 2008. We are making a donation of £1, to Kidney Research UK, for every copy of the pattern sold. Click here to see why we support this charity. If you would like to start with something smaller, we have a cushion version of Penrose. The cushion pattern is also available in our Cushy Numbers book. June 2017 The original afghan can now be seen in the Science Museum online catalogue.

Effecten breien en haken: Deze patronen zorgen er door de combinatie van blokken, strepen en kleuren allemaal voor dat je diepte ziet die er niet is.

or buy at Payhip or LoveCrafts An optical illusion afghan or wall-hanging. The original (green and brown) version you see in the photos is only about one metre square. If you want to make it bigger, the pattern gives instructions for changing the overall size in a variety of ways. There are also several variations of the design given, including one that will allow you to use up lots of oddments of yarn. You can use any yarn of your choice though smooth, plain yarns are recommended. As with all our patterns, there is a colouring-in sheet so you can plan your own colour combinations. The name comes from a quote by Albert Einstein The mere formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. August 2016 The pattern now includes an extra file with pages for several variations that you can colour in to plan your design. You can also download this file from the Afghan Colouring page of the Woolly Thoughts website.

or buy at Payhip or LoveCrafts 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. Numbers have been replaced by colours. The outer L-shapes show the first solution, the inner L-shapes show the second and the squares show the third. The solutions all follow normal Sudoku rules so that each colour appears only once in each row, column and block of nine squares. The design in Alex and Edmund’s book shows squares inside squares inside squares. We changed to L-shapes to make the construction easy. We used the same Sudoku solutions that Alex and Edmund used. Our shapes are striped mitred squares. The afghan is constructed in one piece. Each new square is made by picking up stitches from previous squares. We used DK yarn to make a 112 cm (45”) square to use as a wall-hanging. The pattern includes instructions for using different yarns and for changing the size. The afghan needs equal amounts of nine different colours. We used approximately 210 metres (230 yards) of each colour. There are 81 squares in the afghan. The squares are not all different. The pattern includes a version where there are 81 unique squares and another simpler version. Read the story of this afghan on Ravelry or on Woolly Thoughts web site. Both patterns contain the number grids for three different designs. The difference between the patterns is in the construction methods.