

A214726


Decimal expansion of the perimeter of Cairo and Prismatic tiles.


0



3, 8, 6, 3, 7, 0, 3, 3, 0, 5, 1, 5, 6, 2, 7, 3, 1, 4, 6, 9, 9, 8, 9, 7, 2, 7, 9, 8, 9, 1, 5, 5, 8, 9, 4, 7, 0, 5, 3, 5, 6, 1, 9, 3, 5, 6, 0, 3, 3, 6, 1, 8, 2, 0, 1, 6, 0, 9, 3, 7, 2, 3, 0, 5, 2, 4, 1, 6, 9, 2, 8, 5, 5, 9, 1, 9, 4, 2, 2, 0, 6, 5, 3, 9, 0, 2, 4, 6, 9, 6, 7, 4, 3, 2, 2, 8, 1, 8, 0, 8
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OFFSET

1,1


COMMENTS

Abstract: "We identify leastperimeter unitarea tilings of the plane by convex pentagons, namely tilings by Cairo and Prismatic pentagons, find infinitely many, and prove that they minimize perimeter among tilings by convex polygons with at most five sides."
An algebraic integer with degree 4 and minimal polynomial x^4  16x^2 + 16.  Charles R Greathouse IV, Apr 21 2016


LINKS

Table of n, a(n) for n=1..100.
Ping Ngai Chung, Miguel A. Fernandez, Yifei Li, Michael Mara, Frank Morgan, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vieira, Elena Wikner, Isoperimetric Pentagonal Tilings, Not. AMS, Vol. 59, No. 5, May 2012, pp. 632640.


FORMULA

2*(sqrt(2+sqrt(3))) = 3.8637033051562731469989727989....


PROG

(PARI) 2*sqrt(2+sqrt(3)) \\ Charles R Greathouse IV, Apr 21 2016


CROSSREFS

Cf. A002193, A002194.
Sequence in context: A016627 A175184 A019604 * A106291 A137987 A212007
Adjacent sequences: A214723 A214724 A214725 * A214727 A214728 A214729


KEYWORD

nonn,cons,easy


AUTHOR

Jonathan Vos Post, Jul 26 2012


STATUS

approved



