GEOMETRIJSKI SANGAKU PROBLEMI

U radu se predstavljaju sangakui – drvene ploče s matematičkim zapisima koje su postavljane diljem Japana pod krovišta hramova kao zavjetni darovi ili zahvale bogovima na matematičkim postignućima. Sangaku ploče nastale su u vrijeme Edo razdoblja kojeg karakterizira mir i samonametnuta izolacija Japana od ostatka svijeta. Tijekom Edo razdoblja dolazi do snažnog razvoja autohtone znanosti i umjetnosti, a taj period poznatiji je kao Genroku renesansa. Stoga, u svrhu boljeg razumijevanja nastanka i važnosti sangaku ploča prvo se u radu razmatraju povijesno-kulturni aspekti Japana toga vremena, a zatim se opisuju sadržaji sangaku ploča kako bi se moglo prijeći na središnju temu ovoga rada. U središnjem dijelu rada obrađuje se sedam odabranih geometrijskih sangaku problema sa ploča iz različitih prefektura poredanih prema zahtjevnosti i vrstama koncepata koji su u njima zastupljeni, a odabrani su tako da slijede geometrijski kurikulum elementarnog matematičkog obrazovanja. Problemi se obrađuju tako da prate strukturiranje i vizualno oblikovanje na pločama, a daje se i detaljan prikaz procesa rješavanja, što na originalnim pločama nije postojalo, vjerojatno zbog nedovoljno prostora ili zbog izazova čitateljima. Kako bi se došlo da rješenja problema, figure su konstruirane, zatim je konstrukcija provedena unutar programa dinamičke geometrije, a opis procesa konstruiranja u radu je opisan po koracima. Iako je za otkrivanje odnosa unutar odabranih sangaku problema potrebno suptilno razumijevanje geometrijskih koncepata i vještina rješavanja geometrijskih problema, oni se mogu prepoznati korištenjem samo elementarnih matematičkih znanja koja se stječu unutar osnovnoškolskog matematičkog obrazovanja pa ovaj rad može poslužiti kao koristan nastavni materijal svakom zainteresiranom učitelju matematike.This paper represents sangaku – wooden boards with mathematical writings that were placed under the roofs of temples all over Japan as votive gifts or thanks to the gods for mathematical achievements. Sangaku boards were created during the Edo period, which was characterized by peacetime and self-imposed isolation of Japan from the rest of the world. During the Edo period, there was a strong development of indigenous science and art, and that period was better known as the Genroku renaissance. Therefore, in order to understand better the origin and importance of sangaku boards, the paper first considers the historical and cultural aspects of Japan at that time, then describes the contents of sangaku boards in order to move on to the central topic of this paper which focuses on seven selected geometric sangaku problems which originate from different prefectures. In this paper, sangaku problems are ordered by complexity and concepts that are represented within them, which follow the geometrical curriculum of elementary mathematical education. The problems venerate the structure and visual design on original wooden boards, but unlike original boards, a detailed description of the solving process is given in this paper. Solutions probably weren't given on the original boards due to insufficient space or in order to challenge the readers. In order to find a solution to the problem, the figures were constructed, then the construction was made in the programme of dynamic geometry while the description itself follows the real process of construction step by step. Although subtle understanding of geometric concepts and geometric solving skills are required for solving sangaku problems, they can be solved using only elementary mathematical knowledge acquired within elementary school mathematics education, so this work can be useful teaching material for any interested mathematics teacher