Dirichlet's Box Principle/Historical Note

Historical Note on Dirichlet's Box Principle

Dirichlet's Box Principle appeared in print as early as $1622$ in Selectæ Propositiones in Tota Sparsim Mathematica Pulcherrimæ by Jean Leurechon.

It also appears, in greater detail, in the $1624$ work Récréations Mathématiques by "H. van Etten", also commonly attributed to Jean Leurechon.

It is commonly called Dirichlet's Box (or Drawer) Principle, after an $1834$ treatment by Johann Peter Gustav Lejeune Dirichlet, who called it the Schubfachprinzip (drawer principle or shelf principle).

In Russian and some other languages, it is known as the Dirichlet Principle or Dirichlet's Principle, which name ambiguously also refers to the minimum principle for harmonic functions.

It is usually seen in its simplest form: if you have $N + 1$ objects to put into $N$ boxes, at least one box contains $2$ objects.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Henry van Etten: $124$