A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)

Estimating the weight of large pumpkins before harvest presents an opportunity for applying several diverse mathematical topics. A model that allows an estimation by easy tape measurement is derived. (MP)

This column contains brief notes on graphing in three dimensions; patterns in Pascal's triangle; plotting graphs by computer; and an application of the hypocycloid. (MM)

Solves the problem of defining a smooth piecewise linear approximation to a given function. Discusses some alternative approaches to the problem. (YP)

Describes an activity which uses the computer to produce an environment that encourages an inductive reasoning approach to ratio and proportion through a billiard ball simulation. Provides examples of graphs and bouncing ball data. (RT)