The Encyclopedia of Triangle Centers (ETC) is an on-line list of more than 3,000 points or "centers" associated with the geometry of a triangle. It is maintained by Clark Kimberling, Professor of Mathematics at the University of Evansville.
Each point in the list is identified by an index number of the form X(n) — for example, X(1) is the incentre. The information recorded about each point includes its trilinear and barycentric coordinates and its relation to lines joining other identified points. Links to Geometer's Sketchpad diagrams are provided for key points. The Encyclopedia also includes a glossary of terms and definitions.
The first 10 points listed in the Encyclopedia are:
| ETC reference | Name | Definition |
|---|---|---|
| X(1) | incentre | centre of the incircle |
| X(2) | centroid | intersection of the three medians |
| X(3) | circumcentre | centre of the circumscribed circle |
| X(4) | orthocentre | intersection of the three altitudes |
| X(5) | nine-point centre | centre of the nine-point circle |
| X(6) | symmedian point | intersection of the three symmedians |
| X(7) | Gergonne point | symmedian point of contact triangle |
| X(8) | Nagel point | intersection of lines from each vertex to the corresponding semiperimeter point |
| X(9) | Mittenpunkt | symmedian point of the triangle formed by the centres of the three excircles |
| X(10) | Spieker centre | centre of the Spieker circle |
Other points with entries in the Encyclopedia include:
| ETC reference | Name |
|---|---|
| X(11) | Feuerbach point |
| X(13) | Fermat point |
| X(15), X(16) | first and second isodynamic points |
| X(20) | de Longchamps point |
| X(21) | Schiffler point |
| X(39) | Brocard midpoint |