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Physical Sciences and Mathematics Commons™
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Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Combinatorics Of The Sonnet, Terry S. Griggs
Combinatorics Of The Sonnet, Terry S. Griggs
Journal of Humanistic Mathematics
Using a definition of a sonnet, the number of basic rhyming schemes is enumerated. This is then used to discuss the 86 sonnets which appear in John Clare's The Rural Muse.
A Beautiful Proof By Induction, Lars-Daniel Öhman
A Beautiful Proof By Induction, Lars-Daniel Öhman
Journal of Humanistic Mathematics
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.