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A Resource List of Mathematical Constants

The world of mathematics can be very confusing because it’s difficult to truly understand some concepts. The term mathematical constant refers to a number that arises naturally in math equations. They can arise in different contexts but they are always definable numbers. These mathematical constants are important because they are real numbers and they are always the same, so placing them within the context of a problem means you can solve it.

  • Zero, 0: Zero is a number that also doubles as the numerical digit that represents a number in numerals. It’s used as an additive in algebraic structures.
  • One, 1: 1 is a number as well and is the first non-0 natural number and the first odd number. It also represents a unit of counting.
  • Imaginary unit: An imaginary unit is used to allow the real number system to extend to numbers that cannot be truly “imagined” because they are either so large or so small.
  • Pythagoras’ constant: Pythagoras’ constant is a positive real number that, if multiplied by itself, gives the number 2.
  • Golden mean: The golden mean is a ratio that applies when you compare two quantities and the sum of the quantities of the larger number is equal to the ratio of the larger quantity to the smaller one.
  • Natural logarithmic base: The natural logarithm is the logarithm to the base e where e represents an irrational constant that is approximately equal to 2.718281828.
  • Archimedes’ constant: Archimedes’ constant establishes a way to actually calculate the value if pi instead of just estimating it, which is between 3+10/71 and 3+1/7.
  • Euler-Mascheroni constant: This constant is used in analysis and number theories. It limits the difference between the harmonic series and natural logarithm.
  • Rydberg constant: The Rydberg constant is a formula for figuring out the atomic spectra and relation between the binding energy of a nucleon and an electron.
  • Catalan’s constant: This constant appears when estimating combinatorics. It contains 33 series.
  • Khintchine’s constant: This is a term used to refer to the geometric mean of most real numbers.
  • Feigenbaum constants: These are two mathematical constants that express ratios in a bifurcation diagram, limiting the ratio of each bifurcation interval to the next.
  • Madelung’s constant: This constant is used when determining the electrostatic potential of an ion in a crystal. It’s done by approximating the ions by their point charges.
  • Chaitin’s constant: Used in computer science, it is a real number informally representing the probability that a certain comp uter program will halt.
  • Stolarsky-Harborth constant: Relates to the theory where the number of odd elements in the first rows of Pascal’s triangle and certain equations can be figured out when the number is plugged in.
  • Porter’s constant: This is a constant that usually appears in formulas that are related to the efficiency of the Euclidean algorithm.
  • Glaisher-Kinkelin constant: Denotes that the A in a certain equation that relates to the Barnes G-function and the K-function.
  • Fransen-Robinson constant: This constant says that, for increasing x, the reciprocal gamma function decreases more rapidly than for any c where the value is always the same.
  • Abelian Group Enumeration constants: Refers to a group of constants that deal with finite abelian groups where prime numbers are present.
  • Pythagorean triple constants: The practice of using two numbers, s and t, to generate Pythagorean triples which are always prime numbers and some that are multiple of primitive ones.
  • Renyi’s parking constants: A theory that states that every vertex of a tree particle arrives at rate one and that it sticks to the vertex.
  • Golomb-Dickman constant: This constant is found in the theory of random permutations and number theory.
  • Gauss’ lemniscate constant: Represented by G, it’s the reciprocal of the square root of 2 and the arithmetic-geometric mean of 1.
  • Grossman’s constant: Refers to the proven theory that a certain recurrence defines a specific convergent sequence for only one value of x.
  • Plouffe’s constant: Refers to numbers that arise from a series related to a specific trigonometric function.
  • Lehmer’s constant: Mathematical question that asks if there exists a constant C>1 where every polynomial f with integer coefficients and M(f) > 1 has M(f) > C.
  • Geometric probability constants: A series of mathematical theories that relate to subjects like Electromagnetism.
  • Circular coverage constants: Used when dealing with unit disks that help find the smallest radius required for equal disks to cover that disk.
  • Universal coverage constants: Refers to a table of constants including the speed of light in vacuum and Planck constant.
  • Hermite’s constants: A constant for integers, the square root of which is a matter of historical convention.
  • Calabi’s triangle constant: It’s used to define unique non-equilateral t riangles with three equally large inscribed squares.
  • DeVicci’s tesseract constant: Deals with higher dimensional generalizations of Prince Rupert’s cube.