| Abstract | U ovom radu prikazani su početci i razvitak matematike u staroj Grčkoj. Stari Grci utjecali su na razvoj znanosti, filozofije i arhitekture, a njihov utjecaj na području matematike prisutan je sve do danas. Na početku rada prikazani su brojevni sustavi starih Grka te nedostatci takvog načina zapisa brojeva. Zatim je opisan značaj prvog grčkog matematičara, Talesa Milećanina, koji je koristeći svoje teoreme rješavao mnoge praktične probleme toga vremena. Talesov učenik Pitagora i njegovi učenici postigli su značajne rezultate na području teorije brojeva i geometrije, dokazali Pitagorin poučak i otkrili iracionalne brojeve. Pitagorina škola imala je utjecaj na Platona, osnivača škole pod imenom Akademija. U Akademiji su se proučavale aritmetika, trigonometrija i planimetrija. Jedan od najpoznatijih učenika Akademije, Aristotel, najveći je doprinos dao na području logike. Poseban je naglasak stavljen na doprinos najpoznatijeg grčkog matematičara Euklida, zvanog ocem geometrije. Euklid je ostavio 13 knjiga obuhvaćenih u jedno veliko djelo Elementi. Elementi su stoljećima bili osnovni udžbenik matematike te jedno od najviše proučavanih djela. Naveden je dio definicija, postulata, aksioma i propozicija zapisanih u Elementima te su ukratko opisane teme u svakoj od 13 knjiga. Nakon Euklida opisan je doprinos Arhimeda, s kojim završava starogrčko doba matematike. Rad završava prikazom triju klasičnih problema starogrčke matematike. |
| Abstract (english) | This paper presents the beginnings and historical development of ancient Greek mathematics. The ancient Greeks influenced the development of science, philosophy and architecture, and their influence in the field of mathematics is still present nowadays. In the introductory part of the paper, the number systems of the ancient Greeks and their disadvantages are presented. Then the importance of the first Greek mathematician, Thales of Miletus, who used his theorems to solve many practical problems of that time, is described. Thales' student Pythagoras and his students reached significant results in the field of number theory and geometry, proved Pythagoras' teaching and discovered irrational numbers. The school of Pythagoras influenced Plato, who founded his own school, the famous Academy. Arithmetic, trigonometry and planimetry were studied at the Academy. One of the most famous students of the Academy, Aristotle, made the greatest contribution in the field of logic. A special emphasis is placed on the contribution of the most renowned Greek mathematician Euclid, known as the founder of geometry. Euclid left 13 books incorporated into one great work called Elements. For centuries, Elements was a basic mathematics textbook and one of the most studied works. Some of the definitions, postulates, axioms and propositions presented in the Elements are listed, and the topics in each of the 13 books are briefly described. After Euclid, the contribution of Archimedes is described, who marks the end of the ancient Greek age of mathematics. The paper ends with a presentation of three classical problems of ancient Greek mathematics. |
