Simulation on Sangaku problem using optimization methods




Sangaku problem, packing problem, circle, local optimization


Sangaku problem is one of Japanese Temple Geometry problems which was studied in Hidetoshi Fukugawa[1]. One of the Sangaku problem is packing 6 equal circles in rectangle of 1:1.934798 size. We examine the problem from a view point of optimization theory and algorithm. We show that Sangaku optimization problem belongs to a class of nonconvex optimization and propose a penalty method for solving the problem numerically. In numerical expirements, we consider equal and unequal 6 circles. Computational results obtained on Python Jupyter Notebook are provided.

Сангаку бодлогыг оптимизацийн аргаар бодох нь

Хураангуй: Сангаку бодлого нь Японы эртний геометрийн бодлого юм. Энэхүү судалгаандаа бид Хидетоши Фукугава эрдэмтний судалсан 1:1.934798 хэмжээтэй тэгш өнцөгтөд 6 ижил тойрог багтаах сангаку бодлогыг авч үзэв. Энэ бодлогыг хучилтын бодлогын хүрээнд оптимизацийн аргаар бодсон ба энэ нь гүдгэр бус максимумчлалын бодлого болно.Бодлогыг өргөтгөж, ижил бус 6 тойргын хувьд бодож торгуулийн функцийн аргаар нэмж тооцооллыг хийв. Python Jupyter Notebook программ дээр тооцооллыг хийж үр дүнг гаргасан болно.

Түлхүүр үгс: Сангаку бодлого, хучилтын бодлого, тойрог, оптимизацийн арга



Simulation on Sangaku problem using optimization methods

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How to Cite

Jargalsaikhan, D., Rentsen, E., Bataa, D., & Darkhijav, B. (2023). Simulation on Sangaku problem using optimization methods. Journal of Institute of Mathematics and Digital Technology, 5(1), 19–29.