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The surface area of a polyhedron is the sum of the areas of its faces, for definitions of polyhedra for which the area of a face is well-defined. The geodesic distance between any two points on the surface of a polyhedron measures the length of the shortest curve that connects the two points, remaining within the surface.
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 .
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 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.
Gibbs emphasized that for solids, the surface free energy may be completely different from surface stress (what he called surface tension): [14]: 315 the surface free energy is the work required to form the surface, while surface stress is the work required to stretch the surface. In the case of a two-fluid interface, there is no distinction ...
The multiple choice section is scored by computer, with a correct answer receiving 1 point, with omitted and incorrect answers not affecting the raw score. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score. [26] The free response section is hand-graded by hundreds of AP teachers and professors each June. [27]
The circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality). The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R).
The power law is often used in wind power assessments [4] [5] where wind speeds at the height of a turbine ( 50 metres) must be estimated from near surface wind observations (~10 metres), or where wind speed data at various heights must be adjusted to a standard height [6] prior to use.