Concept
Dirichlet — where it appears
2 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
More things than boxes
If there are more objects than containers, some container holds two. That is the entire principle, it is impossible to disagree with, and it settles questions that look nothing like it.
How close a fraction can get
Drop eight points into seven boxes and two of them share. That one line, applied to the multiples of an irrational number, proves that every irrational has infinitely many astonishingly good rational approximations — and no construction is needed anywhere.
Named alongside it
The objects these essays reach for when they reach for this one.
Counting argumentExistence proofNonconstructivePigeonhole principleContinued fraction convergentGolden ratioLiouville numberRational approximationTranscendence