This is a deceptively simple way of constructing a sock by reducing the flap to a very small strip and working an extended gusset in its place. The rounds form a right angle around the ankle and instep, which gradually softens into a continuous round; hence the reference to the mathematical problem of ‘squaring the circle’.
The specific construction makes this ideal to use up the heaps of small leftovers that every sock knitter seems to acquire, but it will also showcase nicely a self-striping yarn with more substantial stripes.
As befits a mathematically-inspired sock, you will be able to adapt this pattern to any stitch count needed by doing some very basic math.
Please read the whole pattern to the end before starting; at several points in the pattern you will have a distinct advantage if you know what’s coming afterwards…
At the point of publishing I have only completed a single sock, so there is a good chance there could be mistakes or omissions - please let me know if you spot anything.
UPDATE August 6 2015: There is now a Finnish version available. Thanks to Hannele Rahkonen for the translation !