半径

Four circles of radius 1 are each tangent to two sides of a square and externally tangent to a circle of radius 2, as shown. What is the area of the square?

A 32 22+12 2 16+16 3 48 36+16 2 中文：如图所示，四个半径是 1 的圆分别与正方形的两边相切且与一个半径是 2 的圆外切，这个正方形的面积是多少？

The relation of the surface shape error to f-number and relevant spherical radius was achieved according to the reducing analysis model ignoring the local f-number. Two kinds of rhombic prism model are established by ZEMAX. According to the simulation results from ZEMAX, the correctness and limitation of the former methods are proved and analyzed. The results are used to analyze the effect of the surface shape error of the rhombic prism on parallelism of the emergent beam. The assignation plan of the surface shape error for each working surface is presented.

根据忽略局部光圈数的简化分析模型，获得面形误差对应光圈数与相关球面半径的关系，通过几何处理方法，求得一定面形误差对应的球面半径与平面倾角的关系，将斜方棱镜的工作面倾斜一定角度，运用折射定理，将具体面形误差转化为相应平面的倾斜角度，得到出射光相对于理想光轴的倾斜角度及其关系式，并在ZEMAX中建立斜方棱镜的两种模型。

It is found from the analytical expression that the truncation parameter, which is defined as the ratio between the waist of the Gaussian beam and the radius of the lens, has an important effect on the diffraction field distribution of the lens.

应用这个表达式研究了截断参数（透镜的半径与高斯光束束腰半径的比值）对透镜衍射场分布的影响。

Moreover,the radius of focal spot increases with the spatial phase perturbation of the high-power ultraviolet laser.

研究结果表明：当传输距离超过阈值条件时，焦斑半径随传输距离的增大而明显增大，且相位畸变越大，焦斑半径也越大。

When the ratio of signal Airy disk radius to local oscillator Gaussian 1/e field radius at focal plane is 1.71, maximum heterodyne efficiency of 81.45% can be obtained.

当焦平面上爱里斑半径与本振高斯光束光腰半径之比为1.71时，有最大外差效率81.45%。

It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function.

结果同时表明，斜程湍流大气传输的有限光束光强不仅是发射光束半径、传输距离和球面波长期平均相干长度的函数，同时也是发射孔半径的函数。

It is often seen that only lower order modes of the beam without large overallmotions are chosen to reduce the number of the generalized coordinates,the simulation,however,is able to reach certain accuracy.

本章对不同转速和中心刚体半径下模态截断法和有限元法的仿真结果进行比较，根据两种方法的振动基频的相对误差确定了模态截断的阶数与转速、中心刚体半径的关系，提出了模态截断的准则，解决了模态截断法的精度问题。

The problem of geometric inequalities for Ceva simplex by analytic method and geometric theory is studied.

利用解析方法和几何不等式理论，研究了Ceva 单形的几何不等式问题，建立了单形和它的Ceva 单形外接球半径与内切球半径两个不等式。

In this paper,the anthor study problem of geometric inequalities for Ceva simplex by analytic method and geometric theory.

利用解析方法和几何不等式理论，研究了Ceva 单形的几何不等式问题，建立了单形和它的Ceva 单形外接球半径与内切球半径的两个不等式。

Using analytic method and theory of geometric inequality,we study the problem of geometric inequalities concerning n-dimensional simplex and its interior point in.

应用解析方法和几何不等式理论研究了n维欧氏空间En中n维单形Ωn的外接球半径及Ωn中内点之间的几何不等式问题，建立了涉及单形Ωn的外接球半径以及Ωn中内点到各侧面距离之间的几何不等式，作为其应用，进一步改进了著名的M.S。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