Systolic geometryIn mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in its arithmetical, ergodic, and topological manifestations. See also a slower-paced Introduction to systolic geometry. The systole of a compact metric space X is a metric invariant of X, defined to be the least length of a noncontractible loop in X (i.e.
Mass–energy equivalenceIn physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicist Albert Einstein's formula: . In a reference frame where the system is moving, its relativistic energy and relativistic mass (instead of rest mass) obey the same formula. The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c2).
