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Beyond Euler: Simple Geometry Unifying Vectors, Scalars and Complex Numbers

Michael Studencki
Year: 2011
Vectors, scalars and complex numbers are mathematical concepts which evolved separately and nowadays they are considered different. Although they have been around for many years, there are still lots of misconceptions and problems with understanding of their true nature, which brings even more confusion to their applications in modern physics, especially Quantum Mechanics. My goal is to show that all these three mathematical concepts are in fact one and the same animal, but seen from different perspectives. A simple geometry shows that the unification of notation is possible, which could allow us to use one tool for all these applications. This can lead to several simplifications in physics.