Research output: Contribution to journal › Article › peer-review
On Subdivisions of Polygons. / Никанорова, Мария Юрьевна; Романовский, Юрий Рэмович.
In: Journal of Mathematical Sciences, Vol. 251, No. 4, 12.2020, p. 524-530.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - On Subdivisions of Polygons
AU - Никанорова, Мария Юрьевна
AU - Романовский, Юрий Рэмович
PY - 2020/12
Y1 - 2020/12
N2 - By a subdivision of a polygon, we mean an orthogonal net such that the vertices of the polygon are nodes of the net, and the edges are composed of diagonals and sides of its cells. We study the subdivisions of convex polygons in which all edges have only diagonal directions. Such a polygon has four supporting vertices lying on different sides of the circumscribed rectangle. From each nonsupporting vertex, toward the interior of the polygon, there emanates a pair of broken lines in the directions of the orthogonal net. After a finite number of reflections in the boundary (the sum of the incidence and reflection angles is equal to 90°), the broken lines of such a pair can either get stuck at the supporting vertices or meet each other and form a closed orbit. It is proved that in the case of the pentagon, the second variant is not possible.
AB - By a subdivision of a polygon, we mean an orthogonal net such that the vertices of the polygon are nodes of the net, and the edges are composed of diagonals and sides of its cells. We study the subdivisions of convex polygons in which all edges have only diagonal directions. Such a polygon has four supporting vertices lying on different sides of the circumscribed rectangle. From each nonsupporting vertex, toward the interior of the polygon, there emanates a pair of broken lines in the directions of the orthogonal net. After a finite number of reflections in the boundary (the sum of the incidence and reflection angles is equal to 90°), the broken lines of such a pair can either get stuck at the supporting vertices or meet each other and form a closed orbit. It is proved that in the case of the pentagon, the second variant is not possible.
UR - http://www.scopus.com/inward/record.url?scp=85095719734&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/0bbd82ff-2d12-33dd-a04a-fe79b4816026/
U2 - 10.1007/s10958-020-05113-4
DO - 10.1007/s10958-020-05113-4
M3 - Article
VL - 251
SP - 524
EP - 530
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 4
ER -
ID: 71205612