A Beautiful Proof by Induction

Journal of Humanistic Mathematics

Öhman, Lars-Daniel¹ 

[1] Department of Mathematics and Mathematical Statistics, Umeå University

关键词: proof;    mathematical induction;    beauty;    planar graphs;    graph coloring;   

DOI  :  10.5642/jhummath.201601.06

学科分类：卫生学

来源: Cleveland Clinic Educational Foundation

【 摘 要 】

The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

【 授权许可】

Unknown