Even though mathematicians are well-schooled in the wide applicability of their craft, there are times when a new (to you) application is surprising and there are times when it is not. When I first read the title of this book my reaction was, “Well, that seems like an obvious application.” For a fish net is of course a linked collection of optimized holes designed to capture the fish and let the water and smaller detritus flow through easily. The twines could correspond to the elements of the mesh and the area between them would be the holes.
What is interesting is the complexity of the partial differential equations used to optimize the solution of the most efficient fishnet. The twines of the nets have to have some flexibility, which means that the size and shape of the openings in the nets are not static. Too large and the fish get through and too small and the drag is too great. Furthermore, the knots that bind the sections together also have to allow for some movement, further modifying the structure of the shapes made by the twines. For large nets, an efficient model would have a dramatic difference in the strain on the winches when the net is being deployed and then reeled in. Being able to deploy and recover larger nets with the same equipment would have a positive economic return for the fishing boat.
My suspicion is that with the long human history of fishing with nets, a great deal of the conclusions in this book has already been discovered via trial and error. Whether you have a need to know about fish nets or not, if you love mathematics you will appreciate this application of mathematics to one of the historically most important industries.
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.
2. Finite element method
3. Equilibrium calculation
4. The triangular finite element for netting
5. The bar finite element for cable
6. The node element