Zhenbing Zeng

Mathematics Education over the Internet Based on Vega Grid Technology

This paper presents research work conducted at the Chinese Academy of Sciences, on the Vega Grid technology and dynamic geometry technology, and how the two can integrate to provide a dynamic geometry education system based on grid technology. Such an approach could help solve the interconnect problem, the performance problem and the intellectual property problem for Internet-based education systems.

The Vega Grid and Grid-Based Education

This paper presents research work conducted at Chinese Academy of Sciences, on the Vega Grid technology and dynamic geometry technology, and how the two can integrate to provide a dynamic geometry education system based on grid technology.

Heilbronn Problem for Seven Points in a Planar Convex Body

Let K be a planar convex body (that means a compact convex set with non-empty interior), \K\ the area of K\ for any triangle ri7*27*3, by (rir2r3) denote its area; and let

Image retrieval based on salient points from DCT domain

\begin{array}{*{20}{c}} {({{r}_{1}}{{r}_{2}} \cdots {{r}_{n}}) : = \min \{ ({{r}_{i}}{{r}_{j}}{{r}_{k}})|1 \leqslant i < j < k \leqslant n\} ;} \hfill \\ {{{H}_{n}}(K) : = \frac{1}{{|K|}}\sup \{ ({{r}_{1}}{{r}_{2}} \cdots {{r}_{n}})|{{r}_{i}} \in K,i = 1, \cdots ,n\} .} \hfill \\ \end{array}

Constructing a tetrahedron with prescribed heights and widths

In ISSAC 2000, P. Lisoněk and R.B. Israel [3] asked whether, for <i>any</i> given positive real constants V,R,A<inf>1</inf>,A<inf>2</inf>,A<inf>3</inf>,A<inf>4</inf>, there are always <i>finitely many</i> tetrahedra, all having these values as their respective volume, circumradius and four face areas. In this paper we present a negative solution to this problem by constructing a family of tetrahedra T<inf>(x,y)</inf> where

Automated and readable simplification of trigonometric expressions

(x,y)

Symbolic solution of a piano movers' problem with four parameters

varies over a component of a cubic curve such that all tetrahedra T<inf>(x,y)</inf> share the same volume, circumradius and face areas.