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      Volume 21, Issue 6

      June 2016,   pages  489-577

    • Editorial

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    • Science Smiles

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    • Sir William Rowan Hamilton: Life, Achievements, Stature in Physics

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      Against the background of the development ofphysics, and in particular of mechanics, over thecenturies since Galileo and Newton, we describethe life and work of William Rowan Hamilton inthe 19th century. The depth of his ideas whichbrought together the understanding of ray opticsand classical mechanics, and the remarkableways in which his work paved the way to theconstruction of quantum mechanics in the 20thcentury, are emphasized.

    • Hamilton's Optics: The Power of Wavefronts

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      Building on work by Fermat and Huygens, Hamiltontransformed the study of geometrical opticsin his very first paper, presented when still inhis teens. His ‘characteristic function’ was ananalytical way to describe wavefronts, and in hishands a powerful tool to look at families of raysrather than isolated ones. His prediction of internaland external conical refraction in somecrystals and its spectacular verification in a fewmonths established his reputation among his contemporaries.This formulation of optics uncoveredmany general properties, not easy to seein the conventional method of tracing individualrays. The deepest outcome of his early opticalwork was a parallel view of the mechanics ofparticles, which played a fundamental role in thebirth of quantum mechanics and continues to bethe standard framework for classical mechanicsup to the present time.

    • Algebra and Geometry of Hamilton's Quaternions: 'Well, Papa, Can You Multiply Triplets?'

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      Inspired by the relation between the algebra ofcomplex numbers and plane geometry, WilliamRowan Hamilton sought an algebra of triples forapplication to three-dimensional geometry. Unableto multiply and divide triples, he inventeda non-commutative division algebra of quadruples,in what he considered his most significantwork, generalizing the real and complex numbersystems. We give a motivated introduction toquaternions and discuss how they are related toPauli matrices, rotations in three dimensions, thethree sphere, the group SU(2) and the celebratedHopf fibrations.

    • Animal Locomotion in Different Mediums: The Adaptations of Wetland Organisms

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      Wetlands are repositories of unique biodiversity. Wetlandorganisms are well adapted to their habitat, lying at theinterface of aquatic and terrestrial environments. In order tounderstand their adaptations in a better way, it is essential tograsp the basic properties of the medium in which variousorganisms live. This is attempted here by first examining theproperties of the two contrasting environments, terrestrialand aquatic. We focus primarily on locomotion, touchingupon related life processes like respiration, body size andmaintaining body balance by employing basic principles ofbiology and physics.

    • Products of Sets: Ordered and Unordered

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      In this article we study the (Cartesian) Productsof sets. As a prelude to it, we examine variousdefinitions offered by different mathematicians tothe concept of an ordered pair. The subtle differencebetween the notions of ordered productsof sets and unordered products of sets is highlighted.

    • The Bohr Correspondence Principle: Kepler Orbits of the Electron in a Hydrogen Atom

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      We consider the quantum-mechanical non-relativistichydrogen atom. We show that for boundstates with size much larger than the Bohr radius,one can construct a wave packet that is localizedin space corresponding to a classical particlemoving in a circular orbit.

    • A Charged Particle in Perpendicular Electric and Magnetic Fields

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