Norbert Hungerbühler

Last Name

Hungerbühler

First Name

Norbert

ORCID

0000-0001-6191-0022

Organisational unit

03874 - Hungerbühler, Norbert / Hungerbühler, Norbert

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Publications 1 - 10 of 50

The Hidden Twin of Morley’s Five Circles Theorem
Halbeisen, Lorenz; Hungerbühler, Norbert; Loureiro, Vanessa (2023)
The American Mathematical Monthly
We give an algebraic proof of a slightly extended version of Morley’s Five Circles Theorem. The theorem holds in all Miquelian Möbius planes obtained from a separable quadratic field extension, in particular in the classical real Möbius plane. Moreover, the calculations bring to light a hidden twin of the Five Circles Theorem that seems to have been overlooked until now.
The Pentagon Theorem in Miquelian Möbius Planes
Halbeisen, Lorenz; Hungerbühler, Norbert; Loureiro, Vanessa (2023)
International Electronic Journal of Geometry
We give an algebraic proof of the Pentagon Theorem. The proof works in all Miquelian Möbius planes obtained from a separable quadratic field extension. In particular, the theorem holds in every finite Miquelian plane. The arguments also reveal that the five concyclic points in the Pentagon Theorem are either pairwise distinct or identical to one single point. We also identify five additional quintuples of points in the pentagon configuration which are concyclic.
Transition Gymnase – Université I
Wintgens, David; Hungerbühler, Norbert (2011)
Gymnasium Helveticum
Verbesserung des Übergangs vom Gymnasium an die Universität
Hungerbühler, Norbert; Wintgens, David (2012)
Gymnasium Helveticum
Closing Theorems for Circle Chains
Hungerbühler, Norbert (2025)
International Electronic Journal of Geometry
We consider closed chains of circles $C_1,C_2,\ldots,C_n,C_{n+1}=C_1$ such that two neighbouring circles $C_i,C_{i+1}$ intersect or touch each other with $A_i$ being a common point. We formulate conditions such that a polygon with vertices $X_i$ on $C_i$, and $A_i$ on the (extended) side $X_iX_{i+1}$, is closed for every position of the starting point $X_1$ on $C_1$. Similar results apply to open chains of circles. It turns out that the intersection of the sides $X_iX_{i+1}$ and $X_jX_{j+1}$ of the polygon lies on a circle $C_{ij}$ through $A_i$ and $A_j$ with the property that $C_{ij}, C_{jk}$ and $C_{ki}$ pass through a common point. The six circles theorem of Miquel and Steiner's quadrilateral Theorem appear as special cases of the general results.
Transition Gymnase – Université I
Wintgens, David; Hungerbühler, Norbert (2011)
Gymnasium Helveticum
A geometric approach to elliptic curves with torsion groups Z/10Z, Z/12Z, Z/14Z, and Z/16Z
Halbeisen, Lorenz; Hungerbühler, Norbert; Shamsi Zargar, Arman; et al. (2023)
Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti
We give new parametrisations of elliptic curves in Weierstrass normal form y2 = x3 + ax2 + bx with torsion groups Z/10Z and Z/12Z over Q, and with Z/14Z and Z/16Z over quadratic fields. Even though the parametrisations are equivalent to those given by Kubert and Rabarison, respectively, with the new parametrisations we found three infinite families of elliptic curves with torsion group Z/12Z and positive rank. Furthermore, we found elliptic curves with torsion group Z/14Z and rank 3 - which is a new record for such curves - as well as some new elliptic curves with torsion group Z/16Z and rank 3.
Jahresbericht der Kommission Gymnasium - Universität (KGU) 2016/2017
Hartmann, Lucius; Hungerbühler, Norbert (2018)
Gymnasium Helveticum
Ceva-triangular points of a triangle
Hungerbühler, Norbert; Wanner, Gerhard (2022)
Elemente der Mathematik
Jahresbericht der Kommission Gymnasium - Universität Jahr 2021
Hartmann, Lucius; Hungerbühler, Norbert (2022)
Gymnasium Helveticum

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Norbert Hungerbühler

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