## Welcome to mikematics

On this website I present some of my work, thoughts and ideas on selected topics in mathematics. These range from conjectures over abstract ideas to rigorous proofs. My work is mostly in the areas of number theory, combinatorics and discrete geometry, including graph theory. If a problem has grabbed me, I worked on it over many years. My favorite topics are the 3x + 1 problem, regular matchstick graphs, nonperiodic tilings and Heesch’s problem. In addition to math, I’m an keen cyclist and horse lover, I create websites, play and teach piano and guitar, swim a bit, and occasionally paint.

Have fun reading and exploring this website.

## Mike Winkler

## Latest research

**Currently best approximation of a 4-regular matchstick graph with 61 vertices** (December 2021)

**Currently best approximation of a 4-regular matchstick graph with 52 vertices** (November 2021)

**Aperiodic Sets of Prototiles Extracted From the Penrose Rhomb Tiling** (August 2021)

**Approximate Solutions of 4-regular Matchstick Graphs with 50 – 62 Vertices** (October 2020)

**4-regular planar unit triangle graphs without additional triangles** (November 2019)

**A 3-regular matchstick graph of girth 5 consisting of 54 vertices**. (November 2019)

Please view the matchstick graphs with the