MRB constant
Encyclopedia
The MRB constant, named after Marvin Ray Burns, is a mathematical constant
for which no closed-form expression
is known. It is not known whether the MRB constant is algebraic
, transcendental
, or even irrational
.
The numerical value of MRB constant, truncated to 6 decimal places
, is
:
Its partial sums
are bounded so that their limit point
s form an interval
[−0.812140…,0.187859…] of length 1. The upper limit point 0.187859… is what is known as the MRB constant.
The MRB constant can be explicitly defined by the following infinite sums:
There is no known closed-form expression
of the MRB constant.
that such a constant had not already been discovered or at least not widely published, Burns called the constant "rc" for root constant. At Plouffe's suggestion, the constant was renamed Marvin Ray Burns's Constant, and then shortened to "MRB constant" in 1999.
Mathematical constant
A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory and calculus.What it means for a...
for which no closed-form expression
Closed-form expression
In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a bounded number of certain "well-known" functions...
is known. It is not known whether the MRB constant is algebraic
Algebraic number
In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Numbers such as π that are not algebraic are said to be transcendental; almost all real numbers are transcendental...
, transcendental
Transcendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...
, or even irrational
Irrational number
In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number....
.
The numerical value of MRB constant, truncated to 6 decimal places
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
, is
- .
Definition
The MRB constant is related to the following divergent seriesDivergent series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a limit....
:
Its partial sums
are bounded so that their limit point
Limit point
In mathematics, a limit point of a set S in a topological space X is a point x in X that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself. Note that x does not have to be an element of S...
s form an interval
Interval (mathematics)
In mathematics, a interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers satisfying is an interval which contains and , as well as all numbers between them...
[−0.812140…,0.187859…] of length 1. The upper limit point 0.187859… is what is known as the MRB constant.
The MRB constant can be explicitly defined by the following infinite sums:
There is no known closed-form expression
Closed-form expression
In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a bounded number of certain "well-known" functions...
of the MRB constant.
History
Marvin Ray Burns published his discovery of the constant in 1999. The discovery is a result of a "math binge" that started in the spring of 1994. Before verifying with colleague Simon PlouffeSimon Plouffe
Simon Plouffe is a Quebec mathematician born on June 11, 1956 in Saint-Jovite, Quebec. He discovered the formula for the BBP algorithm which permits the computation of the nth binary digit of π, in 1995...
that such a constant had not already been discovered or at least not widely published, Burns called the constant "rc" for root constant. At Plouffe's suggestion, the constant was renamed Marvin Ray Burns's Constant, and then shortened to "MRB constant" in 1999.