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# tkz-elements — for euclidean geometry
Release 2.25c 2024/04/28
## Description
`tkz-elements v.2.25c` 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](https://www.latex-project.org/lppl/), version 1.3 or greater.
## Requirements
The package compiles with utf8 and lualatex. You need actually to load:
- [tkz-euclide](https://ctan.org/pkg/tkz-euclide)
- or [tikz](https://ctan.org/pkg/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](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 2.25c
- French documentation at my site: [http://altermundus.fr](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`.
- 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
\tkzDN[nb_decimal]{number}
- added the macro \tkzDrawLuaEllipse draw an ellipse in tikz knowing its center, vertex and covertex.
- correction de la documentation
- 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
- 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
- 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
- version 1.60c
- 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
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