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-This is a list of [[mathematical constant]]s sorted by their representations as [[continued fraction]]s.
+I am 23 years old and my name is Velda Rosales. I life in Lofsdalen (Sweden).<br><br>Here is my website :: [http://hemorrhoidtreatmentfix.com/hemorrhoid-relief hemorrhoid relief]
-Continued fractions with more than 20 known terms have been truncated, with an [[ellipsis]] to show that they continue.  Rational numbers have two continued fractions; the version in this list is the shorter one.  Decimal representations are [[rounding|rounded]] or padded to 10 places if the values are known.
-{| class="wikitable sortable"
-|-
-! [[List of letters used in mathematics and science|Symbol]]<ref group="lower-greek">Although some of the symbols in the leftmost column are displayed in black due to math markup peculiarities, all are clickable and link to the respective constant's page.</ref>
-! [[set (mathematics)|Member of]]
-! [[Decimal representation|decimal]]
-! [[Continued fraction]]
-! Notes
-|-
-| [[0 (number)|<math>0</math>]]
-|| [[integer|<math>\mathbb{Z}</math>]]
-|| 0.00000 00000
-|| [0; ]
-||
-|-
-| [[Golden ratio#Golden ratio conjugate|<math>\phi^{-1}</math>]]
-|| [[algebraic number|<math>\mathbb{A}\setminus\mathbb{Q}</math>]]
-|| 0.61803 39887
-|| [0; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …]
-|| irrational
-|-
-| [[Cahen's constant|<math>C</math>]]
-|| [[real number|<math>\mathbb{R}</math>]]
-|| 0.64341 05463
-|| [0; 1, 1, 1, 4, 9, 169, 16641, 639988804, 177227652025317609, 72589906463585427805281295977816196, …]
-|| Continued fraction truncated at 10 terms due to large size.
-|-
-| [[Twin prime#First Hardy–Littlewood conjecture|<math>C_2</math>]]
-|| [[real number|<math>\mathbb{R}</math>]]
-|| 0.66016 18158
-|| [0; 1, 1, 1, 16, 2, 2, 2, 2, 1, 18, 2, 2, 11, 1, 1, 2, 4, 1, 16, 3, …]
-|| Hardy–Littlewood's twin prime constant.  Presumed [[irrational]], but not proved.
-|-
-| [[Euler–Mascheroni constant|<math>\gamma</math>]]
-|| <math>\mathbb{R}</math>
-|| 0.57721 56649
-|| [0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, …]
-|| Presumed irrational, but not proved.
-|-
-| [[Omega constant|<math>\Omega</math>]]
-|| [[transcendental number|<math>\mathbb{R}\setminus\mathbb{A}</math>]]
-|| 0.56714 32904
-|| [0; 1, 1, 3, 4, 2, 10, 4, 1, 1, 1, 1, 2, 7, 306, 1, 5, 1, 2, 1, 5, …]
-||
-|-
-| [[Embree–Trefethen constant|<math>\beta^\star</math>]]
-|| <math>\mathbb{R}</math>
-|| 0.70258
-|| [0; 1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5, …]
-|| Value only known to 5 decimal places.
-|-
-| [[Landau–Ramanujan constant|<math>K</math>]]
-|| <math>\mathbb{R} (\setminus\mathbb{Q}?)</math>
-|| 0.76422 36535
-|| [0; 1, 3, 4, 6, 1, 15, 1, 2, 2, 3, 1, 23, 3, 1, 1, 3, 1, 1, 7, 2, …]
-|| May have been proven irrational.
-|-
-| [[Gauss's constant|<math>\frac 1{M(1,\sqrt 2)}</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{A}</math>
-|| 0.83462 68417
-|| [0; 1, 5, 21, 3, 4, 14, 1, 1, 1, 1, 1, 3, 1, 15, 1, 3, 8, 36, 1, 2, …]
-|| Gauss's constant
-|-
-| [[Brun's theorem#Brun's constant|<math>B_4</math>]]
-|| <math>\mathbb{R}</math>
-|| 0.87058 83800
-|| [0; 1, 6, 1, 2, 1, 2, 956, 8, 1, 1, 1, 23, …]
-|| Brun's prime quadruplet constant.  Estimated value; 99% confidence interval ± 0.00000 00005.
