The Mathematical Symbol "Tilde Operator (∼)"

The ∼ Symbol: Tilde Operator

The ∼ symbol, commonly known as the "tilde operator" or just "tilde", is used in various fields of mathematics, representing different concepts depending on the context. In this article, we'll explore its primary uses, accompanied by some illustrative examples.

Usage

In mathematics, the tilde often denotes similarity, equivalence, or an approximation. Here are some common usages:

  • Geometry: Represents similarity between two figures.
  • Algebra and other branches: Represents an approximation.

Examples

  • Example 1: Geometry
    Given two triangles, ΔABC and ΔXYZ. If the corresponding angles of these triangles are congruent, then ΔABC ∼ ΔXYZ, which means triangle ABC is similar to triangle XYZ.
  • Example 2: Approximation
    Consider the value of π. Often, for simplicity in calculations, π ∼ 3.14. Here, the tilde indicates that 3.14 is an approximation of π.

To wrap up, the ∼ symbol is versatile and widely adopted in various mathematical contexts. Its usage mainly revolves around the concepts of similarity, equivalence, or approximation. It's an efficient way to convey these concepts without the need for verbose explanations.

Mathematical symbol 'Tilde Operator'

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Codes for the ∼ Symbol

The Symbol∼
Alt CodeAlt 8764
HTML Code∼
HTML Entity∼
CSS Code\223C
Hex Code∼
UnicodeU+223C

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 8764. 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: &#8764;</b>My symbol: ∼

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

HTML TextOutput
<b>My symbol: &sim;</b>My symbol: ∼

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

CSS and HTML TextOutput
<style>
span:after {
content: "\223C";}
</style>
<span>My symbol:</span> 		My symbol: ∼

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

HTML TextOutput
<b>My symbol: &#x223C;</b>My symbol: ∼
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x223C 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+223C. 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
223C
[Hold down Alt]
[Press x]		∼
(The 223C turns into ∼. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u223C. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u223C"
document.write("My symbol: " + str)		My symbol: ∼