The ∻ (Homothetic) Symbol: Meaning, Math, and Typing Guide
The ∻ (Homothetic) symbol, located at Unicode code point U+223B, is a mathematical operator consisting of a tilde with a single dot placed above and another below. In geometry, this symbol represents a homothetic transformation—a uniform scaling of objects that alters their size while preserving their original shape and proportions. While its primary home is in advanced mathematical equations, this visually striking character often finds its way into digital typography and aesthetic social media text.
The ∻ symbol was officially introduced in the Mathematical Operators Unicode block, a dedicated section covering standard symbols used in arithmetic, calculus, logic, and set theory. Its official Unicode hex value is U+223B. Because it is part of this fundamental block, the symbol enjoys widespread font support across most modern operating systems, word processors, and web browsers.
In the realms of math and science, ∻ heavily denotes homothety or similarity. If two geometric figures are homothetic, one is an exact, scaled version of the other, expanding or shrinking from a central point. Outside of academic papers, programmers rarely use this symbol as a default operator. However, modern programming languages that support extensive Unicode math notation, such as Julia, allow developers to map the ∻ character to custom geometric scaling functions. On platforms like Twitter, Instagram, and TikTok, the symbol steps completely out of its mathematical boundaries. Users frequently repurpose it as a decorative bullet point, an artistic text divider, or a creative element within complex text-based emoticons, leaning entirely on its symmetrical, wavy aesthetic.
Typing the ∻ symbol natively requires knowing a few keyboard shortcuts. On Windows devices, you can type '223B' followed by Alt+X in programs like Microsoft Word, or locate it manually using the system Character Map utility. Mac users can press Control+Command+Space to bring up the Character Viewer and simply search for 'homothetic' to insert it. For web developers, the HTML decimal code ∻ or hex code ∻ will render the symbol perfectly on any webpage. When all else fails, copying and pasting the symbol directly from an online encyclopedia is the quickest universal method.
Visually, the ∻ symbol has several lookalikes in the Unicode standard. It shares obvious design traits with the standard division sign (÷), swapping the straight horizontal bar for a wavy tilde (~). It is also visually related to the minus tilde (≂) and the proportional to symbol (∝), though those lack the distinct dual dots. This unique stacked design makes the ∻ symbol a fascinating blend of geometry and typography.