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The world of pentagonal numbers

Polona Črep (2014) The world of pentagonal numbers. MSc thesis.

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    Abstract

    The master’s thesis accurately discusses the subject of the world of pentagonal numbers. First chapter generally describes what exactly power series are, when the power series converge and how do we calculate with power series. Further there is written what is generating function. Derivations of a generating function for pentagonal numbers have been made as well as for inverse pentagonal numbers etc. As the figurate numbers intertwine each other in some way the connection between pentagonal numbers and some other figurate numbers has been presented. Solving these kinds of questions brings us to Pell’s and Diophantine equations, that is why there is a section about the mathematician Diophantus and his equations. It is also explained, why the equation is named after Pell. As the object number can be ordered also spatially there is one of the chapters explaining the pyramidal numbers. This chapter explains what exactly pyramidal numbers are and how we get them. But the main theme of this master’s thesis is the world of pentagonal numbers that is why the pyramidal numbers of rank five have been set out, therefore the pyramidal numbers, which are connected with pentagonal numbers. The last chapter talks about figurate and pyramidal numbers regarding the elementary education. It has been written when the pupils meet the figurate numbers and how are these presented to them or in what way they get acquainted with this kind of numbers.

    Item Type: Thesis (MSc thesis)
    Keywords: graphical and spatial ordering of number of objects, pentagonal numbers, power series, convergence of power series, generating function, connection of pentagonal numbers with other figurate numbers, pyramidal numbers, figurate and pyramidal numbers in elementary school
    Number of Pages: 68
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko RazpetMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=10334537)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 2635
    Date Deposited: 03 Dec 2014 08:32
    Last Modified: 03 Dec 2014 08:32
    URI: http://pefprints.pef.uni-lj.si/id/eprint/2635

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