In this paper by using the symplectic transformation condition,some new formulas including Chebyshev Polynomial,trigonometric identity,hyperbolic identity were obtained.

The author explores the solution to the best time problem according to three ways of thinking,including basic trigonometric identity,geometrical optics of physics and Geometer\'s Sketchpad.

Besides its application to multinomial exact dividedness,unit solution is widely used in multinomial factorization,trigonometric equation,determinant calculation and geometric proposition.

By this integral and Jacobi triple product identity, a new proof of the Rogers-Ramanujan identities is given.

q-series theory of the development of more than two hundreds, Jacobi triple product identity is one of very important q-series identities.

Based on the complex number triangle inequality the thesis arrives at a new inequality and an exceptional case of n= 2,also a verification under general situation is put forward in the thesis.

To those peers having no common partners,it uses triangle inequality to calculate their global average departure degree through their trust path built by other peers.

In this paper,we consider two new types of sorting problems-Minimum cost sorting problem with cost function satisfies triangle inequality and minimum cost sorting problem without cost function does not satisfy triangle inequality.

Strengthening of the weighted trigonometric inequality;

This paper combines with the concept of convex function, uses Jensen s inequality to make up trigonometric inequality of the kinds.

As a theoretical reference,the "eternal triangle" explanation is limited.