En çok kullanılan matematiksel sabitler pi sayısı ($\pi$), e sayısı (doğal logaritma tabanı) ve i sayısıdır.
pi sayısı bir çemberin çevresinin çapına oranı ya da bir dairenin alanının yarıçap karesine oranı olarak ifade edilir.
e sayısı, Leonard Euler'in isminden gelir ve kabaca tanımı $f(x) = 1 / x$ fonksiyonunun eğrisi altında bir birim karelik alan sınırlanabilmesi için $x=1$ doğrusunun sağında seçilecek doğrunun $x$ eksenini kestiği noktadır. Yani doğru $x = e$ olarak seçilirse altta kalan şekil bir birim kare olacaktır. Bu eşitlik integral ile :
$\int_{1}^{e} \frac 1 x dx = 1$ şeklinde ifade edilir.
e sayısının başka bir tanımıysa bir dizi limiti tarafından verilir (integral Riemann toplamına açıldığında aslında iki tanımın özdeş olduğu ortaya çıkar.)
$\lim_{x \to \infty} \left( 1 + \frac 1 x \right) ^x$
Pi ve e sayıları reel sayılardır.
i sayısı ise karmaşık sayıların tanımlanmasında kullanılan bir sabittir ve $\sqrt{-1}$ olarak tanımlıdır.
Bunlar temel sabitler olup, bunların haricinde pek çok sabit bulunmaktadır.
Kullanılan kısaltmalar:
I - irraasyonel sayı, A - Cebirsel sayı, T - transendental sayı, ? - bilinmeyen
Gen - General, NuT - Sayılar Teorisi, ChT - Kaos Teorisi, Com - Kombinatorik, Inf - Bilgi Teorisi, Ana - Matematiksel analiz
<table> <thead> <tr class="header"> <th><p>Sembol</p></th> <th><p>Yaklaşık Değer</p></th> <th><p>İsim</p></th> <th><p>Alan</p></th> <th><p>N</p></th> <th><p>Keşif Yılı</p></th> <th><p>Bilinen basamaklarının sayısı</p></th> </tr> </thead> <tbody> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>π</p> </div></td> <td><p>≈ 3.14159 26535 89793 23846 26433 83279 50288</p></td> <td><p><a href="Pi_sayısı" title="wikilink">Pi</a>, <a href="Archimedes" title="wikilink">Archimedes</a>' sabiti veya <a href="Ludolph" title="wikilink">Ludolph</a> sayısı</p></td> <td><p><strong><a href="Matematik" title="wikilink">Gen</a></strong>, <strong><a href="Matematiksel_analiz" title="wikilink">Ana</a></strong></p></td> <td style="text-align: center;"><p><em><a href="transcendental_number" title="wikilink">T</a></em></p></td> <td style="text-align: right;"><p>by c. <a href="2000_BC" title="wikilink">2000 BC</a></p></td> <td style="text-align: right;"><p>1,241,100,000,000</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p><em>e</em></p> </div></td> <td><p>≈ 2.71828 18284 59045 23536 02874 71352 66249</p></td> <td><p><a href="e_(mathematical_sabiti)" title="wikilink">Napier's sabiti</a>, <a href="Logaritma" title="wikilink">Doğal Logaritman</a>ın tabanı)</p></td> <td><p><strong><a href="Matematk" title="wikilink">Gen</a></strong>, <strong><a href="Matematiksel_analiz" title="wikilink">Ana</a></strong></p></td> <td style="text-align: center;"><p><em><a href="transcendental_number" title="wikilink">T</a></em></p></td> <td style="text-align: right;"><p>1618</p></td> <td style="text-align: right;"><p>50,100,000,000</p></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>√2</p> </div></td> <td><p>≈ 1.41421 35623 73095 04880 16887 24209 69807</p></td> <td><p><a href="Pisagor" title="wikilink">Pisagor</a> sabiti,</p></td> <td><p><strong><a href="Matematik" title="wikilink">Gen</a></strong></p></td> <td style="text-align: center;"><p><em><a href="irrational_number" title="wikilink">I</a> <a href="algebraic_number" title="wikilink">A</a></em></p></td> <td style="text-align: right;"><p>by c. <a href="800_BC" title="wikilink">800 BC</a></p></td> <td style="text-align: right;"><p>137,438,953,444</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>√3</p> </div></td> <td><p>≈ 1.73205 08075 68877 29352 74463 41505</p></td> <td><p><a href="Theodorus_of_Cyrene" title="wikilink">Theodorus</a>' sabiti,</p></td> <td><p><strong><a href="Matematik" title="wikilink">Gen</a></strong></p></td> <td style="text-align: center;"><p><em><a href="irrational_number" title="wikilink">I</a> <a href="algebraic_number" title="wikilink">A</a></em></p></td> <td style="text-align: right;"><p>by c. <a href="800_BC" title="wikilink">800 