The Catalogue of Triangle Cubics is an online resource containing detailed information about more than 1200 cubic curves in the plane of a reference triangle. [1] The resource is maintained by Bernard Gilbert. Each cubic in the resource is assigned a unique identification number of the form "Knnn" where "nnn" denotes three digits. The identification number of the first entry in the catalogue is "K001" which is the Neuberg cubic of the reference triangle ABC. The catalogue provides, among other things, the following information about each of the cubics listed:
The equations of some of the cubics listed in the Catalogue are so incredibly complicated that the maintainer of the website has refrained from putting up the equation in the webpage of the cubic; instead, a link to a file giving the equation in an unformatted text form is provided. For example, the equation of the cubic K1200 is given as a text file. [2]
The following are the first ten cubics given in the Catalogue.
| Identification number | Name(s) | Equation in barycentric coordinates |
|---|---|---|
| K001 | Neuberg cubic, 21-point cubic, 37-point cubic | |
| K002 | Thomson cubic, 17-point cubic | |
| K003 | McCay cubic, Griffiths cubic | |
| K004 | Darboux cubic | |
| K005 | Napoleon cubic, Feuerbach cubic | |
| K006 | Orthocubic | |
| K007 | Lucas cubic | |
| K008 | Droussent cubic | |
| K009 | Lemoine cubic | |
| K010 | Simson cubic | |
GeoGebra, the software package for interactive geometry, algebra, statistics and calculus application has a built-in tool for drawing the cubics listed in the Catalogue. [3] The command
prints the n-th cubic in the Catalogue for the triangle whose vertices are the three points listed. For example, to print the Thomson cubic of the triangle whose vertices are A, B, C the following command may be issued:
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