# 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](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 2.30c - 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. - 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