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Dudeneyjev Haberdasherov problem
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U radu se obrađuje jedan stari, ali još uvijek aktualni, problem dijeljenja jednakostraničnog trokuta na najmanji broj dijelova tako da se preslagivanjem nastalih dijelova, bez preokretanja, može oblikovati kvadrat. Problem je poznat pod nazivom Haberdasherov problem, ali unatoč brojnim pokušajima, jedino do danas poznato valjano rješenje dao je engleski matematičar Dudeney, još 1903. godine. Uz opis konstrukcije i opravdanja valjanosti Dudeneyjeva rješenja, posebno se razmatra jedno rješenje koje pokazalo pogrešnim, a zapravo se radi samo o dobroj aproksimaciji kvadrata. Također, razmatra se klasa rješenja dijeljenja trokuta na dijelove koji se daju oblikovati u pravokutnik među kojima je i jedan kvadrat. Konačno, navode se i razlozi zašto su ovakvi i slični problemi korisni i prikladni za korištenje na svim razinama obrazovanja.
Faculty of Science, University of Split
Title: Dudeneyjev Haberdasherov problem
Description:
U radu se obrađuje jedan stari, ali još uvijek aktualni, problem dijeljenja jednakostraničnog trokuta na najmanji broj dijelova tako da se preslagivanjem nastalih dijelova, bez preokretanja, može oblikovati kvadrat.
Problem je poznat pod nazivom Haberdasherov problem, ali unatoč brojnim pokušajima, jedino do danas poznato valjano rješenje dao je engleski matematičar Dudeney, još 1903.
godine.
Uz opis konstrukcije i opravdanja valjanosti Dudeneyjeva rješenja, posebno se razmatra jedno rješenje koje pokazalo pogrešnim, a zapravo se radi samo o dobroj aproksimaciji kvadrata.
Također, razmatra se klasa rješenja dijeljenja trokuta na dijelove koji se daju oblikovati u pravokutnik među kojima je i jedan kvadrat.
Konačno, navode se i razlozi zašto su ovakvi i slični problemi korisni i prikladni za korištenje na svim razinama obrazovanja.
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