Geometry and algorithm

Geometry in some way is a phenomenon of spatial and structural organization of matters as a result of system optimization. For instance, soap bubbles or air bubbles (under water) are perfectly spherical in shape if there's no uneven disturbance. We all know well that the spheres are the result of the surface tension of the continuous soap membrane /water surrounding the air bubble in the latter example which tends to minimize the surface area.The hexagonal pattern in honeycomb is the other good example of optimized structural and spatial organization of materials for bees to build homes. Basically, all naturally emerged geometries are the most effective form for matters to exist and for dynamic systems to operate. Ineffective geometry emerges since we learn how to manipulate system willfully. That is when natural systems become artificial. Despite the invention of ineffective geometry by us, many other effective geometries are created by artificial processes such as alloy.

It is invalid to say all algorithms are related to geometry. Because there are algorithms dealing with formless tasks. However, because of the computational nature of algorithmic operations, most of them can always be expressed in geometrical language e.g. plotting graphs with numerical data. Algorithm is artitifical manipulations of matters and systems through systematic undertaking of procedures which are believed to have specific effects in specific context. The primitive idea about algorithm is methods by which people can get things done. In geometrical discussion, algorithm must be involved in creation or alteration of geometry based on the notion of algorithm as methods.