We review the construction of integral Apollonian circle packings. There are a number of Diophantine problems that arise in the context of such packings. We discuss some of them and describe some recent advances. 1. AN INTEGRAL PACKING. The quarter, nickel, and dime in Figure 1 are placed so that they are mutually tangent. This configuration is unique up to rigid motions. As far as I can tell t...

To a rhombic embedding of a planar graph with quadrilateral faces and vertices colored black and white there is an associated isoradial circle pattern C 1 with centers of circles at white vertices and radii equal to the edge length. Let C 2 be another circle pattern such that the rhombi correspond to kites of intersecting circles with the same intersection angles. We consider the mapping g C wh...

The purpose of this study was to compare the muscular power and strength endurance level between Circle Style Male Kabaddi Players Panjab University Chandigarh Guru Nank Dev Amritsar. A total one hundred twelve (N=112) circle style male kabaddi players eight teams both universities were selected. In Medicine Ball Throw Test Dips used measure players. had been analyzed with help mean, SD, SED co...

In this paper, we make an overview of the existing algorithms concerning the discrete curvature estimation. We extend the Worring and Smeulders [WS93] classification to new algorithms and we present a new and purely discrete algorithm based on discrete osculating circle estimation.

e 80th anniversary of the Prague Linguistic Circle offers an occasion to think about how to document the Prague School related events, how to keep whatever related to the Prague School, and how to make the Prague School resources easily accessible. In the following I will first chronologically list some Prague School related events in the past ten years (1996–2006). en I will refer to several...

First, we may assume, without loss of generality, that the points of the sets ƒ > > are located on the unit circle, by projecting these points on the circumference of the circle. Second, by Carathéodory Theorem (see [3]), we may assume, without loss of generality, that the cardinality of each set + is at most ? , for 4„5X2= >8 @? . In fact, we can further assume that * + *…5†? , for 4„5X2' 98( ...

In this paper we seek for inner product dependent strictly positive definite kernels on subsets of C. We present separated necessary and sufficient conditions in order that a positive definite kernel on C be strictly positive definite. One emphasis is on strictly positive definite kernels on the unit circle. Since positive definite kernels on the circle were already characterized in [1], the st...

The numbers on the inner circle are those that exist in the modular arithmetic. If we continue beyond 7, as shown in the outer ring, the numbers wrap around the wheel. Numbers on the same spoke are equivalent. For example, 0 and 8 are equivalent, 1 and 9 are equivalent, 2 and 10 are equivalent, and so on. Another way to look at it is that when 9 is introduced into modular arithmetic with 8 shaf...

2 Representing a Circle 3 2.1 Quarter of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Degree 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Degree 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Half a Circle . . . . . . . . . . . . . . . . ....

The English literature component has been around in the Malaysian Education system since 2000. However, literature as a subject has always been learned more for transactional purposes rather than for its aesthetic value. Basically, a regurgitation of knowledge from years of learning, poured out in one major examination. In this research, the researcher applies a teaching method, called the lite...