id: 06448939
dt: j
an: 2015d.00727
au: Akveld, Meike; Jobbings, Andrew
ti: Knots in the classroom.
so: Math. Sch. (Leicester) 44, No. 2, 27-29 (2015).
py: 2015
pu: Mathematical Association (MA), Leicester
la: EN
cc: H70 G90 I90 K30
ut: topology; knots; knot theory; knot diagrams; trefoil knot;
three-colourability; knot invariants; lower secondary; upper secondary;
teaching; approach
ci:
li:
ab: From the text: Everybody knows what a knot is ‒ we have all had to deal
with a tangle of string. This in itself provides some motivation for
the study of knots as a mathematical topic. But studying knots from a
mathematical point of view also has real value in the classroom because
it provides a pleasing contrast between the ‘abstract’ thought
processes involved and the ‘concrete’ nature of such examples. Of
course, it would be helpful if it were possible to classify knots in
some way. We wish to ask questions like “are two knots the same?",
“is the trefoil knotted?", “is a knot the same as its mirror
image?" Answering these questions would assist with classification, but
they are also interesting in their own right. However, providing
answers is far harder than you might think; we shall answer only one of
them here, as a way of showing the types of approach mathematicians
use. Mathematicians define two knots to be equivalent (or simply the
same) if one can be deformed into the other. Studying knots is made
much easier by projecting them onto a plane. The result is called a
knot diagram and this is also where the first difficulties come in,
because one and the same knot can have many different knot diagrams.
How are all these diagrams related?
rv: