We define and construct bicentric circles with respect to three-sided polygons. Then using inherent properties of these circles, we explore both tangent properties, and areas generated from bicentric circles.

No description available.

No description available.

Thesis (M.S.)--Kutztown University. / Source: Masters Abstracts International, Volume: 45-06, page: 2810. Typescript. Includes bibliographical references (leaves 35-36).

Thesis (doctoral)--Bonn, 1998. / Includes bibliographical references (p. 111-112).

Thesis (M.F.A.)--Washington State University, May 2007. / Includes bibliographical references (p. 12).

Multivalent aptamer refers to a technique that joins two or more identical or different types of aptamer monomers together, with or without the presence of structural or other functional elements. As a rapid and easy method for fabricating the multivalent aptamer constructs, rolling circle amplification (RCA) has attracted great attention in recent decades. The incorporation of properly designed structural elements, such as intra-molecular spacers, have been shown to greatly enhance the efficiency of the multivalent aptamer system [1]. The objective of this current study is to systemically investigate the effect of different lengths of poly thymine spacer designs (polyT, from no spacer/NT, 5T, 10T, and 15T) on the capturing performance of RCA-generated multivalent system. To achieve this, we designed four circular probe templates by inserting zero, five, ten, and fifteen adenine bases (polyA). These polyA domains in the circular probe template are complementary to polyT with respective lengths in between the adjacent aptamers on the resultant RCA products (RCAPs). We found that the resultant RCAPs with length shorter than 10T showed a lack or low ability to capture target cells E.Coli O157:H7. When spacer lengths reach or exceed 10T, the capturing performance of the respective multivalent aptamer chain is significantly enhanced. This phenomenon can be explained by larger hydrodynamic sizes and less nonspecific secondary structures observed in RCAP with spacer length no less than 10T. Moreover, we found that there is also a trade-off that the number of polyA bases added into the circular probe template can significantly impair the efficiency of RCA reaction in respective to cyclization yield and amplification rate. The results of this research explain with details how the design of spacer affects RCA reaction efficiency and RCAPs’ capturing performance, which provides ideas in designing an efficient RCA-generated multivalent system.

Doctor Educationis / Euclidean geometry was recently re-introduced as a compulsory topic in the Mathematics Curriculum for learners in the Further Education and Training (FET) band in 2012. The diagnostic analysis reports on the National Senior Certificate (NSC) Mathematics Paper 2 examinations since 2014 has repeatedly expressed concern of the poor performance of leaners in proof and reasoning items linked to circle geometry. Various efforts have been made to examine the composition of the curriculum to find ways of motivating learners in the study of circle geometry and enhancing their performance but not much has been realized. The use of technology or cooperative learning approaches for the teaching of geometry is beneficial for pedagogical purposes, particularly for improving learners’ performance in geometry. Hence, this study investigated the impact of using technology through cooperative learning on learners’ performance on grade circle 11 geometry. It was thus an attempt to focus on blending these two teaching methods with an emphasis on the use of technology. The research took place at a Khayelitsha school and the scope of technology was limited to using a mathematical computer programme called Heymath. This research was grounded on the cognitive level framework that is used by the Department of Basic Education (DBE) in the setting of National Senior examination mathematics papers, as well as the set of social constructivist views of mathematics teaching and learning. In the case of the latter, both social constructivism and cognitive constructivism views were considered and applied for the purposes of this study. Using a positivist paradigm, this convergent parallel mixed methods study employed a quasi-empirical design, where the control group consisted of a group 26 grade 11 learners who were comparable to the group of 27 grade learners that made up the experimental group.

This thesis looks at the interplay between neighborhood space and public space as they come together in the circles and squares of Washington D.C.. The outcome of the thesis is a designed landscape that would perform the same roles as traditional circles in serving both neighborhood and public needs, at the site of the former Truxton Circle, a place where there had been a traffic circle and a public space but where it is not possible to make a traffic circle today. / Master of Landscape Architecture

Given a graph that defines a triangulation of a simply connected surface, it is possible to associate a radius with each vertex so that the vertices represent centers of circles, and the edges denote patterns of tangency. Such a configuration of circles is called a circle packing. We shall give evidence for the existence and uniqueness of circle packings generated by such graphs, as well as an explanation of the algorithms used to find and output a circle packing on the complex plane and hyperbolic disc. / Master of Science