Irrational numbers

real number that cannot be expressed as a ratio of integers

national flag of the Federal Democratic Republic of Nepal

right|thumb|Hippasus, engraving by Girolamo Olgiati, 1580 Hippasus of Metapontum (; , Híppasos; c. 530 – c. 450 BC) was a Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this and crediting it to himself instead of Pythagoras, which was the norm in Pythagorean society. T

value of the Riemann zeta function when given the input 3

real number whose infinite sequence of digits in every positive integer base is distributed uniformly

transcendental number possessing an excellent sequence of rational number approximations

mathematical proof

sum of the reciprocal of the Mersenne numbers

integer sequence

number whose decimal representation is the concatenation of "0." with the base 10 representations of the prime numbers in order

mathematical proof that Euler's number (e) is irrational

real number, approximately 3.36, the sum of the reciprocals of the Fibonacci numbers

algebraic irrational number

numerical constants

irrational number produced by taking the sine or cosine of a rational multiple of a full circle

real number whose nth binary digit is 1 if n is prime and 0 if n is composite or 1

Irrational numbers which appear to be rational