The Honeycomb Conjecture by Fiona Oliver

The Honeycomb Conjecture

March 2019
Fingering (14 wpi) ?
3.0 mm
1039 yards (950 m)
One size fits all. Finished dimensions are 23 cm/9 ins wide and 162 cm/64 ins in circumference.
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About this design
Geometry is the branch of mathematics concerned with questions of shape, size, relative position of figures and the properties of space (Wikipedia). This is also a really good definition of some elements of crochet, particularly when working with geometric crochet motifs. My favourite crochet motif shape is the hexagon because it is such a versatile shape that can be formed in many different ways.

Whilst watching a recent documentary about honeybees, my interest was caught by a mention of the Honeycomb Conjecture. This is an ancient geometry conjecture that was eventually proven in 1999 by Thomas C. Hales. It states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter … which is a rather fancy way of saying that honeybees really know their stuff when it comes to optimising the space in the hive!

So, with my mind buzzing again about the possibilities of hexagons, I have designed the Honeycomb Conjecture Cowl so that we can all ponder the marvels of both nature and geometry, while at the same time making a beautiful accessory for those cooler days when the busy honeybees are taking a break.

This design is a fabulous stash buster as it provides an opportunity to use up all those lovely little nubbins of left over yarn that we all have kicking around in our stash. It is also a design where you can let your inner colourist run wild. My finished Honeycomb Conjecture Cowl has taken the colour palette of the hive and honeybees as its inspiration, but this design would work equally well with wild and vibrant colours, or a more subdued and less varied palette. I’ve included a colouring in sheet so that you can play with your colours before you begin.

A single blocked hexagon crocheted with a 3 mm (US size C2, UK size 11) size measures 5 cm/2 ins when measured diagonally from corner to corner.

This design requires a range of colours in fingering/4 ply weight yarn and the yarn amounts needed for each colour will vary from project to project. For a single hexagon, you will need:

• 2.14 metres/2.3 yards for the centre disc.
• 2.14 metres/2.3 yards for the hexagon edge.

The finished Honeycomb Conjecture Cowl contains 222 completed hexagon units, which means that you will need a total of:

• 475 metres/510.6 yards for all the centre discs.
• 475 metres/510.6 yards for all the hexagon edges.

The sample Honeycomb Conjecture Cowl used a total of 20 colours, all drawn from leftovers in my stash.

3.0 mm (US size C2, UK size 11) crochet hook.

Tapestry/darning needle.
Colouring pencils/crayons/textas.

The Pattern
The pattern includes written instructions, charts and links to instructional videos and picture tutorials created by other people.