Maģiskie daudzstūri un to īpašības
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Latvijas Universitāte
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lav
Abstract
Darbā aplūkoti maģiskie daudzstūri – polimino, kuriem visu malu garumi ir dažādi naturāli skaitļi no 1 līdz n, un pētītas vairākas to īpašības: eksistences nepieciešamie un pietiekamie nosacījumi, laukumu vērtību kopa, malu garumu monotonitāte. Izstrādāta datorprogramma, ar kuras palīdzību ir atrasti visi maģiskie 8-stūri un visi perfektie n-stūri, ja n = 8 un 16. Aplūkoti arī maģiskie polimondi. Vairāki iegūtie rezultāti ir jauni un pagaidām nav atrodami literatūrā.
In this research paper magic polygons – polyominoes whose lengths of edges are all different integers from 1 to n are examined, and several their properties are studied: sufficient and necessary conditions of existence, set of area values, monotonicity of edge lengths. The computer program allowing to find all magic octagons and all perfect n-gons, if n = 8 and 16, has been elaborated. Magic polyiamonds are also examined. Several of the obtained results are new and are not found in literature yet.
In this research paper magic polygons – polyominoes whose lengths of edges are all different integers from 1 to n are examined, and several their properties are studied: sufficient and necessary conditions of existence, set of area values, monotonicity of edge lengths. The computer program allowing to find all magic octagons and all perfect n-gons, if n = 8 and 16, has been elaborated. Magic polyiamonds are also examined. Several of the obtained results are new and are not found in literature yet.