ISSN:
1572-9168
Keywords:
dissections
;
glass-cuts
;
polygonal cuts
;
regular polygons
;
squares
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1005292125553
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