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Unit 7 Constants and Other Common Math Symbols

Constants

A mathematical constant is a fixed value for a mathematical definition that can represent a mathematical concept. The following are some common constants and the concept for infinity.

pi $\pi$	⠨⠏
Euler's Number 𝑒	⠰⠑
Imaginary Number 𝒾	⠰⠊
Infinity ∞	⠼⠿

pi

The ration between the circumference and the diameter of a circle is represented by the lowercase Greek letter pi.

$\pi =3.14159\dots$

⠨⠏⠀⠐⠶⠀⠼⠉⠲⠁⠙⠁⠑⠊⠀⠲⠲⠲

Euler's Number

Also known as the exponential growth constant is represented by lowercase letter e.

$e=2.7182\dots$

⠰⠑⠀⠐⠶⠀⠼⠃⠲⠛⠁⠓⠃⠀⠲⠲⠲

Phi

Known as the golden ratio. It is represented by the lowercase Greek letter phi.

$\phi ={\displaystyle \frac{1+\sqrt{5}}{2}}$

⠨⠋⠀⠐⠶⠀⠰⠷⠼⠁⠐⠖⠩⠼⠑⠬⠨⠌⠼⠃⠾

Imaginary Number

It is called an imaginary number because in reality there is no such thing as a negative square root. It is used like a number in equations.

$i=\sqrt{-1}$

⠰⠊⠀⠐⠶⠀⠰⠩⠐⠤⠼⠁⠬

Infinity

Infinity is the concept of endlessness. It is often used as if it is a real number, but it does not behave as a real number.

$x\to \infty$

⠰⠭⠀⠰⠳⠕⠀⠼⠿

More Common Signs of Operation

Hollow dot (dot product) $\circ$	⠐⠴
Cross product $\times$	⠐⠦
Asterisk (star product) $*$	⠐⠔
Minus or plus $\mp$	⠸⠤
Plus minus $\pm$	⠸⠖

As with all signs of operation, these signs are unspaced from their related numbers or other symbol.

Examples:

Dot product

$a\circ b$

⠁⠐⠴⠃

Cross product

$a⨯b$

⠁⠐⠦⠃

Star product

$a*b$

⠁⠐⠔⠃

Plus/minus minus/plus
$-\left(a\pm b\right)=-a\mp b$

⠐⠤⠐⠣⠁⠸⠖⠃⠐⠜⠀⠐⠶⠀⠐⠤⠁⠸⠤⠃

More Common Signs of Comparison

Proportional to $\propto$	⠸⠐⠶
Approximately Equal ≈	⠘⠔
Tilde/similar $\sim$	⠈⠔
Congruent $\cong$	⠐⠸⠔
Identical to/equivalent ≡	⠸⠿
Line through previous, Cancellation, not	⠈⠱
Parallel $\parallel$	⠼⠇
Perpendicular $\perp$	⠼⠤

As with all signs of comparison, a space is required before and after the comparison sign.

Examples:

Is similar to

$A~A^{\prime }$

⠠⠁⠀⠈⠔⠀⠠⠁⠶

Is congruent to

$B^{\prime }\cong B^{″}$

⠠⠃⠰⠶⠀⠐⠸⠔⠀⠠⠃⠰⠶⠶

Note: The signs for prime and double prime need a grade 1 indicator because they also have a contracted meaning, and the expression is not already in uncontracted mode.

Is proportional to

$V\propto r^3$

⠰⠠⠧⠀⠸⠐⠶⠀⠗⠰⠔⠼⠉

Note: The grade 1 indicator is needed before the level change indicator.

Is approximately equal to

$\measuredangle \mathrm{PQR}\cong {60}^{°}$

⠨⠸⠪⠠⠠⠏⠟⠗⠀⠘⠔⠀⠼⠋⠚⠘⠚

Is equivalent to

$△\mathrm{\alpha }\equiv △\mathrm{\beta }$

⠰⠫⠼⠉⠀⠨⠁⠀⠸⠿⠀⠰⠫⠼⠉⠀⠨⠃

Note: The shape terminator is not needed because there is a space after the triangle.

Parallel

$\mathit{ab}\parallel \mathit{cd}$

⠰⠁⠃⠀⠼⠇⠀⠰⠉⠙

Note: The grade 1 indicators are used because ab and cd are also shortform words.

Perpendicular

$\mathit{BD}\perp \mathit{EG}$

⠠⠠⠃⠙⠀⠼⠤⠀⠠⠠⠑⠛

More Examples:

$\angle \mathrm{Q}\ne \angle \mathrm{R}$

⠸⠪⠠⠟⠀⠐⠶⠈⠱⠀⠸⠪⠠⠗

$6+i\sqrt{5}$

⠼⠋⠐⠖⠊⠩⠼⠑⠬

$A\propto r^2$

⠠⠁⠀⠸⠐⠶⠀⠗⠰⠔⠼⠃

${\log }_{e}10=0.434$

⠇⠕⠛⠰⠢⠑⠼⠁⠚⠀⠐⠶⠀⠼⠚⠲⠙⠉⠙

$S=(n-2)\pi$

⠰⠠⠎⠀⠐⠶⠀⠐⠣⠝⠐⠤⠼⠃⠐⠜⠨⠏

$P\cong P^{\prime }$

⠰⠠⠏⠀⠐⠸⠔⠀⠰⠰⠠⠏⠶

Note: Notice how the grade 1 word indicator can be used instead of two grade 1 symbol indicators for P prime.

$\measuredangle \mathit{PQR}\not\approx \measuredangle \mathit{OPQ}$

⠨⠸⠪⠀⠠⠠⠏⠟⠗⠀⠘⠔⠈⠱⠀⠨⠸⠪⠀⠠⠠⠕⠏⠟