prikaz prve stranice dokumenta Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi
  Download
PDF 2.48 MB
master's thesis
Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:636312
Mikulin, Elvira
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mikulin, E. (2019). Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:636312

Mikulin, Elvira. "Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:636312

Mikulin, Elvira. "Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:636312

Mikulin, E. (2019). 'Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi', Master's thesis, University of Zagreb, Faculty of Science, accessed 09 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:636312

Mikulin E. Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2025 January 09] Available at: https://urn.nsk.hr/urn:nbn:hr:217:636312

E. Mikulin, "Istraživanja pravilnosti u nastavi matematike: mnogokutni brojevi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:636312

Metadata
TitleIstraživanja pravilnosti u nastavi matematike: mnogokutni brojevi
AuthorElvira Mikulin
MentorŽeljka Milin Šipuš (mentor)
Committee memberŽeljka Milin Šipuš (predsjednik povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Mnogokutni brojevi su prirodni brojevi koji se mogu geometrijski prikazati rasporedom odgovarajućeg broja točaka u pravilne mnogokute. U prvom poglavlju ovog rada opisano je prvih nekoliko mnogokutnih brojeva, izvedene su opće formule za \(n-\)ti \(k-\)mnogokutni broj i veze između različitih mnogokutnih brojeva. U drugom poglavlju opisani su centralni mnogokutni brojevi i spomenuti su zvjezdasti brojevi, njihova posebna skupina. U trećem poglavlju dan je opis pravokutnih i trapeznih brojeva, te su izvedene njihove veze s ostalim mnogokutnim brojevima. U sva tri poglavlja dani su geometrijski prikazi navedenih brojeva, izvedenih formula i veza. Ukoliko točke pravilno rasporedimo u prostoru, u trodimenzionalna tijela, nastaju trodimenzionalni mnogokutni brojevi, opisani u četvrtom poglavlju. Peto poglavlje sastoji se od aktivnosti primjerenih izvođenju na nastavi. Prve dvije aktivnosti tiču se algebarskih veza kod mnogokutnih brojeva i njihovog geometrijskog prikaza. Treća aktivnost predviđena je za izvođenje pomoću didaktičkog materijala (Cuisenaireovih štapića).
Abstract (english)
Polygonal numbers are natural numbers that can be geometrically represented by arranging the corresponding number of points into regular polygons. In the first chapter of this thesis we describe the first few polygonal numbers, then derive formulas for the \(n-\)th \(k-\)gonal number and finally describe many properties of polygonal numbers. In the second chapter centered polygonal numbers are described, in particular their special subgroup, star numbers. In the third chapter we define and analyse rectangular and trapezoidal numbers and their relations to other polygonal numbers. Geometrical representations of different polygonal numbers visualizing their properties are given in all three chapters. When putting points in a special order in space, instead of plane, one obtains space polygonal numbers, which are described in the fourth chapter. The fifth chapter consists of activities that are appropiate for teaching in school. The first two activities are concerned with algebraic connections of polygonal numbers and their geometrical representation. The third activity is intended to be performed using didactic material (Cuisenaire rods).
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:636312
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-02-11 12:43:23