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'Designing Table Mats' printed from http://nrich.maths.org/

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rope mat

 

The photo on the right shows a table mat made from a coiled rope.

Chris wants to produce and sell sets of table mats like this.  Her initial plan is to make them by coiling a thin rope into a rectangular pattern, sewing each layer to the next with 'thread' made of a strand of the material the rope is made from.  Measuring a mat she already has, she decides that 30cm x 24 cm is a good size to aim for.

  • Is this size possible using this method - coiling a length of rope as in this image?
  • How might she rethink the design so she can make a bigger range of lengths and widths of mat?
This problem is asking you to create a mathematical model for the design of a table mat.

You will need to make sensible assumptions about the thickness of the rope, and the construction of the mat including the length of the starting section of rope in the centre of the mat.  Write down all the assumptions you make so you can revisit them and decide if they are acceptable.