![]() Isobronts, lines at which a given phase of thunderstorm activity occurred simultaneously.Isochalazs, lines constant frequency of hail storms.Isonephs, lines indicating equal cloud cover.Isohumes, lines of constant relative humidity.Isodrosotherms, is a line of equal or constant dew point.Isosteres, lines of equal atmospheric density.Isobars, lines of equal atmospheric pressure.Isohels, lines of equal or constant solar radiation.Isotheres, lines of equal mean summer temperature.Isocheims, lines of equal mean winter temperature.Isogeotherms, lines of equal annual mean temperature.Contour lines, lines of equal elevation.There are many different types of isarithmic lines. Isolines join all connected points of same value, whether measured or interpolated. Computer cartography tools and methods make it easy to create.It is flexible and adaptable to various levels of scale.The distribution of a smooth continuous field can be effectively represented.The advantages of creating an isarithmic map include the following: Common isarithmic maps are of temperature, rainfall, or elevation. The visualization is derived from the original point data gathered by the weather stations. Based on the method used, boundaries are drawn upon the map to represent zones in which the temperature is assumed to be the same and then color, value, or saturation is added to enhance the map. These values are then classified into groups (ex. Because it is a field, at any given geographical point within that country or region, it will have a measurable temperature value. , 2 (1901) pp.An Isarithmic map of temperatures'.Isarithmic maps are usually created by interpolating from raster data or from a set of sample points for example, one could draw isolines between temperature values recorded at individual weather stations across a country. Hilbert, "Ueber Flächen von konstanter Gausscher Krümmung" Trans. Darboux, "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal", 1–4, Chelsea, reprint (1972)ĭ. Bianchi, "Vorlesungen über Differentialgeometrie", Teubner (1910) (Translated from Italian) Zbl 41.0676.01 Efimow, "Flachenverbiegung im Grössen", Akademie Verlag (1957) (Translated from Russian) MR0105722 MR0085569 ![]() Wendland, "Beweismethoden der Differentialgeometrie im Grossen", Lect. Pogorelov, "Extrinsic geometry of convex surfaces", Amer. It follows readily that the sphere is the only closed (singularity-free) surface of constant positive curvature, a result first proved by H. Hilbert's theorem on the maximal principal curvature radius mentioned above can be found in. 4 for a great deal of material on infinitesimal bendings and rigidity. A closed regular surface of positive Gaussian curvature is rigid (Blaschke's theorem). In character, the problem of isometric deformation of surfaces in Euclidean space can be divided conventionally into that of local isometric deformation, that is, deformation of some small neighbourhood $ U _ $).Ī rigid surface is one which admits no non-trivial infinitesimal bendings. Ruled surface) are comprised in this class) 3) surfaces allowing a deformation over a principal base etc. Such are, for example: 1) surfaces where the mean curvature is preserved under isometric deformation (surfaces of constant mean curvature, and, in particular, minimal surfaces and some surfaces applicable on a surface of revolution) 2) surfaces where some family of asymptotic lines is preserved under isometric deformation (the ruled surfaces (cf. Gauss, and is a fundamental problem in differential geometry.Īpart from the general case, isometric deformations of surfaces preserving some external characteristic have been fairly thoroughly investigated it usually turned out that only surfaces of a definite class allow of such deformations. The problem of isometric deformation of surfaces originated with C.F. A deformation under which the lengths of curves in $ M $Īre unchanged.
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