# Directory `macros/latex/contrib/tkz/tkz-elements`

# tkz-elements — for euclidean geometry

Release 2.30c 2024/07/16

## Description

`tkz-elements v.2.30c`

is the new version of a library written in lua, allowing to make all the necessary calculations to define the objects of a Euclidean geometry figure. You need to compile with `LuaLaTeX`

. With `tkz-elements`

, the definitions and calculations are only done with `Lua`

.

The main possibility of programmation proposed is oriented "object programming" with object classes like point, line, triangle, circle and ellipse. For the moment, once the calculations are done, it is `tkz-euclide`

or `TikZ`

which allows the drawings. You can use the option `mini`

with `tkz-euclide`

to load only the modules required for tracing.

## Licence

This package may be modified and distributed under the terms and conditions of the LaTeX Project Public License, version 1.3 or greater.

## Requirements

The package compiles with utf8 and lualatex. You need actually to load:

- tkz-euclide
- or tikz

## Installation

The package `tkz-elements`

is present in TeXLive and MiKTeX, use the package manager to install.

You can experiment with the `tkz-elements`

package by placing all of the distribution files in the directory containing your current tex file.

The different files must be moved into the different directories in your installation `TDS`

tree or in your `TEXMFHOME`

:

## How to use it

To use the package `tkz-elements`

, place the following lines in the preamble of your LaTeX document:

% !TEX TS-program = lualatex \usepackage[mini]{tkz-euclide} \usepackage{tkz-elements} \begin{document} \begin{tkzelements} your code \end{tkzelements} \begin{tikzpicture} \tkzGetNodes your code \end{tikzpicture}

If you use the `xcolor`

package, load that package before `tkz-euclide`

to avoid package conflicts.

## Examples

Some examples will be stored on my site : http://altermundus.fr. An important example `Golden Arbelos`

using the package is on the site. All the files of the documentation are on the site.

## History

- version 2.30c
- new version of the macro
`\tkzGetNodes`

written by Sanskar Singh. This version now fixes a bug that prevented a figure from being centred with`centering`

or the`center`

environment.- adding methods
`bevan_circle`

,`symmedial_circle`

.- correction of the methods
`function triangle: bevan_point ()`

and`function triangle: mittenpunkt_point ()`

. - adding
`function triangle: similar ()`

- adding
`function line : perpendicular_bisector ()`

which is similar to`function line : mediator ()`

- correction of documentation.

- correction of the methods

- adding methods

- version 2.25c
- French documentation at my site: http://altermundus.fr
- Added
`colinear_at`

a new method for the classe`line`

- Added
`cevian`

,`pedal`

,`conway_circle`

,`conway_points`

new methods to the class`triangle`

.

- Added

- French documentation at my site: http://altermundus.fr

- new version of the macro

- version 2.20c
- Package:
- Added class matrix; methods are mainly of order 2, sometimes of order 3.
- Added function solve
*quadratic. This function can be used to solve second-degree equations with real or complex numbers.* - Added method print for the class point. Example z.A : print ()
- Correction of the macro tkzDN. I deleted a spurious space
- Modification of vector class attributes. Attributes h and t become head and tail.
- The mtx attribute is introduced for point and vector. z.A.mtx represents the column matrix whose coefficients are the point's coordinates. Same for vectors.
- Documentation:
- Rewriting of all texts
- Correction of example: pentagon
- Documentation about matrices

- version 2.00c
- class development
`vector`

- added attribute
`vec`

- added
`at`

and`orthogonal`

methods to the class`point`

- rewriting the function angle_normalize_
- modification of the slope attribute for the
`line`

, now the result is normalized. - the angles of a triangle are also normalized
- added function format_number(number,decimal) sets the number of digits in the decimal part.
- added tkzDN a macro pour formater les nombres dans la partie TikZ tkzDNnb
*decimal*{number} - added the macro tkzDrawLuaEllipse draw an ellipse in tikz knowing its center, vertex and covertex.
- correction de la documentation

- added attribute

- class development
- version 1.82c
- Point object : name like z.App now gives a node with name A''
- Modification of methods north,south
- Added the function length(z.A,z.B) shortcut for point.abs(z.A-z.B).
- Line object added some methods
- Added method in_out_segment
- (sacred triangle)
- gold
- sublime or euclide
- cheops
- divine
- pythagoras or isis or egyptian
- golden

- (classic triangles)
- two_angles (side between)
- sss (three sides)
- ssa (two sides and an angle)
- sas (an angle between two sides)
- school (30°, 60° and 90°)
- half right triangle in A with AB= 2AC

- Circle object
- added method common
*tangent (gives the common tangents of two circles)* - Correction for a bug and an oversight in the circles
*position method.* - Rewriting the radical
*axis methods*

- added method common
- Triangle object
- method trilinear (to use trilinear coordinates)
- method barycentric (to use barycentric coordinates)

- Added some functions
`bisector (a,b,c)`

`altitude (a,b,c)`

`bisector_ext(a,b,c)`

`equilateral (a,b)`

`midpoint (a,b)`

to avoid creating unnecessary objects.

