## Welcome to mikematics

Hello and welcome to my private math pages. My name is Mike Winkler aka mikematics. On this website I present some of my ideas, conjectures and proofs on selected topics of mathematics from my private research, which I do completely non-commercially exclusively in my free time. My work is mostly in the areas of number theory, combinatorics and discrete geometry, including graph theory. When a problem has grabbed me, I work on it for many years. My favorite topics are the 3x + 1 problem, regular matchstick graphs, nonperiodic tilings and Heesch’s problem. Besides math, I love horses and cycling, play the piano and guitar, swim a little, and paint occasionally.

Have fun reading and exploring this website.

## Mike Winkler

## Latest research and publications

**Aperiodic Sets of Prototiles Extracted from the Penrose Rhomb Tiling** (December 2022)

**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)

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

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

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