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

Based on Pythagoras' theorem and the square root of 2.

I love this design because each row has one less stitch than the row before. The stitches disappear before your eyes.

The afghan in the photo is distorted because it has been hanging for many years.

Scroll down for more information about

Square Root



From Square to Eternity

Best of Both Whirls


Square to Eternity

Best of Both Whirls


Knitted in one piece.

The centre square is knitted first. All other shapes are added by picking up stitches and knitting on.

Subtle shading can be created with four yarns. using two strands of colour 1 for the first square, one strand of colour 1 and one strand of colour 2 for the second square, two strands of colour 2 for the third square, and so on.


The original was worked in eight shades of yellow and brown. The palest yellow was used at the centre and each new square was slightly darker than the one before. Two strands of DK were used throughout.

The size will vary according to the yarn chosen. Extra squares can be added, if required.

The relationship between one square and the next is the same throughout. Thick yarns will automatically make bigger squares than thin yarns.

The starting square can be of any size. The next square - which is not really a square but merely four triangles arranged round the first square, to give the impression of a square sitting underneath, is 1.4142 times as wide. Every square is 1.4142 times as wide as the one before. This number comes from working out the square root of 2.

In real life it is impossible to measure with that degree of accuracy. This is especially true of something stretchy - like knitting. Using 1.4 as the square root of 2 gives an adequate answer in these circumstances. 1.4 is a much friendlier number and produces some nice multiples.

Did this afghan get its name because it uses the square root of 2? Or because it branches out from the centre root which is a square? Or does it depict a route through a series of squares?


CreativeCrocheter has been a Woolly Thoughts fan for a very long time - but she doesn’t knit. When she attended one of our knitting workshops she used many of the mathematical principles to interpret the shapes in crochet. Working in crochet is more difficult as there is always some testing to be done to achieve the correct angles. In knitting this happens as if by magic.

She has recently been working with a group of people who wanted to crochet Square Root. Click here for her tutorial.