### Irrational Ribbons---Golden Ratio (*phi*); Cherry Pi (*pi*); Natural Log Base (*e*)$; Square Root of Blue (sqrt(2))

Materials and Methods: Crocheted from colored 3-ply cotton with a 2mm hook

Designer & Artist: Aisha Mahmood

Year: 2013

The golden ratio (*phi*), *pi*, *e*, and sqrt(2) are all well-defined irrational numbers. Accordingly, they cannot be expressed as finite decimal expansions, though it is in principle possible for any of them to be enumerated to arbitrarily many decimal places. These ribbons represent 1m long approximations of each constant, with significant figures varying according to the stitch length of each design.

The crochet is worked in chains (*pi* and *e*) or rows (*phi* and sqrt(2)) rather than turned, which would give static, unalterable lengths of ribbon; these are only the initial meters, and could be lengthened ad infinitum according to whim. To make sense of the numbers represented, the ribbons should be viewed from what is conventionally the "wrong" side of the stitching, which may be taken to reflect the ribbons' status as imperfect worldly imitations of ideal Platonic numbers.

Colors and forms have been chosen both to evoke characteristic features of the constants, and also in the spirit of word play; the semi-circular stitches of Cherry Pi appeal to the ratio between the circumference and diameter of a circle, the leafy green picots of *e* play on the terminology of the "Natural" Log Base, and the square spaces between the digits of Square Root of Blue are an homage to Pythagoras.