球冠表面积计算公式

球冠表面积计算公式 计算方法 假定球冠最大开口部分圆的半径为 r ,对应球半径 R 有关系:r = Rc osθ,则有球冠积分表达: 球冠面积微分元 dS = 2πr*Rdθ = 2πR^2*cosθ dθ 积分下限为θ,上限π/2 所以:S = 2πR*R(1 - sinθ) 其中:R(1 - sinθ)即为球冠的自身高度H 所以:S = 2πRH of vision Yibin formation in the Center surrounded by, organic dispersion band of bead-space layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a long-term basis in a reasonable space to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multi-center" strategic vision of space frame. Yibin Center City development construction steering extension type extended and connotation type upgrade simultaneously of mode, in Metro construction of while is committed to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban green space system, promoting the construction of peripheral green space and protection of historical S=?dS =?2πr*Rdθ=? 2πR^2*cosθ dθ=2πR^2?cosθ dθ= 2πR*R(1 - sinθ) 注 1》2πR^2中^2为2πR的平方 2》? 要有写上下标,分别为π/2 ,θ of vision Yibin formation in the Center surrounded by, organic dispersion band of bead-space layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a long-term basis in a reasonable space to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multi-center" strategic vision of space frame. Yibin Center City development construction steering extension type extended and connotation type upgrade simultaneously of mode, in Metro construction of while is committed to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban green space system, promoting the construction of peripheral green space and protection of historical 球冠的面积计算公式 推导过程如下: 假定球冠最大开口部分圆的半径为 r ，对应球半径 R 有关系:r = Rcosθ，则有球冠积分表达: 球冠面积微分元 dS = 2πr*Rdθ = 2πR^2*cosθ dθ 积分下限为θ，上限π/2 所以:S = 2πR*R(1 - sinθ) 其中:R(1 - sinθ)即为球冠的自身高度H 所以:S = 2πRH of vision Yibin formation in the Center surrounded by, organic dispersion band of bead-space layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a long-term basis in a reasonable space to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multi-center" strategic vision of space frame. Yibin Center City development construction steering extension type extended and connotation type upgrade simultaneously of mode, in Metro construction of while is committed to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban green space system, promoting the construction of peripheral green space and protection of historical 球冠概念的分析 :1:球冠不是几何体,而是一种曲面,它是球面的一部分,是球面被一个平面截成的,也可以看成由一段弧绕着经过它的一个端点的直径旋转而成的曲面。球冠的任何部分都不能展开平面。 :2:球冠的底面是圆,而不是圆面,故球冠的面积不能包括底面圆的面积。 :3:球面被一个平面截成两个部分,它们都是球冠,其中一个球冠的高小于球的半径,另一个球冠的高大于球的半径。 :4:球冠面积公式S球冠,2πRh对其高小于、等于或大于球 2半径的球冠都适用。球面积公式S球面,4πr可看成球冠面积公式当h,2R的特例。由于同一个球的半径是一个常量,所以球冠面积是它的高的一个正比例函数,即S球冠,f(h) ,2πRh:0，h?2R:。 :5:若用距离为h的两个平行平面去截同一个球面,夹在这两个平行平面间的部分叫做球带,h叫做球带的高。把球带面积看成其高分别为h1,h2:h1，h2:的两个球冠面积之差,则有S球带,2πRh1,2πRh2,2πR(h1,h2),2πRh,其中为球的半径。 of vision Yibin formation in the Center surrounded by, organic dispersion band of bead-space layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a long-term basis in a reasonable space to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multi-center" strategic vision of space frame. Yibin Center City development construction steering extension type extended and connotation type upgrade simultaneously of mode, in Metro construction of while is committed to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban green space system, promoting the construction of peripheral green space and protection of historical 2由此可知,S,tπR可以看成球的表面积、球冠的面积、球带的面 积的统一计算公式。这里体现了特殊与一般可以互相转化的基本数学 思想。 of vision Yibin formation in the Center surrounded by, organic dispersion band of bead-space layout structure, as leading development of the city to the East along the Yangtze River. Shi Gu area, lingang new vision to expand, Naxi district to the North, the East open places to expand, Jiang an eastward connection, Ping Shan, radiation to the West; the South Bank area, the minjiang River area, Golden Sands area on a long-term basis in a reasonable space to develop, perfect urban district along the Yangtze River in Yibin "Ribbon multi-center" strategic vision of space frame. Yibin Center City development construction steering extension type extended and connotation type upgrade simultaneously of mode, in Metro construction of while is committed to old city transformation and built district of perfect, through live and industry with to of reasonable layout optimization city structure, improve city traffic operation efficiency; vigorously improved city environment, shaping city features, upgrade city quality, play city of service function, formed has perfect modern service capacity of big city. Construction of urban green space system, promoting the construction of peripheral green space and protection of historical