# External mathematical formulas

The Encyclopedia of Triangle Centers (ETC) is the work of **Clark Kimberling and its named contributors**, hosted by the University of Evansville:

<https://faculty.evansville.edu/ck6/encyclopedia/etc.html>

Only 85 selected first barycentric-coordinate expressions are included in `data/etc-matches.json`. They are completed cyclically. The full ETC database is not redistributed. The formulas come from the supplied `ETC_X1_X72807.wxf` Triangle Center Tools snapshot, SHA-256 `ace501d40dd83785f89b4de8e4ddcc0c5081d82de82e1baf37816d10e547cbfa`, used previously in the Physically Inspired Triangle Centers project.

That tools repository is distributed under the Unlicense, reproduced in `LICENSE-ETC-TOOLS`. Original ETC attribution remains with Kimberling and the relevant contributors. The MIT license for this explorer does not replace that attribution or assert authorship of the external formulas.

The power-center calculations, comparison protocol adaptation, numerical rankings, and explorer are research by **Ismail Hammoudeh**, developed with extensive use of **ChatGPT**.