This is a new page for stuff related with Euclidean geometry. Other texts on this topic are

• The holomorphic extension of triangle functions (February-August 2004)
• The variety of angles (March 2004)
• Notes on Morley's theorem (August 2003)
• Notes on cubic equations (August 2003)

On the orthocenter

by Markus Rost (Notes, August 2019, 4 pages)

A presentation of the barycentric coordinates of the orthocenter of an Euclidean triangle is given. It is based on a certain general polynomial identity which can be deduced from the residue theorem.

The text is pretty brief but complete. A future extension should perhaps contain a comparison with classical descriptions of the barycentric coordinates of the orthocenter. However, everybody make take this as an exercise.

Full text (version of Aug 14, 2019): [pdf]

A formula for the Euler-Poncelet point

by Markus Rost (Notes, September 2019, 4 pages)

The text provides a formula for the Euler-Poncelet point in complex coordinates.

We don't prove (yet) that the formula yields the Euler-Poncelet point. However we show that it yields a "quadrangle center".

An appendix discusses a general feature of plane "polygon centers". This may serve as an alternative introduction to my text The holomorphic extension of triangle functions (2004).

Full text (version of Oct 14, 2019): [pdf]

Go to: Publications and Preprints · Markus Rost's Web Page