Lov na medvjede na rotacijskim plohama

master's thesis

• Title (english): Hunting bears on rotating surfaces
• Author: Lucija Šainović
• Mentor: Tomislav Došlić (mentor)
• Committee member: Tomislav Došlić (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Tomislav Berić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-05-05, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad bavi se poznatim problemom: ”Lovac kreće iz svog šatora i hoda 10 km prema jugu. Nakon toga skreće i hoda 10 km prema zapadu. Onda skreće prema sjeveru i hoda 10 km. Nakon prehodanih 30 km nalazi se na mjestu s kojeg je krenuo, pred svojim šatorom, no ne može ući jer je unutra medvjed. Koje je boje medvjed?” U prvom poglavlju opisani su osnovni pojmovi sferne geometrije te su navedeni osnovni teoremi i definicije toga područja. U drugom su poglavlju opisana rješenja navedenog zadatka na različitim rotacijskim plohama: sferi, kružnom valjku i kružnom stošcu. Na kraju se spominje postojanost rješenja na općenitoj rotacijskoj plohi.

Abstract (english)

This paper presents a well-known problem: ”A hunter started from his tent and went 10 km strictly south. After that he turns and walks 10 km strictly west. Then he turns to the north and walks 10 km. After walking 30 km he is in front of his tent, but he can’t enter because there is a bear inside. What color is the bear? ” The first chapter presents the basic concepts, definitions and theorems of spherical geometry. The second chapter describes the answers of this problem on different rotational surfaces: a sphere, a cylinder and a cone, and in the end, on general rotational surfaces.

• Keywords: sferna geometrija; sfera; kružni valjak; kružni stožac
• Keywords (english): spherical geometry; sphere; cylinder; cone
• Language: croatian
• URN:NBN: urn:nbn:hr:217:104407
• 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: 2022-06-08 11:54:32