• Journal for History of Mathematics
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• v.21 no.1
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• pp.45-78
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• 2008

Theory of minimal surfaces has always been in the center of differential geometry. The most difficult part in minimal surfaces is how to find meaningful examples. In this paper we survey the history of search for minimal surfaces. We also introduce examples of recently emerging maximal surfaces in the Lorentz-Minkowski space and compare the processes in the search for the minimal and the maximal surfaces.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.1-30
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• 2008

The success of Newton's Gravitational Theory has influenced the theory of capillarity, beginning in the early nineteenth century, by providing a major model of molecular attraction. He used the equation of the attraction of spheroids, which is expressed by second order partial differential equations, to utilize this analogy as the same kind of a particle's force, between gravitational, refractive force of light, and capillarity. The solution of the differential equation corresponds to the geometrical figure of the vessel and the contact angle which is made by the fluid. Unknown abstract functions $\varphi(f)$ represent interaction forces between molecules, giving their potential functions. By conducting several kinds of experimental conditions, it was found that the height of the ascending fluid in the tube is inversely proportional to the rayon of the tube or the distance of the plate. This model is an essential element in the theory of capillarity. Laplace has brought Newtonian mechanics to completion, which relates to the standard model of gravitational theory. Laplace-Young's equation of capillarity is applicable to minimal surfaces in mathematics, to surface tensional phenomena in physics, and to soap bubble experiments.