Two Remarkable Points of the Triangle Geometry

It is shown in the paper the discovery of two remarkable points of the triangle by means of “THE GEOMETER’S SKETCHPAD” software. Some properties of the points are considered too.

Towards the Semiotics of Noosphere

Civilization has brought us into the noosphere world. Besides physical, around (and inside of) us exist and function also mental and cultural entities. It is impossible to perform now knowledge acquisition, knowledge base creation and organizational systems management without adequate consideration of object’s noosphere statuses. I tried here to clarify basic viewpoints concerning this issue, hoping that elaboration of common methodological foundations of semiotic modeling will be useful for developers and also for users of new generation automation systems.

A Real-time Decision Support System Prototype for Management of a Power Block

This paper describes the basic tools for a real-time decision support system of a semiotic type on the example of the prototype for management and monitoring of a nuclear power block implemented on the basis of the tool complex G2+GDA using cognitive graphics and parallel processing. This work was supported by RFBR (project 02-07-90042).

Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints

* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005.

Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.

Piecewise Convex Curves and their Integral Representation

2000 Mathematics Subject Classification: 52A10.