# Category: Irrational numbers

Hippasus
Hippasus of Metapontum (/ˈhɪpəsəs/; Greek: Ἵππασος ὁ Μεταποντῖνος, Híppasos; c. 530 – c. 450 BC) was a Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs
Prime constant
The prime constant is the real number whose th binary digit is 1 if is prime and 0 if is composite or 1. In other words, is the number whose binary expansion corresponds to the indicator function of t
Copeland–Erdős constant
The Copeland–Erdős constant is the concatenation of "0." with the base 10 representations of the prime numbers in order. Its value, using the modern definition of prime, is approximately 0.23571113171
Exact trigonometric values
In mathematics, the values of the trigonometric functions can be expressed approximately, as in , or exactly, as in . While trigonometric tables contain many approximate values, the exact values for c
Particular values of the Riemann zeta function
In mathematics, the Riemann zeta function is a function in complex analysis, which is also important in number theory. It is often denoted ζ(s) and is named after the mathematician Bernhard Riemann. W
Proof that π is irrational
In the 1760s, Johann Heinrich Lambert was the first to prove that the number π is irrational, meaning it cannot be expressed as a fraction , where and are both integers. In the 19th century, Charles H
Schizophrenic number
A schizophrenic number (also known as mock rational number) is an irrational number that displays certain characteristics of rational numbers.
Twelfth root of two
The twelfth root of two or (or equivalently ) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio
Irrational number
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers
Proof that e is irrational
The number e was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that e is irrational; that is, that it c
Apéry's constant
In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number where ζ is the Riemann zeta function. It has an approximate value of ζ(3) = 1
Irrationality sequence
In mathematics, a sequence of positive integers an is called an irrationality sequence if it has the property that for every sequence xn of positive integers, the sum of the series exists (that is, it
Irrational rotation
In the mathematical theory of dynamical systems, an irrational rotation is a map where θ is an irrational number. Under the identification of a circle with R/Z, or with the interval [0, 1] with the bo
Liouville number
In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers (p, q) with q > 1 such that . Liouville numbers are "almos
Reciprocal Fibonacci constant
The reciprocal Fibonacci constant, or ψ, is defined as the sum of the reciprocals of the Fibonacci numbers: The ratio of successive terms in this sum tends to the reciprocal of the golden ratio. Since
Erdős–Borwein constant
The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers. It is named after Paul Erdős and Peter Borwein. By definition it is: