球冠表面积计算
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
Green Tang town middle school young teachers professional development status survey report Luton report summary based on completely found out I school--green Tang town middle school young teachers professional growth of basic situation, we subject group determine has this times research child subject--green Tang town middle school young teachers of professional development status of survey, aimed at through investigation, inquiry I school young teachers of professional growth status, looking for professional growth path, and through research, excavations some can effective upgrade young teachers professional growth of good measures, and good approach, For my school teachers, especially younger teachers professional development proposals so as to enhance the effectiveness of young teachers ' professional development to guide the work, targeted. Keywords: young teacher professional development survey, introduction in the country carrying out the scientific concept of development under the background of the times, and narrowing the development gap between urban and rural areas, is the proper meaning. Improving rural primary and secondary school level and quality will naturally be to achieve balanced development of urban and rural education must urgently address the reality of the subject. But in today's society attaches great importance to the quality of education, "school choice hot" continues unabated, reflecting the regional imbalance in the allocation of teachers; " School choice hot "is the substance behind the" optional. " In other words, the teacher's specialization levels directly determine the quality of school education level, social
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
Green Tang town middle school young teachers professional development status survey report Luton report summary based on completely found out I school--green Tang town middle school young teachers professional growth of basic situation, we subject group determine has this times research child subject--green Tang town middle school young teachers of professional development status of survey, aimed at through investigation, inquiry I school young teachers of professional growth status, looking for professional growth path, and through research, excavations some can effective upgrade young teachers professional growth of good measures, and good approach, For my school teachers, especially younger teachers professional development proposals so as to enhance the effectiveness of young teachers ' professional development to guide the work, targeted. Keywords: young teacher professional development survey, introduction in the country carrying out the scientific concept of development under the background of the times, and narrowing the development gap between urban and rural areas, is the proper meaning. Improving rural primary and secondary school level and quality will naturally be to achieve balanced development of urban and rural education must urgently address the reality of the subject. But in today's society attaches great importance to the quality of education, "school choice hot" continues unabated, reflecting the regional imbalance in the allocation of teachers; " School choice hot "is the substance behind the" optional. " In other words, the teacher's specialization levels directly determine the quality of school education level, social
球冠的面积
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
Green Tang town middle school young teachers professional development status survey report Luton report summary based on completely found out I school--green Tang town middle school young teachers professional growth of basic situation, we subject group determine has this times research child subject--green Tang town middle school young teachers of professional development status of survey, aimed at through investigation, inquiry I school young teachers of professional growth status, looking for professional growth path, and through research, excavations some can effective upgrade young teachers professional growth of good measures, and good approach, For my school teachers, especially younger teachers professional development proposals so as to enhance the effectiveness of young teachers ' professional development to guide the work, targeted. Keywords: young teacher professional development survey, introduction in the country carrying out the scientific concept of development under the background of the times, and narrowing the development gap between urban and rural areas, is the proper meaning. Improving rural primary and secondary school level and quality will naturally be to achieve balanced development of urban and rural education must urgently address the reality of the subject. But in today's society attaches great importance to the quality of education, "school choice hot" continues unabated, reflecting the regional imbalance in the allocation of teachers; " School choice hot "is the substance behind the" optional. " In other words, the teacher's specialization levels directly determine the quality of school education level, social
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。 Green Tang town middle school young teachers professional development status survey report Luton report summary based on completely found out I school--green Tang town middle school young teachers professional growth of basic situation, we subject group determine has this times research child subject--green Tang town middle school young teachers of professional development status of survey, aimed at through investigation, inquiry I school young teachers of professional growth status, looking for professional growth path, and through research, excavations some can effective upgrade young teachers professional growth of good measures, and good approach, For my school teachers, especially younger teachers professional development proposals so as to enhance the effectiveness of young teachers ' professional development to guide the work, targeted. Keywords: young teacher professional development survey, introduction in the country carrying out the scientific concept of development under the background of the times, and narrowing the development gap between urban and rural areas, is the proper meaning. Improving rural primary and secondary school level and quality will naturally be to achieve balanced development of urban and rural education must urgently address the reality of the subject. But in today's society attaches great importance to the quality of education, "school choice hot" continues unabated, reflecting the regional imbalance in the allocation of teachers; " School choice hot "is the substance behind the" optional. " In other words, the teacher's specialization levels directly determine the quality of school education level, social
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。
Green Tang town middle school young teachers professional development status survey report Luton report summary based on completely found out I school--green Tang town middle school young teachers professional growth of basic situation, we subject group determine has this times research child subject--green Tang town middle school young teachers of professional development status of survey, aimed at through investigation, inquiry I school young teachers of professional growth status, looking for professional growth path, and through research, excavations some can effective upgrade young teachers professional growth of good measures, and good approach, For my school teachers, especially younger teachers professional development proposals so as to enhance the effectiveness of young teachers ' professional development to guide the work, targeted. Keywords: young teacher professional development survey, introduction in the country carrying out the scientific concept of development under the background of the times, and narrowing the development gap between urban and rural areas, is the proper meaning. Improving rural primary and secondary school level and quality will naturally be to achieve balanced development of urban and rural education must urgently address the reality of the subject. But in today's society attaches great importance to the quality of education, "school choice hot" continues unabated, reflecting the regional imbalance in the allocation of teachers; " School choice hot "is the substance behind the" optional. " In other words, the teacher's specialization levels directly determine the quality of school education level, social