Atomic Structure & Law (Mathematics Research Developments)

This book discovers four-dimensional space within a sphere with the instantiation of the 2s2p electron octet in a neon shell. Four space dimensions correspond to points, lines, planes, and solids geometrically. This book develops the idea of dynamic calculus that is implemented by circular functions instead of infinitesimal limits. As the law of nature, dynamic calculus of spherical quantities describes harmonic oscillations of electrons in atoms by dimension transformation rather than kinematic movement. In particular, electronic orbitals of 1s2s2p within a neon atom are defined in calculus, trigonometry, and geometry rigorously. A fresh theory of the atomic structure and law is established from scratch that eventually changes the traditional spacetime worldview. The theory derived from atomic spacetime may be extended to the description of molecules, cells, and organisms. For example, both electrons within a helium atom constitute a two-dimensional system, which provides a mathematical model for life phenomena. A husband and a wife are two dimensions of the family; plants and animals are two kingdoms of the advanced lives. The interplay and transformation between both dimensions are the eternal theme of nature. A DNA molecule, composed of space and time strands, is a stepwise LC oscillatory circuitry where each base pair is a capacitor, each phosphate bridge is an inductor, and each deoxyribose is a charge router directed by chiral carbons with anisotropic 2p electronic orbitals. All physical quantities are ordered into a periodic table according to their spacetime dimensions. This original approach provides sharp insight into the properties of and relationships between various physical quantities, paving the way toward the formulation of a grand unification theory. Spherical quantities in dynamic calculus complement physical quantities in linear algebra, comply with the Pythagorean theorem and the general Stokes theorem, observe Maxwells equations, and characterize the rhythms of entities and life essentially. The spherical view also endorses the core concepts of traditional Chinese medicine, such as yin and yang theory, five element theory, and eight trigram philosophy.