# Irrational numbers

$\large \mathbb{I}\Gamma \Gamma \AA \Upsilon \mathbb{I}\varnothing \mathbb{N}\alpha \L \ \mathbb{N}\mho\xi \beta \Sigma \Re \S$
Irrational numbers are real numbers that cannot be expressed as $\large \frac{a}{b}$
For example: $\large \frac{1}{9}=0.\overset{.}{1}$
But:$\large \pi\approx 3.141592387 = \frac{52163}{16604}$
there is no way of defining pi as a recurring decimal or as a
$\large \frac{a}{b}$ fraction

### A list of irrational numbers:

#### Pi

Symbol: π
Other names:Archimedes' Constant
Description : A circle's ratio of - circumference (c) : diameter.
One interesting fact: Pi day is celebrated on March 14th after 3.14

#### Euler–Mascheroni constant

Symbol: γ
Other names: The Euler Constant
Description: It is defined as the limiting difference between the harmonic series and the natural logarithm:
$\gamma =\underset{n \to \infty }{lim}(\sum_{k=1}^{n}\frac{1}{k}-\ln (n))=\int_{1 }^{\infty } (\frac{1}{\left \lfloor x \right \rfloor}-\frac{1}{x})dx$

#### The Golden ratio

Symbol: ø
Other names:golden section, golden mean, extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number, mean of Phidias.
Description: two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.
Algebraically expressed as:
$\frac{1 + \sqrt{5}}{2}$

#### Apéry's constant

Symbol: ζ(3)
Other names: (none)
Description:a number that occurs in a variety of situations- the second- and third-order terms of the electron's gyromagnetic ratio using quantum electrodynamics and when evaluating the two-dimensional case of the Debye model
$\large \zeta (3)=\sum_{k=1}^{\infty }\frac{1}{k^{3}}=1+\frac{1}{2^{3}}+\frac{1}{3^{3}}+\frac{1}{4^{3}}+\cdots$

#### Square root of 2

Symbol:√2
Other names: Pythagoras' Constant.
Description: the positive algebraic number that, when multiplied by itself, gives the number 2

#### Plastic Number

Symbol: ρ
Other names: (Silver number)
Description: the unique real solution of the cubic equation-
 x^3=x+1, .

It has the value:

[[image:http://latex.codecogs.com/gif.latex?%5Clarge%20%5Crho%20=%5Csqrt[3]%7B%5Cfrac%7B1%7D%7B2%7D+%5Cfrac%7B1%7D%7B6%7D%5Csqrt%7B%5Cfrac%7B23%7D%7B3%7D%7D%7D+%20%5Csqrt[3]%7B%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7B1%7D%7B6%7D%5Csqrt%7B%5Cfrac%7B23%7D%7B3%7D%7D%7D;]]

By Muhammed Ubaid Khan and Ashley Hung