Homothetic Symbol ∻

In mathematics, "Homothetic" refers to a transformation that enlarges or reduces figures while maintaining their shape and proportionality. It represents a type of transformation that preserves the relative properties of geometric shapes.

Defining Homothetic Transformation

A homothetic transformation is a type of similarity transformation that changes the size of a figure while keeping its shape and proportions intact. It involves a dilation or contraction centered at a fixed point, known as the center of dilation.

Characteristics

Key characteristics of homothety include:

Preservation of shape: Homothetic transformations maintain the shape of figures, altering their size but not their internal angles or proportions.
Scaling factor: The ratio by which the figure is enlarged or reduced remains constant throughout the transformation.
Center of dilation: The fixed point about which the dilation occurs determines the nature and direction of the transformation.

Representation in Geometry

In geometry, homothetic transformations are often represented using equations involving scaling factors and coordinates of the center of dilation.

Applications

Homothety finds applications in geometry, especially in the study of similar figures, transformations, and geometric constructions. It's utilized in architectural designs, map scaling, and computer graphics for scaling objects while maintaining their proportions.

Relation to Similarity

Homothetic transformations are closely related to similarity transformations, as both preserve shape and proportions, albeit homothety specifically involves scaling without altering the shape.

Homothetic transformations play a significant role in geometry, preserving the shape and proportions of figures while altering their size through dilation or contraction. Understanding homothety provides insights into geometric transformations, similarity, and applications in various fields relying on scaled representations of objects or shapes.

Mastering the concept of homothetic transformations enhances geometric reasoning and enables the manipulation of shapes and figures while maintaining their essential properties.

∻

Copy to Clipboard

Homothetic Symbol Information

Symbol Name	Homothetic
Unicode Version	1.1 (June 1993)
Unicode	U+223B
CSS Code	\223B
HTML Entity	&homtht;

Hex Code	∻
HTML Code	∻
Latex	\homothetic

Homothetic Symbol Encoding

UTF-8	0xE2 0x88 0xBB
UTF-16	0x223B
UTF-32	0x0000223B

Homothetic PNG and SVG files
How to type homothetic on Microsoft Word
How to type homothetic on Microsoft Windows
How to type homothetic on Mac OS
How to type homothetic on Linux
How to type homothetic on IOS and Android
How to use homothetic in CSS
How to use homothetic in HTML
Homothetic representation in programming languages

Homothetic symbol's PNG and SVG files

Download
PNG

Download
SVG

How to add homothetic symbol via keyboard on different Operating systems

You can type the homothetic on most modern devices with the help of following methods:

How to type homothetic symbol on Microsoft Word

You can type the homothetic on microsoft Microsoft Word using steps mentioned below:

Place your cursor in the text area where you need to insert the symbol and type 2 2 3 B
Without moving the cursor press keys Alt + x together
The original 2 2 3 B is now transformed into ∻

How to type homothetic symbol on Microsoft Windows

You can type the homothetic on Microsoft windows using following steps:

Hold Alt and press to type homothetic on your windows machine.

How to type homothetic symbol on Mac OS

You can type the homothetic on Mac OS using following steps:

Place your cursor in the text area where you need to insert the symbol
Press Ctrl + ⌘ Command + ⎵ Space to bring up the Character Viewer. Alternatively, choose Edit ⇒ Emoji & Symbols
Type “Homothetic” in the search field at the top and press Enter
The symbol should appear. Click on it to insert it into your text

How to type homothetic symbol on Linux

You can type the homothetic on Linux using following steps:

Place your cursor in the text area where you need to insert the symbol
Hold ⇧ Shift + Ctrl and press the letter + U
Press keys 2 2 3 B consecutively
And then press ↵ Enter , the desired symbol will be added to your document

How to type homothetic symbol on IOS and Android

The easiest way to type the homothetic on ios and android is to copy and paste it wherever you need it.

How to use homothetic in CSS

Copy // css example


                                            span {

                                            content: "\223B";

                                        }

How to type homothetic in HTML

Copy // html example


                                            <span>&#8763;</span>

Homothetic symbol representation in programming languages

homothetic's representation in different programming languages can be found in table below:

Language	Representation
Rust	\u{223B}
Ruby	\u{223B}
Python	\u223B
PHP	\u{223B}
Perl	"\x{223B}"
Java	\u223B
Modern JavaScript - Since ES6	\u{223B}
JavaScript	\u223B
Go	\u223B
C#	\u223B
C and C++	\u223B
Bash and Zsh - inside echo -e	\u223B
RFC 5137	\u'223B'