Didi's Knot Theory Exploration

This term, Didi studied knot theory, the concept of mathematical knots. Unlike regular knots, mathematical knots are joined loops with no ends. Mathematicians spend lots of time thinking about how to differentiate one knot from another or prove that one knot is different from another. To familiarize herself with this concept, Didi demonstrated two ways that mathematicians use to show whether two knots are the same. Below, you will see the 5₁ knot, which looks like a star. Didi showed that the 5₁ knot is 5-colorable, meaning it can be colored using 5 different colors. On the right, Didi calculated the Alexander Polynomial for the 5₁ knot by using matrices. The other knot image is also 5-colorable and has the same Alexander Polynomial. This supports the idea that both of these knots are the same, even though they look so different! In fact, if you were to make the knot out of string or wire, you could manipulate one knot into the other.