BC</a></p></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>γ</p> </div></td> <td><p>≈ 0.57721 56649 01532 86060 65120 90082 40243</p></td> <td><p><a href="Euler-Mascheroni_sabiti" title="wikilink">Euler-Mascheroni sabiti</a></p></td> <td><p><strong><a href="Matematik" title="wikilink">Gen</a></strong>, <strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1735</p></td> <td style="text-align: right;"><p>108,000,000</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>φ</p> </div></td> <td><p>≈ 1.61803 39887 49894 84820 45868 34365 63811</p></td> <td><p><a href="Golden_mean" title="wikilink">Golden mean</a></p></td> <td><p><strong><a href="Matematik" title="wikilink">Gen</a></strong></p></td> <td style="text-align: center;"><p><em><a href="algebraic_number" title="wikilink">A</a></em></p></td> <td style="text-align: right;"><p>by <a href="3rd_century_BC" title="wikilink">3rd century BC</a></p></td> <td style="text-align: right;"><p>3,141,000,000</p></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>β<sup>*</sup></p> </div></td> <td><p>≈ 0.70258</p></td> <td><p><a href="Embree-Trefethen_sabiti" title="wikilink">Embree-Trefethen sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>δ</p> </div></td> <td><p>≈ 4.66920 16091 02990 67185 32038 20466 20161</p></td> <td><p><a href="Feigenbaum_sabiti" title="wikilink">Feigenbaum sabiti</a></p></td> <td><p><strong><a href="chaos_theory" title="wikilink">ChT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1975</p></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>α</p> </div></td> <td><p>≈ 2.50290 78750 95892 82228 39028 73218 21578</p></td> <td><p><a href="Feigenbaum_sabiti" title="wikilink">Feigenbaum sabiti</a></p></td> <td><p><strong><a href="chaos_theory" title="wikilink">ChT</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>C<sub>2</sub></p> </div></td> <td><p>≈ 0.66016 18158 46869 57392 78121 10014 55577</p></td> <td><p><a href="Twin_prime_conjecture" title="wikilink">Twin prime sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td style="text-align: right;"><p>5,020</p></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>M<sub>1</sub></p> </div></td> <td><p>≈ 0.26149 72128 47642 78375 54268 38608 69585</p></td> <td><p><a href="Meissel-Mertens_sabiti" title="wikilink">Meissel-Mertens sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1866 1874</p></td> <td style="text-align: right;"><p>8,010</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>B<sub>2</sub></p> </div></td> <td><p>≈ 1.90216 05823</p></td> <td><p><a href="Brun's_sabiti" title="wikilink">Brun's sabiti</a> for twin prime</p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1919</p></td> <td style="text-align: right;"><p>10</p></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>B<sub>4</sub></p> </div></td> <td><p>≈ 0.87058 83800</p></td> <td><p><a href="Brun's_sabiti" title="wikilink">Brun's sabiti</a> for prime quadruplets</p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>Λ</p> </div></td> <td><p>> – 2.7 · 10<sup>−9</sup></p></td> <td><p><a href="de_Bruijn-Newman_sabiti" title="wikilink">de Bruijn-Newman sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1950?</p></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>K</p> </div></td> <td><p>≈ 0.91596 55941 77219 01505 46035 14932 38411</p> </td></td> <td><p><a href="Catalan's_sabiti" title="wikilink">Catalan's sabiti</a></p></td> <td><p><strong><a href="combinatorics" title="wikilink">Com</a></strong></p></td> <td></td> <td></td> <td style="text-align: right;"><p>201,000,000</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>K</p> </div></td> <td><p>≈ 0.76422 36535 89220 66</p></td> <td><p><a href="Landau-Ramanujan_sabiti" title="wikilink">Landau-Ramanujan sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td style="text-align: center;"><p><em><a href="irrational_number" title="wikilink">I</a></em> (<em>?