Physics

Nonlinear system

Underdetermined system

Calculus (dental)

Mathematics

Maxwell's equations

Unit vector

Optics

Linearization

Limit (mathematics)

Mathematical analysis

Holography

Geodesic

Dentistry

Geometry

Quantum mechanics

Medicine

Ellipse

Open Science Journal

In this paper equations in R3 which are illustrations of “linear” ellipses, i.e. ellipses which tend to become segments of a geodesic of R2, because their eccentricities tend to unit () will be found. During a linearization process of ellipses, varying vectors will be mapped, from which ellipses and their relations in R2 , to varying vector fields and their relations in R3 are defined. These vector fields and their relations in R3 are called “holographic”. At the limit , the holographic relationships are formalistically similar to Maxwell's equations. This is a theoretical derivation of Maxwell’s equations and not a systematic classification of experimental data as Maxwell did.

Foundations of the Electromagnetic Theory