一类构造性几何定理的数值并行法证明器。
A prover for parallel numerical verification of a class of constructive geometry theorems.
这些结果可与阿基·米德斯的几何定理相比。
同时，也对四色问题与初等几何定理证明作了简单的讨论。
Additionally, the well-known four colour problem and elementary geometry theorem-proving problem have been discussed.
为了生成传统形式的几何定理可读证明，前推法必不可少。
To produce the traditional readable proving of geometry theorem, the forward reasoning is necessary.
通常，几何定理的证明是依据公理系统，按一定的逻辑规则演绎地进行。
Generally, the proving of geometry theorem is based on the axiom system, and is deducted according to certain logic rules.
在几何定理机器证明方法中，常用的有几何代数方法、演绎数据库方法和例证法等方法。
Methods, including geometric algebraic method, deductive database method and paradigmatic prove method have been widely applied in the geometric theorem prove field.
本文对一道著名几何定理进行了推广与证明，从而用纯几何方法解决了一般的费尔玛问题。
This paper generalized and proved a famous geometry theorem, and obtained general solution of Fermat Problem by pure geometric method thereby.
几何定理证明的前推法能够产生传统形式的可读证明，在定理机器证明领域占有重要的地位。
The forward reasoning for geometry theorem proving can produce the traditional readable proving, thus plays a special role in the mechanical theorem proving.
用机械化方法证明几何定理，适当选取坐标系是一个关系到问题解决得难易程度的重要步骤。
In applying the method of mechanization to verifying geometric problems, to choose a proper coordinate system is an important step that concerns the complexity of the solution to the problem.
在微分几何定理证明中，一个定理成立的辅助条件(非退化条件)不是惟一的，但越简单越好。
The subsidiary conditions (or called non-degeneracy conditions) are not one and only that a theorem holds in differential geometry theorem proving.
半个世纪前，IBM的赫伯特·格勒恩特尔编写了一个程序，据称再现了欧几里德几何定理，但是，批评家们说它过于依赖程序员提供的规则。
Half a century ago, IBM's Herbert Gelernter authored a program that purportedly rediscovered Euclid's geometry theorems, but critics said it relied too much on programmer-supplied rules.
看起来毕达哥拉斯的定理，似乎来自于欧几里德的三角形理论，从欧几里德几何学的发现中可以简单地推理出来。
It seems that the proof of Pythagoras's theorem comes pretty much from just consulting the ideas of Euclidean triangle, the exhume of Euclidean geometry and simply doing inferences from those.
于是余弦定理从此不再是一个纯粹的初等几何问题。
Then cosine theorem is no longer a pure problem from elementary geometry.
平面几何的定理、公式、法则反映了几何概念的内在联系，揭示了它们之间的基本规律。
The theorems, formulas and principles in plane geometry reveal the intrinsic relations and basic laws of geometrical concepts.
圆幂定理是初中平面几何《圆》中重要定理之一。
The circle-power theorem is one of important theorems in plane geometry.
通过对QBD过程某些条件的限定，应用马尔可夫更新定理，得出在一定合理的条件下，当水平趋于无穷时的尾概率的几何衰变。
Applying the Markov renewal theorem, it is shown that certain reasonable conditions of the QBD process lead to the geometric decay of the tail probabilities as the level goes to infinity.
本文首先采用不同的几何手段，引进相应的辅助函数，对拉格朗日定理的证明进行了探索。
In this paper, using different geometric means, the introduction of the corresponding auxiliary function of the Lagrange theorem proof explored.
对一类非线性问题的空间分解算法证明了两个几何收敛性定理，改进了已有的结果。
Two geometrical convergence theorems of a space decomposition method for solving a kind of nonlinear problems have been proved, which are improvements of existing results.
这种方法基于任意几何形状网格的抽样定理，利用六边形网格来实现空间离散化。
In the H-FDTD method, Hegxagon grid is used for the spatial discretization by virtue of peridodical sampling theorem based on arbitrary geometry.
严格、详细地证明了弯曲时空几何光学中的聚焦定理。
The focusing theorem of geometric optics in curved space-time be proved strictly and in detail.
本文研究特征为2的有限域上正交几何中的计数问题，给出了一个计数定理。
In this paper, enumeration problems in the orthogonal geometry over a finite field with characteristic 2 are studied, and an enumeration theorem is proved.
文章利用射影几何方法及配极原理给出二次曲线中点弦存在性定理的证明。
In this paper, the existence theorem of midpoint chord of quadratic curve, as well as its proof, is given via methods of projective geometry and polarity principle.
接着，仿微分几何的曲线论，建立了基本公式和唯一存在定理。
Then the basic formulae and the theorem on its unique existence have been established as doing in the curve theory in Differential Geometry.
以HTCR径向转向架导向机构为例，应用泰勒定理进行了系统误差分析，本文导出了使系统误差最小而结构上应满足的几何关系；
Taking the HTCR radial steering bogies for example, the geometrical mechanism relation fitted for minimum error is discussed by means of Taylor's formula to analyze the mechanism system error.
刚性理论是子流形几何中久盛不衰的重要方向，其根源可追溯到经典曲面论的高斯绝妙定理。
Rigidity theory is one ever-flourishing subject in geometry of submanifolds, which can be traced back to Gauss' Theorema Egregium in the classical theory of surfaces.
用几何法证明了等视角定理和低副运动可逆性在铰链四杆机构设计中的等价性，以求揭示它们之间的本质联系。
The equivalence between theorem of equal angle of view and reversible property of low pair, applied in synthesis of plane four-bar linkage, is demonstrated to reveal essence of their relation.
系统地讨论了代数多项式的算术-几何均值定理，并对原型几何规划理论作出了简明的推导与分析。
This paper discussed the theorem of the average arithmetic geometric mean of algebraic polynomials systematically, then derived and analyzed the original geometric programming (GP) briefly.
利用类似微分几何理论的方法，通过引入微分代数系统的m导数，利用微分代数系统无源性定义以及kvp特性的等价定理。
Similar to methods of differential geometry theory, equivalent theorem between differential algebraic systems passivation and KVP property was used by introducing m derivative.
根据啮合基本定理提出的复杂曲面加工表面几何仿真算法是对几何仿真新的探索，具有较强的实际意义。
Algorithm of geometry simulation in machining complex curve surface depending on engagement theory is the new exploration for geometry simulation, it has better practical meaning.
摘要将《解析几何》教材中抛物面的两个性质定理推广到更一般的情形。
In this paper, two properties of paraboloid in the textbook analytic geometry is generalized.
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