-|-
-| [[Champernowne constant|<math>C_2</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{A}</math>
-|| 0.86224 01259
-|| [0; 1, 6, 3, 1, 6, 5, 3, 3, 1, 6, 4, 1, 3, 298, 1, 6, 1, 1, 3, 285, …]
-|| Base 2 Champernowne constant. The binary expansion is <math>C_2 = 0.1 10 11 100 101 110 111 1000\ldots_2</math>
-|-
-| [[Catalan's constant|<math>G</math>]]
-|| <math>\mathbb{R}</math>
-|| 0.91596 55942
-|| [0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, …]
-|| Presumed irrational, but not proved.
-|-
-| [[One half|<math>\frac 12</math>]]
-|| [[rational number|<math>\mathbb{Q}</math>]]
-|| 0.50000 00000
-|| [0; 2]
-||
-|-
-| [[Bernstein's constant|<math>\beta</math>]]
-|| <math>\mathbb{R}</math>
-|| 0.28016 94990
-|| [0; 3, 1, 1, 3, 9, 6, 3, 1, 3, 13, 1, 16, 3, 3, 4, …]
-|| Presumed irrational, but not proved.
-|-
-| [[Meissel–Mertens constant|<math>M</math>]]
-|| <math>\mathbb{R}</math>
-|| 0.26149 72128
-|| [0; 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, …]
-|| Presumed irrational, but not proved.
-|-
-| [[MRB constant|<math> C_{{}_{MRB}}</math>]]
-|| <math>\mathbb{R}</math>
-|| 0.18785 96424
-|| [0; 5, 3, 10, 1, 1, 4, 1, 1, 1, 1, 9, 1, 1, 12, 2, 17, 2, 2, 1, 1, …]
-||
-|-
-| [[Champernowne constant|<math>C_{10}</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{A}</math>
-|| 0.12345 67891
-|| [0; 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15, <math>4.57540\times 10^{165}</math>, 6, 1, …]
-|| Base 10 Champernowne constant.  Champernowne constants in any base exhibit sporadic large numbers; the 40th term in <math>C_{10}</math> has 2504 digits.
-|-
-| [[1 (number)|<math>1</math>]]
-|| [[natural number|<math>\mathbb{N}</math>]]
-|| 1.00000 00000
-|| [1; ]
-||
-|-
-| [[Golden ratio|<math>\phi</math>]]
-|| <math>\mathbb{A}\setminus\mathbb{Q}</math>
-|| 1.61803 39887
-|| [1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …]
-||
-|-
-| [[Erdős–Borwein constant|<math>E</math>]]
-|| [[irrational number|<math>\mathbb{R}\setminus\mathbb{Q}</math>]]
-|| 1.60669 51524
-|| [1; 1, 1, 1, 1, 5, 2, 1, 2, 29, 4, 1, 2, 2, 2, 2, 6, 1, 7, 1, 6, …]
-|| Not known whether algebraic or transcendental.
-|-
-| [[Brun's theorem#Brun's constant|<math>B_2</math>]]
-|| <math>\mathbb{R}</math>
-|| 1.90216 05823
-|| [1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, …]
-|| Brun's twin prime constant. Estimated value; best bounds <math>1.8304<B_2<2.347</math>.
-|-
-| [[Backhouse's constant|<math>B</math>]]
-|| <math>\mathbb{R}</math>
-|| 1.45607 49485
-|| [1; 2, 5, 5, 4, 1, 1, 18, 1, 1, 1, 1, 1, 2, 13, 3, 1, 2, 4, 16, 4, …]
-||
-|-
-| [[Apéry's constant|<math>\zeta(3)</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{Q}</math>
-|| 1.20205 69032
-|| [1; 4, 1, 18, 1, 1, 1, 4, 1, 9, 9, 2, 1, 1, 1, 2, 7, 1, 1, 7, 11, …]
-||
-|-
-| [[Random Fibonacci sequence|<math>V</math>]]
-|| <math>\mathbb{R}</math>
-|| 1.13198 82488
-|| [1; 7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 17, 1, 1, 2, 1, 2, 4, 1, 2, …]
-|| Viswanath's constant. Apparently, Eric Weisstein calculated this constant to be approximately 1.13215 06911 with Mathematica.
