The Mathematical Symbol "Proportion (∷)"
The "Proportion" Symbol (∷): A Fundamental Ratio Notation
The world of mathematics is rich with symbols, each carrying its unique significance. The ∷ symbol, known as the "Proportion" notation, is among such vital symbols. Often used in geometry, algebra, and other branches of mathematics, it denotes a relationship of equality between two ratios. This article will delve into the intricacies of the ∷ symbol and its primary applications.
Understanding the ∷ Symbol
The concept of proportionality is essential in many mathematical scenarios. A proportion is an equation that expresses the equality of two ratios. The ∷ symbol is used to convey this relationship succinctly.
Example 1: Direct Proportionality
If two quantities \(a\) and \(b\) are directly proportional, and two other quantities \(c\) and \(d\) also maintain the same ratio, the relationship can be expressed as \(a : b ∷ c : d\).
Example 2: Geometry and Ratios
In triangles, if the sides of one triangle are in proportion to the sides of another triangle, this relationship of proportionality can be represented using the ∷ symbol. For instance, if triangle ABC is similar to triangle DEF, and the sides are proportional, it can be expressed as \(AB : DE ∷ BC : EF\).
Applications of the ∷ Symbol
The ∷ symbol finds its place in various mathematical contexts:
- Mathematics: To denote ratios in algebra, geometry, and arithmetic.
- Physics: To represent proportionality constants or relationships between variables.
- Statistics: In expressing odds or likelihoods of events.
- Economics: For indicating growth rates or other ratios of interest.
The notation, while simple, provides an elegant way to express complex relationships between numbers, quantities, or even functions. It's a testament to how mathematics often distills intricate ideas into concise symbols.
In summary, the ∷ symbol plays an instrumental role in representing proportions, an idea fundamental to various scientific, economic, and mathematical disciplines. Its utility underscores the beauty and precision of mathematical notation.
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Codes for the ∷ Symbol
| The Symbol | ∷ | |
| Alt Code | Alt 8759 | |
| HTML Code | ∷ | |
| HTML Entity | ∷ | |
| CSS Code | \2237 | |
| Hex Code | ∷ | |
| Unicode | U+2237 |
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 8759. 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: ∷</b> | My symbol: ∷ |
(Method 4) Use the HTML Entity Code (for webpages).
| HTML Text | Output |
|---|---|
| <b>My symbol: ∷</b> | My symbol: ∷ |
(Method 5) Use the CSS Code (for webpages).
| CSS and HTML Text | Output |
|---|---|
|
<style> span:after { content: "\2237";} </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: ∷</b> | My symbol: ∷ |
| 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+2237. 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 |
|---|---|
| 2237 [Hold down Alt] [Press x] | ∷ (The 2237 turns into ∷. Note that you can omit any leading zeros.) |
| JavaScript Text | Output |
|---|---|
| let str = "\u2237" document.write("My symbol: " + str) | My symbol: ∷ |