- Added new examples and a cheat sheet in the documentation

- Point object : name like z.App now gives a node with name A''

- Package:

- version 1.72c
- added a line method (apollonius) set of points M with MA/MB = k
- example with line : apollonius
- example: three circle
- example: pentagons on golden arbelos
- descriptions of several cases with 'midcircle'
- added soddy method and examples
- added example with circles
*position* - correction of the documentation

- example with line : apollonius
- version 1.60c

- added a line method (apollonius) set of points M with MA/MB = k

- added Internal and external tangents common to two circles: - function circle : `external_tangent(C)` - function circle : `internal_tangent(C)` - radical_center and radical_circle are also valid for two circles - function `radical_center (C1,C2,C3)` - function `radical_circle (C1,C2,C3)` - function `circles_position (C1,C2)` - function `midcircle (C1,C2)` powerful tool for working with inversions - Bug corrected in midarc now use get_angle instead of get_angle_ - Modification of a triangle attribute `ca` replaces `ac` to designate the line passing through the third and first points - The center of symmetry of a parallelogram is named "center" instead of `i`. - Correction documentation - Correction of examples using the circle:point (k) method, where k is now a real number rather than an angle.

- version 1.50c Correction of the documentation

- Added `swap` option to create triangles from the "line" object. - `iscyclic` is a new method to know if a quadrilateral is inscribable in a circle. - Added function `diameter` to create a circle. - Added function `swap` to swap two points. - Correction method `gold` of object rectangle. - Correction method `in_circle_` of object triangle. - Correction method `incentral_tr_` of object triangle. - Added method `soddy_center` of object triangle. - Added option `swap` for method `square` of object line. - Added method `report` for object line. Transfer a defined length from a point - Added option `swap` to the function "square : side"

- Version 1.40c Restructuring objects

- New version for all transformations. Now, they accept all objects as parameters. - Symmetry_axial has changed its name to reflection. - Added scale to north south etc.. (point object). - Change the "point" method of the objects circle and ellipse. now the parameter is un real t (between 0 and 1) and not an angle - Added the method `check_equilateral` to know if a triangle is equilateral. - Added option "indirect" to the method equilateral for a line object. - Correction of the documentation. (Added sections).

- Version 1.20 Memory management: tables are emptied when the tkzelements environment is opened.

- `set_lua_to_tex` has been replaced by `tkzUseLua` to transfer data between the `tkzelements` and `tikzpicture` environments. - New version of `inversion` with respect to a circle method. It selects the correct algorithm based on the object passed as a parameter. - Added an `in_out_disk` method for the `circle` object, which indicates whether or not a point is in the disk. `in_out` is for the circle. - Added two methods: `radical_center (C1,C2,C3)` radical center of three circles. `radical_circle (C1,C2,C3)` orthogonal circle of three circles. - Added function `circle : radius` to define a circle with a centre and a radius. - Added methods `normalize` and `normalize_inv` for `line`. - Added methods `translation` and `set_translation` to the `line` object. - Added an example to illustrate combinations of methods and attributes.

- First version 1.00b

## Author

Alain Matthes, 5 rue de Valence, Paris 75005, al (dot) ma (at) mac (dot) com

Download the contents of this package in one zip archive (991.3k).

## tkz-elements – A Lua library for drawing Euclidean geometry with TikZ or tkz-euclide

This package provides a library written in Lua, allowing to make all the necessary calculations to define the objects of a Euclidean geometry figure. You need to compile with LuaLaTeX. The definitions and calculations are only done with Lua.

The main possibility of programmation proposed is oriented “object programming” with object classes like point, line, triangle, circle and ellipse. For the moment, once the calculations are done, it is tkz-euclide or TikZ which allows the drawings.

Package | tkz-elements |

Home page | https://altermundus.fr |

Version | 2.30c |

Licenses | The LaTeX Project Public License 1.3 |

Copyright | 2024 Alain Matthes |

Maintainer | Alain Matthes |

Contained in | TeX Live as tkz-elements MiKTeX as tkz-elements |

Topics | Maths LuaTeX Calculation |