Miscellaneous Mathematical Constants

by Unknown

The Hard hexagons Entropy Constant

The hard-hexagons entropy constant is algebraic (see below z number).

The value is :

1.3954859724793027352295006635668880689541037281446611908174721561357608803586 977746898378730852754279026689685607685657184842212457119511639349818266947083 252547173794947534862281229126187281554340126162747356973585709823756812898414 948800016934903723995652094568253572538633572005211925074739811015138086289661 268136787831885630404682747107477204686894756657580905530270066675404962427719 060854536142216836296933016900330937276956621269398726823104923047442882514781 702966107270054292812280795061336321550953581179745072336957434963259935073449 490894249329307540816210555328068610619705545037955077580725537613858033619505 210958967729699416630942601615566925218549336476968551824281894615092855649748 501359906929152571833851080212811049755339847366927914398892041851355831303575 673710465224807454744982583885183287167357146092090743402851746571565499082292 999884612996137479952358336507860770516087879631202738350102895965881076822440 14681214726789035888008851819053742866660552775722734105313225337

Taken from
The Favorite mathematical constants of Steven Finch, Mathsoft Inc.

The constant is given by this (see z below)…

124 1/3
a := - —- 11
363

2501 1/2
b := ——- 33
11979

/ 31 1/3 // 2501 1/2 \1/3 / 2501 1/2 \1/3\\1/3
c := |1/4 - —- 11 ||——- 33 + 1| - |——- 33 - 1| ||
\ 242 \\11979 / \11979 / //

1/4 7/12
3 11
z1 := 3/44 —————————————————————————————————
/ 31 1/3 // 2501 1/2 \1/3 / 2501 1/2 \1/3\\2/3
|1/4 - —- 11 ||——- 33 + 1| - |——- 33 - 1| ||
\ 242 \\11979 / \11979 / //