Fibonaccijeva Practica Geometriae

master's thesis

• Author: Mihaela Šimić
• Mentor: Franka Miriam Bruckler (mentor)
• Committee member: Franka Miriam Bruckler (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U radu se upoznajemo s istaknutim djelom Practica Geometriae značajnog srednjovjekovnog europskog matematičara Leonarda Fibonaccija. Na samom početku navodimo biografske podatke o Leonardu Fibonacciju, govorimo o njegovom utjecaju i važnosti njegovih djela te njegovim doprinosima u matematici. U drugom poglavlju upoznajemo se sa sadržajem Fibonaccijeve Practica Geometriae. Ovo poglavlje sadrži devet potpoglavlja s nazivima koje je koristio Fibonacci u Practica Geometriae pri čemu se svako potpoglavlje bavi drugačijom problematikom. Tako je u Uvodu Fibonacci naveo 22 definicije i aksiome vrlo slične onima u Euklidovim Elementima, a potom i opisao pisanske mjerne jedinice za duljinska i površinska mjerenja. U idućem potpoglavlju Fibonacci se bavi opisivanjem metoda za izračunavanje površine pravokutnika i kvadrata. Nadalje, u trećem potpoglavlju opisan je postupak pronalaženja drugog korijena pisanskih mjernih jedinica te osnovnim računskim operacijama s drugim korijenima. Četvrto potpoglavlje opisuje postupke za izračunavanje površine polja svih oblika. Peto potpoglavlje opisuje dijeljenje polja koja imaju oblik trokuta, četverokuta, mnogokuta i kruga uz različite uvjete. Šesto potpoglavlje bavi se pronalaženjem trećeg korijena brojeva i osnovnim računskim operacijama s trećim korijenima. Sedmo potpoglavlje bavi se izračunavanjem volumena geometrijskih tijela. Osmo potpoglavlje opisuje metodu mjerenja visine stabla i izračunavanje duljine luka i tetive. Zadnje potpoglavlje bavi se izračunavanjem duljine stranice pravilnog peterokuta i pravilnog deseterokuta, kao i duljine promjera njima upisanih i opisanih kružnica. Diplomski rad završava poglavljem u kojem opisujemo Fibonaccijeve metode i postupke iz Practica Geometriae iz perspektive današnje nastave matematike s naglaskom na razlikama i sličnostima Fibonaccijevog i suvremenog pristupa u današnjoj nastavi matematike.

Abstract (english)

In this thesis we discuss the prominent work Practica Geometriae of the notable medieval European mathematician Leonardo Fibonacci. At the very beginning, we give biographical information on Leonardo Fibonacci and review his influence and the importance of his works and his contributions to mathematics. In the second chapter, we discuss in detail the content of Fibonacci Practica Geometriae. This chapter contains nine subsections with the names used by Fibonacci in the Practica Geometriae, where each subsection deals with a different topic. In the Introduction Fibonacci listed 22 definitions and axioms that were very similar to those in Euclid’s Elements, and then described Pisian measurements. In the next subsection Fibonacci deals with the description of the method for calculating rectangle and square areas. Further, in the third subsection, the procedure for finding the second roots of Pisan units and basic calculations with second roots are described. The fourth subsection describes procedures for calculating the area of various forms of fields. The fifth subsection describes the division of fields that have the form of triangles, quadrangles, polygons, and circles under different conditions. The sixth subsection deals with the finding of the third roots of numbers and the basic calculations with third roots. The seventh subsection deals with the calculation of the volume of solids. The eighth subsection describes the method of measuring the height of trees and calculating the length of arcs and chords. The last subsection deals with the calculation of the length of the sides of the regular pentagons and decagons and the diameter of an inscribed and circumscribed circles. The thesis ends with a chapter in which we discuss Fibonacci’s topics and methods from Practica Geometriae from the perspective of contemporary maths teaching, focusing on the differences and similarities of Fibonacci’s and contemporary approaches.

• Keywords: Fibonacci; Practica Geometriae; pisanske mjerne jedinice; nastava matematike
• Keywords (english): Fibonacci; Practica Geometriae; Pisian measurements; teaching mathematics
• Language: croatian
• URN:NBN: urn:nbn:hr:217:468055
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-06-28 12:30:45