Students use mathematics in other curriculum areas. Students use mathematics in their daily lives. Students describe, extend, analyze, and create a wide variety of patterns.
Students recognize, describe, extend and create a wide variety of patterns.
Students learn that similar patterns may show up in many places in nature and in the things people make. Mathematicians have distinguished 13,000 single-component knots with 13 or fewer crossings, not counting mirror objects. The problem lies in the fact that two equivalent knots may have very different planar projections. This leads to the need for characterizing knots algebraically. The idea is to associate algebraic functions with knots such that equivalent knots possess the same identical function.