Archimedo „problema bovinum" ir Pelio lygtys /

Archimedes’ Problema Bovinum and Pell’s Equations The aim of this thesis is to discuss Pell's equation and its link to Archimedes' Problema Bovinum. First chapter introduces to Diophantine equations, while providing examples on various cases that famous mathematicians stood upon. In the begining of second chapter Pell's equation, its history, applications are presented, while also including the main related definitions. We then start introducing theory related to Pell's equation non-trivial solutions, their representation using the fundamental solution of the problem. The biggest section of the chapter includes theory on simple continued fractions, quadratic irrationals to provide an explanation on how the fundamental solution can be found. Later in the chapter we also include a program code of "Python 3.8.2" based on earlier discussed theory to find the fundamental solution of Pell's equation. Third chapter is devoted to Archimedes' Problema Bovinum, where we talk about its origin, text of the problem, show how it is related to Pell's equation and provide history on attempts to solve it. In the last chapter we conclude that Pell's equations are important as they are found in various mathematical contexts and require some knowledge to solve them. Also, Pell's equation could have been challenging in the past, especially if found in Archimedes' Problema Bovinum but cannot be considered a very difficult problem in terms of present concepts, when a modern computer can solve it in a matter of time.

Grantor dc:publisher

Institutional Repository of Vilnius University

Year dc:date

2020

Author dc:creator

• Vaitkus, Šarūnas,

Contributors dc:contributor

• Novikas, Aivaras

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

lit

Repository record dc:identifier

https://repository.vu.lt/VU:ELABAETD81808305&prefLang=en_US

OAI identifier oai:identifier

oai:vu.lt:elaba:81808305