The introduction surveys all alternative approaches to automated geometry theorem proving, giving references to the corresponding literature. After explaining how to obtain correct algebraic translations of geometry theorems, Buchberger's method of Grbner bases is shortly reviewed. Then the application of ...
Euclidean geometry- (mathematics) geometry based on Euclid's axioms elementary geometry,parabolic geometry math,mathematics,maths- a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement geometry- the pure mathematics of points and lines and curves and ...
An application of Pappus' Involution Theorem in euclidean and non-euclidean geometry Pappus' Involution Theorem is a powerful tool for proving theorems about non-euclidean triangles and generalized triangles in Cayley-Klein models. Its powe... R Vigara - 《Mathematics》 被引量: 0发表: 2014年 加载...
Congruent Triangles Proof The quiz below will test your knowledge of all thepostulates and theorems that can prove two triangles are congruent. Problem 1 Which postulate/theorem that proves congruent trianlges could be used to prove that BAC...
The single source localization problem has applications in e.g. navigation, structural engineering, and emergency response [3,4,8,24,26,38]. In general, it is related to distance geometry problems where the input consists of Euclidean distance measurements and a set of points in Euclidean space...
However, it will be useful in the proofs of the theorems that follow. The process that constructs the metric g2 from g1 can then be repeated to create a third metric g3, and so on. This generates a sequence of metrics (gi ), obtained from a sequence of functions (hi ) (Fig. 3)...
In order to derive the best possible estimates of the total mean curvature of a compact submanifold in a Euclidean space in terms of spectral geometry, in the late 1970s, Bang-Yen Chen introduced the theory of finite-type submanifolds, which could be viewed as λ-biharmonic submanifolds in th...
On the decision problem and the mechanization of theorem proving in elementary geometry. Sci. Sin. 1978, 21, 159–172. [Google Scholar] Zhang, J.Z.; Chou, S.C.; Gao, X.S. Automated production of traditional proofs for theorems in Euclidean geometry I. The Hilbert intersection point ...
Euclid’s book “the Elements”, which has been the foundation of Euclidean geometry, presents a list of definitions and postulates based on logic, common sense, and the perceptions of the surrounding space as the basis for proving the rest of the theorems in flat space [1]. Hence, the de...
This is an immediate consequence of Corollary 1 and Theorems 1 and 2. □ Remark 2. In general, the converse of the previous results are not valid. As a counterexample, let ( V , 〈 · , · 〉 ) be the pre-Euclidean space over R , with the basis B : = { e 1 , e 2 ...