# Symbols:Greek/Rho

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## Rho

The $17$th letter of the Greek alphabet.

Minuscules: $\rho$ and $\varrho$
Majuscule: $\Rho$

The $\LaTeX$ code for $\rho$ is \rho .
The $\LaTeX$ code for $\varrho$ is \varrho .

The $\LaTeX$ code for $\Rho$ is \Rho .

## Density

$\rho$

Used to denote the density of a given body:

$\rho = \dfrac m V$

where:

$m$ is the body's mass
$V$ is the body's volume

## Area Density

$\rho_A$

Used to denote the area density of a given two-dimensional body:

$\rho_A = \dfrac m A$

where:

$m$ is the body's mass
$A$ is the body's area.

The $\LaTeX$ code for $\rho_A$ is \rho_A .

## Right Regular Representation

$\rho_a$

Let $\struct {S, \circ}$ be an algebraic structure.

The mapping $\rho_a: S \to S$ is defined as:

$\forall x \in S: \map {\rho_a} x = x \circ a$

This is known as the right regular representation of $\struct {S, \circ}$ with respect to $a$.

The $\LaTeX$ code for $\map {\rho_a} x$ is \map {\rho_a} x .

$\rho$
The radius of curvature of a curve $C$ at a point $P$ is defined as the reciprocal of the absolute value of its curvature:
$\rho = \dfrac 1 {\left\lvert{k}\right\rvert}$