The Mathematical Symbol "Right Triangle (⊿)"

The "Right Triangle" Symbol (⊿)

The ⊿ symbol, often referred to as the "Right Triangle", is a mathematical symbol that signifies a particular geometric relation or property. While the right triangle in geometry is well-known for its 90-degree angle, the ⊿ symbol serves a different purpose in advanced mathematics.

Usage of ⊿

Unlike the standard representation of right triangles in geometry, ⊿ is more abstract and can be applied in various mathematical contexts, especially in relation to set relations and ordering.

Example 1: Ordering Relations

In certain contexts, if we have two elements A and B, the expression A ⊿ B might indicate a particular order or hierarchical relationship between A and B. It could mean A is less than or related to B in a specified manner.

Example 2: Set Inclusions

In set theory, given two sets X and Y, the notation X ⊿ Y might signify a specific inclusion or subset relationship, depending on the precise definition within that mathematical context.

Importance in Mathematical Contexts

The symbol ⊿ might not be a daily reference for many, but for those exploring specific domains of mathematics, it is invaluable:

  • Expressive Power: Specialized symbols like ⊿ allow mathematicians to concisely express complex relations or properties.
  • Niche Applications: Symbols like this often have very specific applications within certain mathematical domains, making them essential for experts in those fields.
  • Evolution of Mathematics: As the field of mathematics expands and evolves, new symbols and notations emerge to cater to newly discovered concepts and relationships.

In summary, while the ⊿ symbol may not be immediately familiar to many, it plays a critical role in conveying specific relationships in particular mathematical contexts. Recognizing and understanding such symbols enrich the toolkit of mathematicians and researchers.

Mathematical symbol 'Right Triangle'

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Codes for the ⊿ Symbol

The Symbol
Alt CodeAlt 8895
HTML Code⊿
HTML Entity⊿
CSS Code\22BF
Hex Code⊿

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 8895. 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: &#8895;</b>My symbol: ⊿

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

HTML TextOutput
<b>My symbol: &lrtri;</b>My symbol: ⊿

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

CSS and HTML TextOutput
span:after {
content: "\22BF";}
<span>My symbol:</span>
My symbol: ⊿

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

HTML TextOutput
<b>My symbol: &#x22BF;</b>My symbol: ⊿
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22BF to place the ⊿ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

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

The Unicode for ⊿ is U+22BF. 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:
[Hold down Alt]
[Press x]

(The 22BF turns into ⊿. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22BF. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22BF"
document.write("My symbol: " + str)
My symbol: ⊿