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International Journal of Mathematical Analysis and Applications

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The Quasi-Squares and their Limit Curve

International Journal of Mathematical Analysis and Applications
Vol.1 , No. 2, Publication Date: Jul. 7, 2014, Page: 31-37

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Authors

[1]	Pellumb Kllogjeri, Lecturer of Statistics and Graph Theory, University “Aleksander Xhuvani”, Elbasan, Albania.
[2]	Adrian Kllogjeri, Actuarial Programmer,Company: AIG Europe Ltd, London (MSc in Statistics,University of Kent; Student in Applied Econometrics, Kingston University, UK).

Abstract

The main theme in the book “Introduction to Quasi-Quadrilaterals” is that of quasi-quadrilaterals and their properties. The first topic is about quasi-square represented by the equation x^2n+y^2=1 or x^2+y^2n=1.It is well-defined: the curve lies between the unit circle and the specified square which has its center at the origin of the Cartesian system and, sides of length 2 which are parallel to the coordinative axes. These type of closed curves do not represent squares but for values of n larger than 100 they are almost squares. From this phenomenon derives the name “quasi-square”.Also, it is proved that the curve, represented by such equation,perfectly fits to the sides of the specified square as n increases beyond bound. In this paper we present a more general case of the sequence of the quasi-squares and confirm the above fitness by proving that there exists the limit curve of such a sequence. Other subsidiary theorems are proved as well.

Keywords

Quasi-Square, Sequence of Functions, Limit Curve

Reference

[01]	Frank Ayres, Robert E. Moyer:Theory and Problems of Trigonometry, 3d Edition. Printed in USA, McGRAW-HILL, 1999, (pp. 78-81, 159-171)
[02]	http://tutorial.math.lamar.edu/sitemap.aspx Paul’s Online Math Notes, Calculus II, Chapter on Parametric Equations and Polar Coordinates
[03]	James StewartP:Calculus: Concepts and Contexts,4th Edition, BROOKS/COLE CENGAGE Learning,USA 2010, (pp. 75-80,218-242)
[04]	Pellumb Kllogjeri, Adrian Kllogjeri:An Introduction To Quasi-Quadrilaterals, ISBN-13: 978-3-659-42488-5, ISBN-10:3659424889, EAN:9783659424885, Published by LAMBERT Academic Publishing, Germany, August 2013, (pp. 3-29)
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