The Mathematical Symbol "Not Parallel To (∦)"

The "Not Parallel To" Symbol (∦): Breaking Parallelism

As mathematical notation continues to evolve, it introduces symbols that help convey ideas with precision. The ∦ symbol, referred to as "Not Parallel To," serves as a testament to this evolution. This article delves into its meaning, significance, and application.

Decoding the ∦ Symbol

The ∦ symbol is used to specify that two lines or entities are not parallel. In geometry, when two lines are parallel, they run alongside each other without ever intersecting. The ∦ symbol is used to denote the exact opposite of this concept, indicating that the lines in question are not parallel and have the potential to intersect.

Example 1: Geometry

If \( l \) and \( m \) are two lines, the statement \( l ∦ m \) means that line \( l \) is not parallel to line \( m \).

Example 2: Vectors

In vector algebra, if vectors \( \mathbf{A} \) and \( \mathbf{B} \) are being compared, the notation \( \mathbf{A} ∦ \mathbf{B} \) suggests that these vectors are not parallel, implying they don't share the same direction.

Domains of ∦ Application

This particular symbol is prominent in several areas of mathematics:

  • Geometry: To discuss relationships between lines or planes.
  • Vector Algebra: When analyzing the direction and magnitude of vectors.

While the concept of parallelism is fundamental to various fields, having a way to explicitly denote its absence is equally crucial. The ∦ symbol facilitates this representation, ensuring clarity in mathematical discussions.

To conclude, the ∦ symbol serves an essential role in mathematics by indicating non-parallel relations. Its introduction aids in ensuring that mathematical expressions remain as lucid and unambiguous as possible.

Mathematical symbol 'Not Parallel To'

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Codes for the ∦ Symbol

The Symbol∦
Alt CodeAlt 8742
HTML Code∦
HTML Entity∦
CSS Code\2226
Hex Code∦
UnicodeU+2226

How To Insert the ∦ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ∦ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8742. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8742;</b>My symbol: ∦

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &npar;</b>My symbol: ∦

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
<style>
span:after {
content: "\2226";}
</style>
<span>My symbol:</span> 		My symbol: ∦

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x2226;</b>My symbol: ∦
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2226 to place the ∦ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output

∦

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ∦ is U+2226. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
TypeOutput
2226
[Hold down Alt]
[Press x]		∦
(The 2226 turns into ∦. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2226. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2226"
document.write("My symbol: " + str)		My symbol: ∦