Par izliektiem minimāliem režģa daudzstūriem, minimāla laukuma atrašanas algoritms
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Latvijas Universitāte
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Abstract
Darbā aplūkota problēma par izliekta režģa n-stūra minimālā laukuma a(n) atrašanu. Pierādīta teorēma par vienāda laukuma n-stūru klasi un apskatītas tās sekas. Pierādīts, ka fiksētam n uzdevumu var reducēt uz galīgu pārlasi. Izstrādāts algoritms un ar tā palīdzību aprēķinātas a(n) vērtības, ja n < 21. Iegūti vairāki jauni rezultāti: a(15) = 51,5; a(17) = 75,5; a(19) = 106,5; a(21) = 144,5.
This paper deals with the problem of determining convex lattice polygon with minimum area a(n). The theorem about the set of polygons with equal area has been proved and the consequences of this theorem have been considered as well. For fixed n we reduce the problem to finite search. The algorithm has been elaborated and by means of it the values of a(n) have been calculated when n < 21. A several new results have been obtained: a(15) = 51.5; a(17) = 75.5; a(19) = 106.5; a(21) = 144.5.
This paper deals with the problem of determining convex lattice polygon with minimum area a(n). The theorem about the set of polygons with equal area has been proved and the consequences of this theorem have been considered as well. For fixed n we reduce the problem to finite search. The algorithm has been elaborated and by means of it the values of a(n) have been calculated when n < 21. A several new results have been obtained: a(15) = 51.5; a(17) = 75.5; a(19) = 106.5; a(21) = 144.5.