Welcome to mikematics
Hello and welcome to my private math pages. My name is Mike Winkler, also known as mikematics. I am a German mathematician and live on a horse farm on the North Sea coast. On this website I present some of my ideas, conjectures and proofs on selected mathematical topics from my private research, which I do entirely non-commercially in my spare time. When a problem grabs 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 and paint occasionally.
Have fun reading and exploring this website.
Mike Winkler

Latest research and publications
Currently best approximation of a 4-regular matchstick graph with 61 vertices (June 2023)
Aperiodic Sets of Prototiles Extracted from the Penrose Rhomb Tiling (December 2022)
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)