Heinrich HERTZ's Contact Law and NPC Passage by the HIV Capsid: Contact Mechanic Is Putative Relevant by the Twelve HIV Pentagons: The FIBONACCI number 5 at the Narrow End, and the LUCAS Number 7 at the Broad End and the FIBONACCI Numbers 3, 8, and 34 in the NPC
Heinrich HERTZ's Contact Law and NPC Passage by the HIV Capsid: Contact Mechanic Is Putative Relevant by the Twelve HIV Pentagons: The FIBONACCI number 5 at the Narrow End, and the LUCAS Number 7 at the Broad End and the FIBONACCI Numbers 3, 8, and 34 in the NPC HIV-1 obeys Euler’s polyhedron formula with 12 CA pentamers capping the ends of the cone: 5 pentamers at the narrow end, 7 at the broad end (see Figure 4 etc. from “Passage of the HIV capsid cracks the nuclear pore“ by Kreysing, Jan Philipp et al., Cell, Volume 188, 2025, Issue4, 930 - 943.e21). This figure shows the fifth FIBONACCI number F(5) = 5 at the narrow end, and the fourth LUCAS Number L(4) = 7 at the broad end of the near ellipsoid cone. Thus, even the substructure of the HIV capsid is in accordance with GEIER’s equations allowing FIBONACCI and LUCAS numbers. As L(n) = √5F(n) this is with 5=F(5) and √5 in direct relation to Daniel SCHECHTMAN’s quasicrystals by 5√5 = 5^(3/2) = 11.180. .. ≈ L(5) (and L(6)/ √5...