Konkurentni pravci

master's thesis

• Author: Maria Gračan
• Mentor: Maja Starčević (mentor)
• Committee member: Maja Starčević (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Konkurentni pravci su pravci koji se sijeku u istoj točki. U ovom radu opisano je sedam metoda dokazivanja konkurentnosti pravaca koje smo zatim primijenili na opravdavanje postojanja raznih točaka vezanih za trokut, četverokut, kružnicu, šesterokut koje su nastale presijecanjem tri ili više pravaca. Riješeno je i nekoliko primjera zadataka s natjecanja iz matematike provedenih u Republici Hrvatskoj u kojima je bilo potrebno dokazati konkurentnost pravaca.

Abstract (english)

Concurrent lines are lines that intersect at the same point. Seven methods of proving the concurrency of lines have been described in this thesis, which we then applied to justify the existence of various points related to triangle, circle, quadrilateral, hexagon, which are result of intersecting three or more lines. A couple of examples from math competitions conducted in the Republic of Croatia have been solved in which it was necessary to prove the concurrency of lines.

• Keywords: konkurentni pravci; metode dokazivanja konkurentnosti pravaca; trokut; četverokut; kružnica; šesterokut; zadaci s natjecanja iz matematike
• Keywords (english): concurrent lines; methods of proving the concurrency of lines; triangle; circle; quadrilateral; hexagon; examples from math competitions
• Language: croatian
• URN:NBN: urn:nbn:hr:217:561220
• 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: Open access
• Created on: 2018-01-26 12:59:25