“sphere”的概念、定义、翻译、参考文献-科学参考

sphere

Physics

The figure generated when a circle is rotated about a diameter. The volume of a sphere is 4π‎r³/3 and its surface area is 4π‎r², where r is its radius. In Cartesian coordinates the equation of a sphere centred at the origin is x²+y²+z²=r².

Mathematics

In 3-dimensional space, the sphere with centre C and radius r is the locus of all points whose distance from C is equal to r. If C has Cartesian coordinates (a,b,c), this sphere has equation

${(x - a)}^{2} + {(y - b)}^{2} + {(z - c)}^{2} = r^{2} .$

The interior of a sphere of radius r has volume $\frac{4}{3} π r^{3}$ , and the surface area equals 4π‎r².

In topology, the n-dimensional sphere is denoted as Sⁿ and is often identified with the unit sphere in ℝⁿ⁺¹, that is,

$S^{n} = {(x_{1}, x_{2}, \dots, x_{n + 1}) | {| (x_{1})}^{2} + {(x_{2})}^{2} + \dots + {(x_{n + 1})}^{2} = 1} .$

The spheres described above are topologically S².

Chemical Engineering

A body formed from the rotation of a circle about its diameter. It has a volume of $\frac{4}{3} π r^{3}$ and surface area of $4 π r^{2}$ where r is the radius. Spherical vessels are commonly used to store process fluids under high pressure, such as liquefied petroleum gas (LPG), since there is an equal distribution of stress throughout the wall of the vessel. Cylindrical vessels and columns that operate under high internal pressure feature domed or hemispherical ends to distribute stresses. See hortonsphere.

单词	sphere
释义	sphere Physics The figure generated when a circle is rotated about a diameter. The volume of a sphere is 4π‎r³/3 and its surface area is 4π‎r², where r is its radius. In Cartesian coordinates the equation of a sphere centred at the origin is x²+y²+z²=r². Mathematics In 3-dimensional space, the sphere with centre C and radius r is the locus of all points whose distance from C is equal to r. If C has Cartesian coordinates (a,b,c), this sphere has equation ${(x - a)}^{2} + {(y - b)}^{2} + {(z - c)}^{2} = r^{2} .$ The interior of a sphere of radius r has volume $\frac{4}{3} π r^{3}$ , and the surface area equals 4π‎r². In topology, the n-dimensional sphere is denoted as Sⁿ and is often identified with the unit sphere in ℝⁿ⁺¹, that is, $S^{n} = {(x_{1}, x_{2}, \dots, x_{n + 1}) \| {\| (x_{1})}^{2} + {(x_{2})}^{2} + \dots + {(x_{n + 1})}^{2} = 1} .$ The spheres described above are topologically S². Chemical Engineering A body formed from the rotation of a circle about its diameter. It has a volume of $\frac{4}{3} π r^{3}$ and surface area of $4 π r^{2}$ where r is the radius. Spherical vessels are commonly used to store process fluids under high pressure, such as liquefied petroleum gas (LPG), since there is an equal distribution of stress throughout the wall of the vessel. Cylindrical vessels and columns that operate under high internal pressure feature domed or hemispherical ends to distribute stresses. See hortonsphere.
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