Knot a Problem — Investigation Ideas

Quick Celtic Knots

One of the points of this app was to be able to quickly draw Celtic Knot diagrams to make it easy to investigate their properties. While it is fun to draw your own, to study them you need a way to draw lots of them.


Here are some ideas of things to investigate. With all of them, start by looking for the pattern and then try to find an explanation.


There is a lot of Mathematics that can be drawn out of studying Celtic Knots. The area of Mathematics that they fit into is Knots and Links. The difference between a knot and a link is the number of ribbons: one ribbon is a knot, more than one is a link. Furthermore, Celtic knots and links are always alternating (can you explain why?).


Of course, one of the things about Celtic knots is how they look. The knots generated by this app have a reasonably fixed appearance, but it can be used as a starting point for designing more intrigate diagrams, either by using the TeX exporter or by drawing the knot again by hand. Below is a video of how to do this on squared paper.