</em>)</p></td> <td></td> <td style="text-align: right;"><p>30,010</p></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>K</p> </div></td> <td><p>≈ 1.13198 824</p></td> <td><p><a href="Viswanath's_sabiti" title="wikilink">Viswanath's sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td style="text-align: right;"><p>8</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>B´<sub>L</sub></p> </div></td> <td><p>≈ 1.08366</p></td> <td><p><a href="Legendre's_sabiti" title="wikilink">Legendre's sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>μ</p> </div></td> <td><p>≈ 1.45136 92348 83381 05028 39684 85892 027</p></td> <td><p><a href="Ramanujan-Soldner_sabiti" title="wikilink">Ramanujan-Soldner sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td style="text-align: right;"><p>75,500</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>E<sub>B</sub></p> </div></td> <td><p>≈ 1.60669 51524 15291 763</p></td> <td><p><a href="Erdős–Borwein_sabiti" title="wikilink">Erdős–Borwein sabiti</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td style="text-align: center;"><p><em><a href="irrational_number" title="wikilink">I</a></em></p></td> <td></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>Ω</p> </div></td> <td><p>depends on <a href="Turing_machine" title="wikilink">computation model</a></p></td> <td><p><a href="Chaitin's_sabiti" title="wikilink">Chaitin's sabiti</a></p></td> <td><p><strong><a href="Algorithmic_information_theory" title="wikilink">Inf</a></strong></p></td> <td style="text-align: center;"><p><em><a href="transcendental_number" title="wikilink">T</a></em></p></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>β</p> </div></td> <td><p>≈ 0.28016 94990</p></td> <td><p><a href="Bernstein's_sabiti" title="wikilink">Bernstein's sabiti</a><a href="http://mathworld.wolfram.com/BernsteinsConstant.html"> </a> </p></td> <td><p><strong><a href="Mathematical_analysis" title="wikilink">Ana</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>λ</p> </div></td> <td><p>≈ 0.30366 30029</p></td> <td><p><a href="Gauss-Kuzmin-Wirsing_sabiti" title="wikilink">Gauss-Kuzmin-Wirsing sabiti</a><a href="http://mathworld.wolfram.com/Gauss-Kuzmin-WirsingConstant.html"> </a> </p></td> <td><p><strong><a href="combinatorics" title="wikilink">Com</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1974</p></td> <td style="text-align: right;"><p>385</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p><em>D</em>(1)</p> </div></td> <td><p>≈ 0.35323 63719</p></td> <td><p><a href="Hafner-Sarnak-McCurley_sabiti" title="wikilink">Hafner-Sarnak-McCurley sabiti</a><a href="http://mathworld.wolfram.com/Hafner-Sarnak-McCurleyConstant.html"> </a> </p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1993</p></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>λ, μ</p> </div></td> <td><p>≈ 0.62432 99885</p></td> <td><p><a href="Golomb-Dickman_sabiti" title="wikilink">Golomb-Dickman sabiti</a><a href="http://mathworld.wolfram.com/Golomb-DickmanConstant.html"> </a> </p></td> <td><p><strong><a href="combinatorics" title="wikilink">Com</a> <a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1930 1964</p></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 0.62946 50204</p></td> <td><p><a href="Cahen's_sabiti" title="wikilink">Cahen's sabiti</a><a href="http://mathworld.wolfram.com/CahensConstant.html">1</a></p></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 0.66274 34193</p></td> <td><p><a href="Laplace_limit" title="wikilink">Laplace limit</a><a href="http://mathworld.wolfram.com/LaplaceLimit.html"> </a> </p></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 0.80939 40205</p></td> <td><p><a href="Alladi-Grinstead_sabiti" title="wikilink">Alladi-Grinstead sabiti</a><a href="http://mathworld.wolfram.com/Alladi-GrinsteadConstant.html"> </a> </p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>Λ</p> </div></td> <td><p>≈ 1.09868 58055</p></td> <td><p><a href="Lengyel's_sabiti" title="wikilink">Lengyel's sabiti</a><a href="http://mathworld.wolfram.com/LengyelsConstant.html"> </a> </p></td> <td><p><strong><a