Gergonne-Schwarz Surface

Visualizing Mathematics - Online -

Modern mathematical visualization has always been related with special graphics workstation although visualization was always part of mathematics. Here we start from historical roots, bring interactive visualization into the classrooms and create online mathematical publications. The topics include Java applets and online videos, a new electronic journal for geometry models, an interactive math...

Heron Triangles: A Gergonne-Cevian-and-Median Perspective

We give effective constructions of Heron triangles by considering the intersection of a median and a cevian through the Gergonne point.

The Lost Daughters of Gergonne

Given a triangle center we can draw line segments from each vertex through the triangle center to the opposite side, this splits the triangle into six smaller triangles called daughters. Consider the following problem: Given a triangle S and a rule for finding a center find a triangle T , if possible, so that one of the daughters of T , when using the rule is S. We look at this problem for the ...

Schwarz boundary problem on a triangle

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

The Gergonne p-pile Problem and the Dynamics of the Function x | => (x + r)/p