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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Abstract: "We identify least-perimeter unit-area 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. 632-640.

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

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Last modified February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)