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.
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)