href="combinatorics" title="wikilink">Com</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1992</p></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 1.18656 91104</p></td> <td><p><a href="Khinchin-Lévy_sabiti" title="wikilink">Khinchin-Lévy sabiti</a><a href="http://mathworld.wolfram.com/Khinchin-LevyConstant.html"> </a> </p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 1.20205 69031 59594 28539 97381</p></td> <td><p><a href="Apéry's_sabiti" title="wikilink">Apéry's sabiti</a><a href="http://mathworld.wolfram.com/AperysConstant.html"> </a> </p></td> <td></td> <td></td> <td style="text-align: right;"><p>1979</p></td> <td style="text-align: right;"><p>1,000,000,000</p></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p>θ</p> </div></td> <td><p>≈ 1.30637 78838 63080 69046</p></td> <td><p><a href="Mills'_sabiti" title="wikilink">Mills' sabiti</a><a href="http://mathworld.wolfram.com/MillsConstant.html"> </a> </p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td><p>?</p></td> <td style="text-align: right;"><p>1947</p></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 1.45607 49485 82689 67139 95953 51116 54356</p></td> <td><p><a href="Backhouse's_sabiti" title="wikilink">Backhouse's sabiti</a><a href="http://mathworld.wolfram.com/BackhousesConstant.html"> </a> </p></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 1.46707 80794</p></td> <td><p><a href="Porter's_sabiti" title="wikilink">Porter's sabiti</a><a href="http://mathworld.wolfram.com/PortersConstant.html">2</a> </p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1975</p></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 1.53960 07178</p></td> <td><p><a href="Lieb's_square_ice_sabiti" title="wikilink">Lieb's square ice sabiti</a><a href="http://www.mathsoft.com/mathresources/sabitis/discretestructures/article/0,,2265,00.html"> </a> </p></td> <td><p><strong><a href="combinatorics" title="wikilink">Com</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1967</p></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 1.70521 11401 05367</p></td> <td><p><a href="Niven's_sabiti" title="wikilink">Niven's sabiti</a><a href="http://mathworld.wolfram.com/NivensConstant.html">3</a> </p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td></td> <td style="text-align: right;"><p>1969</p></td> <td></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 2.58498 17596</p></td> <td><p><a href="Sierpiński's_sabiti" title="wikilink">Sierpiński's sabiti</a><a href="http://mathworld.wolfram.com/SierpinskiConstant.html">4</a> </p></td> <td></td> <td></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"></td> <td><p>≈ 2.68545 2001</p></td> <td><p><a href="Khinchin's_sabiti" title="wikilink">Khinchin's sabiti</a><a href="http://mathworld.wolfram.com/KhinchinsConstant.html">5</a></p></td> <td><p><strong><a href="Number_theory" title="wikilink">NuT</a></strong></p></td> <td><p>?</p></td> <td style="text-align: right;"><p>1934</p></td> <td style="text-align: right;"><p>7350</p></td> </tr> <tr class="odd"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p><em>F</em></p> </div></td> <td><p>≈ 2.80777 02420</p></td> <td><p><a href="Fransén-Robinson_sabiti" title="wikilink">Fransén-Robinson sabiti</a><a href="http://mathworld.wolfram.com/Fransen-RobinsonConstant.html">6</a> </p></td> <td><p><strong><a href="Mathematical_analysis" title="wikilink">Ana</a></strong></p></td> <td></td> <td></td> <td></td> </tr> <tr class="even"> <td style="text-align: center;" data-bgcolor="#d0f0d0"><div style="font-size:200%;"> <p><em>L</em></p> </div></td> <td><p>≈ .5</p></td> <td><p><a href="Landau's_sabiti" title="wikilink">Landau's sabiti</a></p></td> <td><p><strong><a href="Mathematical_analysis" title="wikilink">Ana</a></strong></p></td> <td></td> <td></td> <td style="text-align: right;"><p>1</p></td> </tr> </tbody> </table>Orijinal kaynak: matematiksel sabit. 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