A D993: Real number $a \in \mathbb{R}$ is a

**geometric mean**of $x_1, \dots, x_N$ if and only if \begin{equation} \underbrace{a a \cdots a}_{N \text{ times}} = x_1 x_2 \cdots x_N \end{equation}

Definition D2455

Real geometric mean

Formulation 0

Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.

A D993: Real number $a \in \mathbb{R}$ is a**geometric mean** of $x_1, \dots, x_N$ if and only if
\begin{equation}
\underbrace{a a \cdots a}_{N \text{ times}} = x_1 x_2 \cdots x_N
\end{equation}

A D993: Real number $a \in \mathbb{R}$ is a

Formulation 1

Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.

A D993: Real number $a \in \mathbb{R}$ is a**geometric mean** of $x_1, \dots, x_N$ if and only if
\begin{equation}
\prod_{n = 1}^N a = \prod_{n = 1}^N x_n
\end{equation}

A D993: Real number $a \in \mathbb{R}$ is a

Results