Abstract
This chapter examines the various aspects of handmade structures and periodicity. It is necessary to go higher up in the exponential scale, in order to keep the original characters of the units put together into a continuous function. It is found that going to the exponential scale and adding the same two spheres with different centers with equation gives again complete fusion. Two different functions can be added on the exponential scale so that the sum function is continuous and the properties of the original functions are kept. It is observed that increasing the constant toward unity makes the planes come together and the geometry is approaching the topology for the pseudosphere, famous for having constant negative Gaussian curvature. The topology shows that many structures in nature might well be built with constant negative curvature. The mathematics of the hyperbolic plane is difficult and not possible to use directly. It is found that by starting to vary the constant, the gyroid surface is obtained with the typical monkey saddle.
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