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The World of Illusion Knitting

MUFFLERMATICS

A collection of mathematical scarves, shawls and wraps

All of the patterns in Mufflermatics are wearable designs based on ideas previously used for afghans. They are all items to wrap yourself in, such as scarves and shawls. The patterns can be also bought individually.

All Ways Round

There are 24 ways to arrange four colours in a square. 12 can be seen by looking at one side of this scarf; the other 12, are reflections and can be seen by turning the scarf over. Folding the scarf in half might lead you to believe that there are only 6 completely different possibilities.

Related Afghan

Back to Square One

The square at the centre back of this knitted shawl has triangles on two of its sides. Each of these triangles has a smaller triangle until the last two triangles are added to complete the points. The size of each new triangle is based on Pythagoras Theorem.

Related Afghan

Pythagorean Ripples

Corrugated Comforters

Three separate crochet scarves to show the folds made when you make dragons with 4, 5 or 6 folds. (See Dragon Curves) It can be seen from the photograph that the stripes in the first of these are also in the other two, with extra stripes in between.

Related Afghan

Chromatic Scale

Double Crossed

Each square is a different mixture of two colours. Small amounts of nine yarns are used in each shawl. The nine yarns, used in every possible combination, give a total of 36 mixed squares, making 45 different shades altogether.

(Knit and crochet versions)

Related Afghan

Double Vision

Dragon Drape

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.

Related Afghan

Scaled Up

A series of triangles, growing out from the centre neck. The design could carry on to infinity. The sizes of the triangles are worked out using Pythagoras Theorem. The length of the long side of one triangle becomes the length of the short side of the next.

Related Afghan

From Square to Eternity

Point of Order

Another use of the Fibonacci Sequence, for a crochet shawl. The stripes represent the first 8 terms of the sequence (The first term is 0 so there is no stripe). This gives a pleasing arrangement even when the colours are chosen in a fairly random manner.

Related Afghan

Fibrenacci

Quintessential

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

It is also possible to arrange the 12 pentominoes in other rectangles which might be used for a shawl design. They are 4 x 15, 5 x 12 and 6 x 10.

Related Afghan

Bunch of Fives

Fibonacci Fichu

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.

Related Afghan

Fibo-optic

Stole’n’Secret

Use simple Mathematics to calculate how much space is needed to hide a secret message in a filet crochet scarf. The letters are given in the form of a square grid.

Related Afghan

Code Comfort

The book also includes a few pages to help you design your own geometric scarf or wrap.