A novel method for geometric constraint reasoning is proposed,with which the maximaldecomposition of a geometrical constraint system can be made, This method represents apractically integrated utilization of the constrain network, analysis of the degree of freedomand the sparse matrix.
In the light of the law and demand of Chinese ancient mathematical mechenization this paper shows that the development from rod arithmetic to reckoning by the abacus is inevitable trend and important improvement on Chinese traditional computer technique.
A novel method for geometric constraint reasoning is proposed,with which the maximaldecomposition of a geometrical constraint system can be made, This method represents apractically integrated utilization of the constrain network, analysis of the degree of freedomand the sparse matrix. With maximal reduction, a geometrically constrained system is de-composed into a series of subsystems. The algorithm developed can be used in the fields ofparametric drawing,parametric modelling and assembly.
There exist three kinds of problems on the comparative evaluation between the mathematics during the Song and Yuan Dynasties and the abacus in the Ming Dynasty. They are the tooling algorithm, the value of the concept of skill and the standards of evalua- tion for ancient Chinese mathematics. The use of the abacus may be regarded as a great con- tribution to world mathematics after the mathematics during the Song and Yuan Dynasties.
Mathematlcs of the Ming Dynasty has its specific characteristics. The invention of abacus and the development of calculation with abacus cause a revolution in Chinese arithmetical history. By its distinct social nature and applicability, its mechanical calculating system dominated by calculation with a combination of calculation and principles, and its precedent of absorbing Western mathematics in the history of world mathematics, it fully illustrates that its being judged in the Western way of evaluating m...