Prikazi presjeka tijela pomoću aksonometrije

master's thesis

• Author: Rosanda Radić
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu posebnu pažnju posvetila sam presjecima tijela aksonometrijskim metodama i njihovoj primjeni u srednjoj školi. U prvom poglavlju objasnila sam općenito što je to aksonometrija te nabrojila i ukratko objasnila njene vrste. Kao važnu činjenicu koja nam omogućava proizvoljan odabir pri konstruiranju osnog križa iznijela sam i dokazala Pohlkeov stavak. Iako u radu nije svaki put napisano, ali upravo ovaj stavak nam je omogućio sve konstrukcije. Nadalje sam opisala na koji način se točke, pravci, ravnine i tijela prenose iz Mongeove projekcije u kosu aksonometriju. Kao posebnu cjelinu sam navela i objasnila kutove proporcionalnosti uz pomoć kojih možemo na brži način doći do kosoaksonometrijskih slika točaka. Kroz cijeli rad sam konstruirala slike u kosoj aksonometriji, ali sam isto tako navela i ostale vrste aksonometrije (specijalna kosa aksonometrija, kosa projekcija) te na primjeru kocke prikazala kako izgledaju slike u prirodnom izgledu, a kako u neprirodnom. U četvrtom poglavlju sam obradila razne primjere presjeka tijela i ravnine u kosoj aksonometriji. Uvijek sam polazila od jednostavnijih presjeka (presjek tijela i projicirajuće ravnine) prema složenijima (presjek tijela i opće ravnine). Nastojala sam obuhvatiti sva tijela, pa sam tako napravila presjek prizmi, piramida, stošca i valjka sa zadanim ravninama. U petom i posljednjem poglavlju u ovom radu, posvetila sam se primjeni u srednjoj školi. Na nekoliko primjera sam pokazala kako bi se u srednjoj školi došlo do presjeka tijela i ravnine.

Abstract (english)

Throughout this dissertation I have dedicated attention towards axonometric methods and their use in high schools. In the first chapter I provided a general idea of axonometric projections and further enlisted and explained their various variants. I have shown the important concept which allows arbitrary selection when constructing the axial cross by proving the Pohlke’s theorem. This theorem allowed us to create all constructions. I have described how to construct an oblique projection of points, lineas, surfaces and some figures. An entire section of this dissertation is devoted to the proportional angles which help us to determine the oblique-axonometric constructions in a faster manner. I have also enlisted other types of axonometric projection (special oblique axonometric projection, oblique projection ) and using the cube as an example I showcased how different cases of \(p_x, p_y, p_z, \alpha\) and \(\beta\) give us natural or less natural pictures. In the fourth chapter I constructed several examples of intersections of surfaces and figures using oblique axonometric projection. Throughout this paper, I always started from simpler examples of intersections towards more complicated examples. I endeavoured to cover all of bodies, therefore I made intersections of prisms, pyramids, cones and cylinders with assigned planes. Fifth and last chapter of this paper I dedicated to constructive problems in high school mathematics. Through a couple of examples I showcased methods on how to construct intersections of bodies and planes in high school mathematics.

• Keywords: presjeci tijela aksonometrijskim metodama; nastava matematike; srednja škola; aksonometrija; Pohlkeov stavak
• Keywords (english): axonometric methods; teaching mathematics; high school; middle school; axonometric projections; Pohlke’s theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:353139
• 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: 2019-06-13 12:10:22