4 papers
Constructing Cubic Curves with Involutions
Lorenz Halbeisen, Norbert Hungerbühler
In 1888, Heinrich Schroeter provided a ruler construction for points on cubic curves based on line involutions. Using Chasles' Theorem and the terminology of elliptic curves, we gi…
Pairing Pythagorean Pairs
Lorenz Halbeisen, Norbert Hungerbühler
A pair of positive integers is a pythagorean pair if (i.e., is a square). A pythagorean pair is called a double-pythapotent pair if…
An integral that counts the zeros of a function
Norbert Hungerbühler, Micha Wasem
Given a real function on an interval satisfying mild regularity conditions, we determine the number of zeros of by evaluating a certain integral. The integrand depe…
Non-integer valued winding numbers and a generalized Residue Theorem
Norbert Hungerbühler, Micha Wasem
We define a generalization of the winding number of a piecewise cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computati…