Editing Catalan's constant (section)

==Uses==
In [[low-dimensional topology]], Catalan's constant is 1/4 of the volume of an [[ideal polyhedron|ideal]] hyperbolic [[octahedron]], and therefore 1/4 of the [[hyperbolic volume]] of the complement of the [[Whitehead link]].<ref>{{citation
 | last = Agol | first = Ian | author-link = Ian Agol
 | doi = 10.1090/S0002-9939-10-10364-5
 | issue = 10
 | journal = [[Proceedings of the American Mathematical Society]]
 | mr = 2661571
 | pages = 3723–3732
 | title = The minimal volume orientable hyperbolic 2-cusped 3-manifolds
 | volume = 138
 | year = 2010| arxiv = 0804.0043| s2cid = 2016662 }}.</ref> It is 1/8 of the volume of the complement of the [[Borromean rings]].<ref>{{Citation |author=William Thurston|author-link=William Thurston |date=March 2002 |title=The Geometry and Topology of Three-Manifolds |url=http://library.msri.org/books/gt3m/ |chapter=7. Computation of volume |chapter-url=http://library.msri.org/books/gt3m/PDF/7.pdf |archive-url=https://web.archive.org/web/20110125012649/http://library.msri.org/books/gt3m/PDF/7.pdf |archive-date=2011-01-25 |url-status=live |page=165}}</ref>

In [[combinatorics]] and [[statistical mechanics]], it arises in connection with counting [[domino tiling]]s,<ref>{{citation
 | last1 = Temperley | first1 = H. N. V. | author1-link = Harold Neville Vazeille Temperley
 | last2 = Fisher | first2 = Michael E. | author2-link = Michael Fisher
 | date = August 1961
 | doi = 10.1080/14786436108243366
 | issue = 68
 | journal = [[Philosophical Magazine]]
 | pages = 1061–1063
 | title = Dimer problem in statistical mechanics—an exact result
 | volume = 6| bibcode = 1961PMag....6.1061T }}</ref> [[spanning tree]]s,<ref>{{citation
 | last = Wu | first = F. Y.
 | doi = 10.1088/0305-4470/10/6/004
 | issue = 6
 | journal = Journal of Physics
 | mr = 489559
 | pages = L113–L115
 | title = Number of spanning trees on a lattice
 | volume = 10
 | year = 1977| bibcode = 1977JPhA...10L.113W
 }}</ref> and [[Hamiltonian cycle]]s of [[grid graph]]s.<ref>{{citation
 | last = Kasteleyn | first = P. W. | author-link = Pieter Kasteleyn
 | doi = 10.1016/S0031-8914(63)80241-4
 | journal = [[Physica (journal)|Physica]]
 | mr = 159642
 | pages = 1329–1337
 | title = A soluble self-avoiding walk problem
 | volume = 29
 | year = 1963| issue = 12 | bibcode = 1963Phy....29.1329K }}</ref>

In [[number theory]], Catalan's constant appears in a conjectured formula for the asymptotic number of primes of the form <math>n^2+1</math> according to [[Ulam spiral#Hardy and Littlewood's Conjecture F|Hardy and Littlewood's Conjecture F]]. However, it is an unsolved problem (one of [[Landau's problems]]) whether there are even infinitely many primes of this form.<ref>{{citation
 | last = Shanks | first = Daniel | author-link = Daniel Shanks
 | journal = Mathematical Tables and Other Aids to Computation
 | mr = 105784
 | pages = 78–86
 | title = A sieve method for factoring numbers of the form <math>n^2+1</math>
 | volume = 13
 | year = 1959| doi = 10.2307/2001956 | jstor = 2001956 }}</ref>

Catalan's constant also appears in the calculation of the [[mass distribution]] of [[spiral galaxy|spiral galaxies]].<ref>{{citation
 | last1 = Wyse | first1 = A. B. | author1-link=Arthur Bambridge Wyse
 | last2 = Mayall | first2 = N. U.
 | bibcode = 1942ApJ....95...24W
 | date = January 1942
 | doi = 10.1086/144370
 | journal = [[The Astrophysical Journal]]
 | pages = 24–47
 | title = Distribution of Mass in the Spiral Nebulae Messier 31 and Messier 33.
 | volume = 95| doi-access = free
 }}</ref><ref>{{citation
 | last = van der Kruit | first = P. C.
 | bibcode = 1988A&A...192..117V
 | date = March 1988
 | journal = [[Astronomy & Astrophysics]]
 | pages = 117–127
 | title = The three-dimensional distribution of light and mass in disks of spiral galaxies.
 | volume = 192}}</ref>