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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
A mathematical coincidence often involves an integer, and the surprising feature is the fact that a real number arising in some context is considered by some standard as a "close" approximation to a small integer or to a multiple or power of ten, or more generally, to a rational number with a small denominator.
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
I sometimes ask the question: what is the most remarkable coincidence you have experienced, and is it, for the most remarkable one, remarkable? (With a lifetime to choose from, 10 6 : 1 is a mere trifle.) [1] Littlewood uses these remarks to illustrate that seemingly unlikely coincidences can be expected over long periods.
In mathematics, the exponential of pi e π, [1] also called Gelfond's constant, [2] is the real number e raised to the power π. Its decimal expansion is given by: e π = 23.140 692 632 779 269 005 72... (sequence A039661 in the OEIS) Like both e and π, this constant is both irrational and transcendental.
The efficiency of the coincidence counting was of the order of 1 for 10 events. [2] Bothe and Geiger observed 66 coincidences in 5 hours, of which 46 were attributed to false counts, with a statistical fluctuation of 1 in 400,000. [2] The measurements and data treatment took over a year. [1]
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ζ(3) was named Apéry's constant after the French mathematician Roger Apéry, who proved in 1978 that it is an irrational number. [4] This result is known as Apéry's theorem . The original proof is complex and hard to grasp, [ 5 ] and simpler proofs were found later.