Tricolorability

Some mathematicians (like Dr. Lisa Piccirillo) study objects called knots and their properties. Knots are any object that can be made by taking a piece of string, tangling it around itself, and sticking the ends together.

Drawing of the trefoil knot colored with green, purple, and blue to show that it is tricolorable.
The trefoil knot is tricolorable.

One property of knots is whether or not they are tricolorable. A knot is tricolorable if you can color the knot using at least two different colors following two rules: (1) Each time the picture of the string crosses itself on the page, the string crossing is colored with either a single color or three different colors. (2) The string only changes color when you can’t see it (when it goes under another part of the string on the page). One example of a tricolorable knot is the trefoil knot.


Now it’s your turn! Print the pdf below and grab some colored pencils to see if you can determine which of the following knots are tricolorable.


knots_worksheet
.pdf
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