Knots have always been an integral part of life, and have only been found to have mathematical uses recently.  This paper only explored a brief introduction to knots.  Proving knot equivalence is the core of knot theory, and without invariants this is very difficult.  Hence, invariants are an important part of knot theory. Another more algebraic area of knot theory involves drawing comparisons between knot composition and multiplication within the integers.

Although we only examined a few basic areas of knot theory, they are an important foundation to further understand the field and apply it in areas of physics, chemistry, and molecular biology in the study of the structure of DNA during replication.  DNA structure, when simplified, appears like many knots mathematicians study.  This allows them to understand the function of DNA better, since structure and function are so closely related.  See figure 26 for a diagram of DNA structure being simplified into a knot.

For other interesting knots see:


kMain menu      1. History              2.Intro               3.Invariants     4.Composition    5.Conclusion