• Journal for History of Mathematics
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• v.28 no.5
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• pp.249-262
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• 2015

Simon Stevin, a mathematician active in the Netherlands in early seventeenth century, parlayed his mathematical talents into improving navigation skills. In 1605, he introduced a technique of calculating the distance of loxodrome employed in long-distance voyages in his book, Navigation. He explained how to calculate distance by 8 different angles, and even depicted how to make a copper loxodrome model for navigators. Particularly, Stevin clarified in the 7th copper loxodrome model on the unique features of equiangular spiral curve that keeps spinning and gradually accesses from the vicinity to the center. These findings predate those of Descartes on equiangular spiral curve by more than 30 years. Navigation, a branch of actual mathematics devised for the survival of sailors on the bosom of the ocean, was also the first step to the discovery of new mathematical object.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.817-827
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• 2021

In this paper, we prove that a diffeomorphism f on a normal almost contact 3-manifold M is a CRL-transformation if and only if M is an α-Sasakian manifold. Moreover, we show that a CR-loxodrome in an α-Sasakian 3-manifold is a pseudo-Hermitian magnetic curve with a strength $q={\tilde{r}}{\eta}({\gamma}^{\prime})=(r+{\alpha}-t){\eta}({\gamma}^{\prime})$ for constant 𝜂(𝛄'). A non-geodesic CR-loxodrome is a non-Legendre slant helix. Next, we prove that let M be an α-Sasakian 3-manifold such that (∇_YS)X = 0 for vector fields Y to be orthogonal to ξ, then the Ricci tensor 𝜌 satisfies 𝜌 = 2α²g. Moreover, using the CRL-transformation $\tilde{\nabla}^t$ we fine the pseudo-Hermitian curvature $\tilde{R}$, the pseudo-Ricci tensor $\tilde{\rho}$ and the torsion tensor field $\tilde{T}^t(\tilde{S}X,Y)$.

• Journal of Navigation and Port Research
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• v.38 no.2
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• pp.185-191
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• 2014

With the 500th anniversary commemoration of Gerard Mercator's birth in 2012 now passed, there is the possibility that his name will fade back into obscurity. This would be both unfair and pitiful, because Gerard Mercator's name should be highly regarded as one of the principal contributors to navigational science and the promotion of marine safety. An accomplished cartographer, in 1569 Mercator published a remarkable 18-folio world map, depicting the then-known world in a new format with straight rhumb lines. While this distorted the size of land masses, particularly in higher latitudes, this new projection made navigation much easier for now all sailors had to do was to draw a straight line between two points to plot their course. Mercator clearly had this navigational benefit in mind, though his contemporaries did not immediately recognize its value. It wasn't until after Mercator's death, when Edward Wright (1599) and Henry Bond (1645) used and explained the new projection and demonstrated the use of straight rhumb lines in navigation that the Mercator projection became the standard for sea charts. Today, 450 years later of his death, electronic charts still rely on the projection Mercator invented and developed, confirming his position as a giant in the history of navigation. This paper introduces his life and work, detailing the importance of the 1569 world map and its contribution to navigational science and safety.