On a quadrangular having a circumscribed circle

A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE

One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimede...

a study on rate making and required reserves determination in reinsurance market: a simulation

reinsurance is widely recognized as an important instrument in the capital management of an insurance company as well as its risk management tool. this thesis is intended to determine premium rates for different types of reinsurance policies. also, given the fact that the reinsurance coverage of every company depends upon its reserves, so different types of reserves and the method of their calc...

On circular-arc graphs having a model with no three arcs covering the circle

An interval graph is the intersection graph of a finite set of intervals on a line and a circular-arc graph is the intersection graph of a finite set of arcs on a circle. While a forbidden induced subgraph characterization of interval graphs was found fifty years ago, finding an analogous characterization for circular-arc graphs is a long-standing open problem. In this work, we study the inters...

Covering on a Circle

A Quadrangular Prism of Self Invisibility

A quadrangular prism of self-invisibility is originally reported in this paper. It is a self-invisible unit, which does not depend on any outer refractive materials or reflective mirrors. Four identical triangular prisms with the lateral faces of mirrors, divided into two groups, are symmetrically placed on two transparent rectangular prisms in a symmetrical way. Two identical rectangular prism...