2000-12-01
Efficient Regular Polygon Dissections
Publication
Publication
Geometriae Dedicata , Volume 80 - Issue 1-3 p. 247- 262
We study the minimum number g(m, n) (respectively, p(m, n)) of pieces needed to dissect a regular m-gon into a regular n-gon of the same area using glass-cuts (respectively, polygonal cuts). First we study regular polygon-square dissections and show that ⌈n/2⌉ - 2 ≤ g(4, n) ≤ (n/2) + o(n) and ⌈n/4⌉ ≤ g(n, 4) ≤ (n/2) + o(n) hold for sufficiently large n. We also consider polygonal cuts, i.e., the minimum number p(4, n) of pieces needed to dissect a square into a regular n-gon of the same area using polygonal cuts and show that ⌈n/4⌉ ≤ p(4, n) ≤ (n/2) + o(n) holds for sufficiently large n. We also consider regular polygon-polygon dissections and obtain similar bounds for g(m, n) and p(m, n).
Additional Metadata | |
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Dissections, Glass-cuts, Polygonal cuts, Regular polygons, Squares | |
Geometriae Dedicata | |
Organisation | School of Computer Science |
Kranakis, E, Krizanc, D. (Danny), & Urrutia, J. (Jorge). (2000). Efficient Regular Polygon Dissections. Geometriae Dedicata, 80(1-3), 247–262.
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