| Summary: | By traveling through the inner structure of biological tissues, for instance by means of a scanning or a transmission electron microscope, unexpectedly exact geometries and symmetries in the form of perfect lattices, honeycomb networks, helical macromolecules and polyhedral shapes resulting from minimal surfaces can be observed. Furthermore, by exploring cells and tissues at meso-, micro- and nano-scale levels, one discovers that self-similarity and hierarchy replicate that geometrical order and surprisingly characterize all the biological architectures, in this way de facto governing the key biomechanical functions and biochemical signaling at the basis of the life. The apparent extreme shape minimalism that nature exhibits when analyzed at sub-macroscopic level is therefore deceptive and thrilling at the same time: the geometrical neatness is indeed often counterbalanced by extremely complex functional relationships and multi-physical interactions – occurring over different spatial and time scales – which force who tries to interpret the dynamics of biological systems through mathematical models to somewhat reconsider matters that he/she previously deemed foundations, the need to respond to new fundamental questions raised by counterintuitive events and seeming paradoxes trouncing the cultural barriers that traditionally separate the disciplines and obscure the beauty.
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