Definition:Binomial (Euclidean)/Second Binomial

Definition
Let $a$ and $b$ be two positive real numbers such that $a + b$ is a binomial.

Then $a + b$ is a second binomial iff:
 * $(1): \quad b \in \Q$
 * $(2): \quad \dfrac {\sqrt {a^2 - b^2}} a \in \Q$

where $\Q$ denotes the set of rational numbers.



Example
Let $a = 2 \sqrt 3$ and $b = 3$.

Then:

Therefore $2 \sqrt 3 + 3$ is a second binomial.

Also see

 * Definition:First Binomial
 * Definition:Third Binomial
 * Definition:Fourth Binomial
 * Definition:Fifth Binomial
 * Definition:Sixth Binomial