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)