From 99bec8ecbb9dbebc9cfa6c7c1893cd70c9630485 Mon Sep 17 00:00:00 2001 From: Mateusz Pusz Date: Wed, 30 Aug 2023 18:56:20 +0200 Subject: [PATCH] docs: math expressions usage improved in the "Glossary" chapter --- docs/appendix/glossary.md | 36 +++++++++++++++++++----------------- 1 file changed, 19 insertions(+), 17 deletions(-) diff --git a/docs/appendix/glossary.md b/docs/appendix/glossary.md index 62fe8a81..fa27c4d0 100644 --- a/docs/appendix/glossary.md +++ b/docs/appendix/glossary.md @@ -106,7 +106,7 @@ representation of the [dimension](#dimension) for such [quantities](#quantity). The term “quantity of dimension one” reflects the convention in which the symbolic representation of the [dimension](#dimension) for such [quantities](#quantity) is - the symbol `1`. + the symbol $1$. - The [measurement units](#unit) and [values](#quantity-value) of quantities of dimension one are numbers, but such quantities convey more information than a number. - Some quantities of dimension one are defined as the ratios of two @@ -121,15 +121,16 @@ - Measurement units are designated by conventionally assigned names and symbols. - Measurement units of [quantities](#quantity) of the same [quantity dimension](#dimension) may be designated by the same name and symbol even when the [quantities](#quantity) are - not of the same `kind`. + not of the same [kind](#kind). - For example, joule per kelvin and J/K are respectively the name and symbol of both a measurement unit of heat capacity and a measurement unit of entropy, which are generally not considered to be [quantities of the same kind](#kind). However, in some cases special measurement unit names are restricted to be used with [quantities](#quantity) of specific [kind](#kind) only. For example, the measurement unit ‘second to the power minus one’ - (1/s) is called hertz (Hz) when used for frequencies and becquerel (Bq) when used for - activities of radionuclides. As another example, the joule (J) is used as a unit of - energy, but never as a unit of moment of force, i.e. the newton metre (N·m). + ($\mathsf{1/s}$) is called hertz ($\mathsf{Hz}$) when used for frequencies and + becquerel ($\mathsf{Bq}$) when used for activities of radionuclides. As another example, + the joule ($\mathsf{J}$) is used as a unit of energy, but never as a unit of moment of + force, i.e. the newton metre ($\mathsf{N·m}$). - Measurement units of [quantities of dimension one](#dimensionless-quantity) are numbers. In some cases, these measurement units are given special names, e.g. radian, steradian, and decibel, or are expressed by quotients such as millimole per mole equal @@ -144,7 +145,7 @@ the centimetre is the base unit of length. - A base unit may also serve for a [derived quantity](#derived-quantity) of the same [quantity dimension](#dimension). - - For number of entities, the number one, symbol `1`, can be regarded as a base unit in + - For number of entities, the number one, symbol $1$, can be regarded as a base unit in any system of units. [`derived unit`](#derived-unit){ #derived-unit } @@ -176,7 +177,7 @@ - For example, the centimetre per second is the coherent derived unit of speed in a CGS system of units but is not a coherent derived unit in the [SI](#si). - The coherent derived unit for every [derived quantity of dimension one](#dimensionless-quantity) - in a given [system of units](#system-of-units) is the number one, symbol `1`. The name and + in a given [system of units](#system-of-units) is the number one, symbol $1$. The name and symbol of the [measurement unit](#unit) one are generally not indicated. [`system of units`](#system-of-units){ #system-of-units } @@ -199,7 +200,7 @@ [`off-system measurement unit, off-system unit`](#off-system-unit){ #off-system-unit } : - [Measurement unit](#unit) that does not belong to a given [system of units](#system-of-units). - - For example, the electronvolt (about $1.602\;18 × 10^{–19} \mathsf{J}$) is an + - For example, the electronvolt (about $1.602\;18 × 10^{–19}\;\mathsf{J}$) is an off-system measurement unit of energy with respect to the [SI](#si). Day, hour, minute are off-system measurement units of time with respect to the [SI](#si). @@ -213,7 +214,7 @@ [`quantity value, value of a quantity, value`](#quantity-value){ #quantity-value } : - Number and reference together expressing magnitude of a [quantity](#quantity). - - For example, length of a given rod: `5.34 m` or `534 cm`. + - For example, length of a given rod: $5.34\;\mathsf{m}$ or $534\;\mathsf{cm}$. - The number can be complex. - A quantity value can be presented in more than one way. - In the case of vector or tensor quantities, each component has a quantity value. @@ -224,10 +225,10 @@ : - Number in the expression of a [quantity value](#quantity-value), other than any number serving as the reference - - For example, in an amount-of-substance fraction equal to `3 mmol/mol`, the numerical - quantity value is `3` and the [unit](#unit) is `mmol/mol`. The [unit](#unit) `mmol/mol` - is numerically equal to `0.001`, but this number `0.001` is not part of the numerical - quantity value, which remains `3`. + - For example, in an amount-of-substance fraction equal to $3\;\mathsf{mmol/mol}$, the numerical + quantity value is $3$ and the [unit](#unit) is $\mathsf{mmol/mol}$. The [unit](#unit) + $\mathsf{mmol/mol}$ is numerically equal to $0.001$, but this number $0.001$ is not part + of the numerical quantity value, which remains $3$. [`quantity equation`](#quantity-equation){ #quantity-equation } @@ -250,8 +251,9 @@ : - Mathematical relation between numerical [quantity values](#quantity-value), based on a given [quantity equation](#quantity-equation) and specified [measurement units](#unit). - For example, in the [quantity equation](#quantity-equation) for kinetic energy of a particle, - $T = (1/2) mv^2$, if $m = 2 kg$ and $v = 3 m/s$, then ${T} = (1/2) × 2 × 3^2$ is a numerical - value equation giving the numerical value $9$ of $T$ in joules. + $T = (1/2) mv^2$, if $m = 2\;\mathsf{kg}$ and $v = 3\;\mathsf{m/s}$, + then ${T} = (1/2)\:×\:2\:×\:3^2$ is a numerical value equation giving the numerical value + $9$ of $T$ in joules. ## Other definitions @@ -342,8 +344,8 @@ : - An explicit, known at compile-time, point on an axis of values of a specific [quantity](#quantity) type serving as a reference for other [quantities](#quantity). - - For example, an ice point is a quantity point with a value of `273.15 K` that is used as - the zero point of a degree Celsius scale. + - For example, an ice point is a quantity point with a value of $273.15\;\mathsf{K}$ that + is used as the zero point of a degree Celsius scale. [`quantity point origin`, `point origin`](#point-origin){ #point-origin }