MultiplyingLabyrinths (Post under Construction)

DONT BE PUT OFF – HURRY down the scroll to the next post!”

Mathematicians will know the rule for multiplying together two complex numbers. If the real part of a number has magnitude a and the imaginary part magnitude b, we can write the number as a + ib, where i is the mysterious but very useful square root of minus one . If you remember those graphs employed to explain school algebra ,you can think of  a + ib as referring to a point on the complex plain with (x,y) coordinates (a,b).

Two complex numbers a + ib  and c + id can be multiplied together to give their product e + if where e = (ac – bd) and f = (ad + bc)

(I’ll insert a diagram and some more text soon after I get back from tonight’s  Buxton

Opera House Christm,as Pantomime. In the mean time there are the two possible ways of constructing the product of Chinese Labyrinths (1,2) and (5,0). If you multiply these numbers together as if they were complex numbers, then you get (5,10) as their product – and this gives you the Supertile size and the repeat unit of the resulting tessellation. Here they are.


A first stab at naming these patterns – MULTICHINS??


About davescarthin

After terminating academic and local government careers, long an independent bookseller/publisher at Scarthin Books, Cromford, Derbyshire, UK. An antiquarian bookseller in two senses, I now have more time to be an annuated independent post-doc, developing the long dormant topic of lattice labyrinth tessellations - both a mathematical recreation and a source of compelling practical tiling and textile designs. Presenting a paper and experiencing so many others at Bridges Seoul 2014 Mathart conference was a great treat, as were the spirited MathsJam Annual Conferences in November 2016 and 2017. I'm building up to a more academic journal paper and trying hard to find practical outlets in graphic design and landscape architecture. I submitted 8 ft square tiling designs to the Wirksworth Festival Art and Architecture Trail in 2016 and 2017. I love giving illustrated talks, tailored to the audience. Get in touch to commission or to collaborate.
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