-|-
-| [[Square root of 2|<math>\sqrt 2</math>]]
-|| <math>\mathbb{A}\setminus\mathbb{Q}</math>
-|| 1.41421 35624
-|| [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …]
-||
-|-
-| [[Ramanujan-Soldner constant|<math>\mu</math>]]
-|| <math>\mathbb{R}</math>
-|| 1.45136 92349
-|| [1; 2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2, 4, 1, 12, 1, 1, 2, 2, 1, …]
-|| Presumed irrational, but not proved.
-|-
-| [[Plastic number|<math>\rho</math>]]
-|| <math>\mathbb{A}\setminus\mathbb{Q}</math>
-|| 1.32471 95724
-|| [1; 3, 12, 1, 1, 3, 2, 3, 2, 4, 2, 141, 80, 2, 5, 1, 2, 8, 2, 1, 1, …]
-||
-|-
-| [[2 (number)|<math>2</math>]]
-|| <math>\mathbb N</math>
-|| 2.00000 00000
-|| [2; ]
-||
-|-
-| [[Gelfond–Schneider constant|<math>2^\sqrt 2</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{A}</math>
-|| 2.66514 41426
-|| [2; 1, 1, 1, 72, 3, 4, 1, 3, 2, 1, 1, 1, 14, 1, 2, 1, 1, 3, 1, 3, …]
-||
-|-
-| [[Feigenbaum constants|<math>\alpha</math>]]
-|| <math>\mathbb{R}</math>
-|| 2.50290 78751
-|| [2; 1, 1, 85, 2, 8, 1, 10, 16, 3, 8, 9, 2, 1, 40, 1, 2, 3, 2, 2, 1, …]
-||
-|-
-| [[e (mathematical constant)|<math>e</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{A}</math>
-|| 2.71828 18285
-|| [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, …]
-||
-|-
-| [[Khinchin's constant|<math>K_0</math>]]
-|| <math>\mathbb{R}</math>
-|| 2.68545 20011
-|| [2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, …]
-||
-|-
-| [[Fransén–Robinson constant|<math>F</math>]]
-|| <math>\mathbb{R}</math>
-|| 2.80777 02420
-|| [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, 1, 1, 1, 5, 1, 1, 1, …]
-||
-|-
-| [[Universal parabolic constant|<math>P_2</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{A}</math>
-||  2.29558 71494
-|| [2; 3, 2, 1, 1, 1, 1, 3, 3, 1, 1, 4, 2, 3, 2, 7, 1, 6, 1, 8, 7, …]
-||
-|-
-| [[3 (number)|<math>3</math>]]
-|| <math>\mathbb{N}</math>
-|| 3.00000 00000
-|| [3; ]
-||
-|-
-| [[Pi|<math>\pi</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{A}</math>
-|| 3.14159 26536
-|| [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, …]
-||
-|-
-| [[Reciprocal Fibonacci constant|<math>\psi</math>]]
-|| <math>\mathbb{R}\setminus\mathbb{Q}</math>
-|| 3.35988 56662
-|| [3; 2, 1, 3, 1, 1, 13, 2, 3, 3, 2, 1, 1, 6, 3, 2, 4, 362, 2, 4, 8, …]
-||
-|-
-| [[4 (number)|<math>4</math>]]
-|| <math>\mathbb N</math>
-|| 4.00000 00000
-|| [4; ]
-||
-|-
-| [[Feigenbaum constants|<math>\delta</math>]]
-|| <math>\mathbb R</math>
-|| 4.66920 16091
-|| [4; 1, 2, 43, 2, 163, 2, 3, 1, 1, 2, 5, 1, 2, 3, 80, 2, 5, 2, 1, 1, …]
-||
-|-
-| [[Gelfond's constant|<math>e^\pi</math>]]
-|| <math>\mathbb R\setminus\mathbb A</math>
-|| 23.14069&nbsp;26328
-|| [23; 7, 9, 3, 1, 1, 591, 2, 9, 1, 2, 34, 1, 16, 1, 30, 1, 1, 4, 1, 2, …]
-|| Gelfond's constant.  Can also be expressed as <math>(-1)^{-i}</math>; from this form, it is transcendental due to the [[Gelfond–Schneider theorem]].
-|}
-{{Reflist|group=lower-greek}}
-==See also==
-* [[Physical constant]]
-* [[Mathematical constants and functions]]
-[[Category:Mathematical constants|*]]
-[[Category:Continued fractions]]

Doppler radar: Difference between revisions

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