
06448939
j
2015d.00727
Akveld, Meike
Jobbings, Andrew
Knots in the classroom.
Math. Sch. (Leicester) 44, No. 2, 2729 (2015).
2015
Mathematical Association (MA), Leicester
EN
H70
G90
I90
K30
topology
knots
knot theory
knot diagrams
trefoil knot
threecolourability
knot invariants
lower secondary
upper secondary
teaching
approach
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?