Approximately Equal To

The Mathematical Symbol "Approximately Equal To (≅)"

Unpacking the ≅ Symbol in Mathematics

The mathematical symbol ≅ stands for "Approximately Equal To". This notation is applied in various mathematical and scientific domains to express that two quantities or expressions are nearly identical, but not exactly so. This short lesson covers two primary contexts of this symbol, presenting two examples for each use.

1. Geometry

In geometry, ≅ often represents congruence between geometric figures, meaning they have the same size and shape.

• Example 1: If two triangles, \( \triangle ABC \) and \( \triangle DEF \), are congruent, it can be denoted as \( \triangle ABC ≅ \triangle DEF \).
• Example 2: Similarly, two congruent circles with the same radius can be represented as Circle \( A ≅ \) Circle \( B \).

2. Approximate Numerical Equivalence

In contexts outside of geometry, the symbol is occasionally used to show that two numbers are approximately, but not exactly, equal.

• Example 1: After performing a mathematical calculation, one might find that the number \( \pi \) is approximately 3.14, represented as \( \pi ≅ 3.14 \).
• Example 2: When working with irrational numbers, the golden ratio \( \phi \) could be approximately expressed as \( \phi ≅ 1.618 \).

To conclude, while the ≅ symbol is versatile in its application, understanding its context is paramount. In geometry, it primarily signifies congruence, whereas in other mathematical contexts, it can indicate approximate numerical equality.

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Codes for the ≅ Symbol

The Symbol	≅	copy
Alt Code	Alt 8773	copy
HTML Code	≅	copy
HTML Entity	≅	copy
CSS Code	\2245	copy
Hex Code	≅	copy
Unicode	U+2245	copy

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 8773. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

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

HTML Text	Output
<b>My symbol: &#8773;</b>	My symbol: ≅

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

HTML Text	Output
<b>My symbol: &cong;</b>	My symbol: ≅

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

CSS and HTML Text	Output
<style> span:after { content: "\2245";} </style> <span>My symbol:</span>	My symbol: ≅

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

HTML Text	Output
<b>My symbol: &#x2245;</b>	My symbol: ≅

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2245 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+2245. 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:

Type	Output
2245 [Hold down Alt] [Press x]	≅ (The 2245 turns into ≅. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u2245. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u2245" document.write("My symbol: " + str)	My symbol: ≅

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