Esoteric Mathematics and Life

One of the most useless mathematical exercises that engineering students do is that of calculating limit of a function using the epsilon-delta definition. The definition is complex, its motivation non-obvious and applications nearly non-existent. While it is true that in many important theoretical calculations this definition is useful, one is not quite sure, where in the day-to-day use would an engineer need to apply it.

However there is a closely related area of mathematics, pertaining to continuity and differentiability of functions which has come to the fore due to new engineering applications in 3D printing and bio engineering. Organ transplants save life, however there are not enough number of human donors to meet the demands.

3D printing of organ’s is an emerging technology that has immense potential. Human organs, however rarely fit into the standard geometric shapes. To design and analyze organs, the mathematics required is that of fractal geometry. Fractal geometry deals with self similar structures, where a big part of a structure looks like a scaled up version of its smaller part. Such structures naturally occur in our bodies, for example lungs, kidneys and the blood circulatory system. Thus to 3D print such organs, the code required will be more efficient if it uses the foundational ideas of fractal geometry, rather than those of the Euclidean geometry.