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The Kelvin problem on minimum-surface-area partitions of space into equal-volume cells, and the optimality of the Weaire–Phelan structure as a solution to the Kelvin problem [75] Lebesgue's universal covering problem on the minimum-area convex shape in the plane that can cover any shape of diameter one [76]
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged.
The term surface used without qualification refers to surfaces without boundary. In particular, a surface with empty boundary is a surface in the usual sense. A surface with empty boundary which is compact is known as a 'closed' surface. The two-dimensional sphere, the two-dimensional torus, and the real projective plane are examples of closed ...
A Rorschach test is a figure invariant by this symmetry, [203] as are butterfly and animal bodies more generally (at least on the surface). [204] Waves on the sea surface possess translation symmetry: moving one's viewpoint by the distance between wave crests does not change one's view of the sea. [205] Fractals possess self-similarity. [206] [207]
[1] [2] In places where trees or structures impede the near-surface wind, the use of a constant 1/7 exponent may yield quite erroneous estimates, and the log wind profile is preferred. Even under neutral stability conditions, an exponent of 0.11 is more appropriate over open water (e.g., for offshore wind farms), than 0.143, [ 3 ] which is more ...
A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.
Apollonius' definition of a circle: d 1 /d 2 constant. Apollonius of Perga showed that a circle may also be defined as the set of points in a plane having a constant ratio (other than 1) of distances to two fixed foci, A and B. [16] [17] (The set of points where the distances are equal is the perpendicular bisector of segment AB, a line.)
A sphere has 2/3 the volume and surface area of its circumscribing cylinder including its bases In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter .