Half-integer

In mathematics, a half-integer is a number $h$ of the form $n+1/2$, where $n$ is an integer. For example, $1/2,3/2,5/2\ldots$ are half-integers, as are $-1/2,-3/2,-5/2\ldots$.

Half-integers occur freqeuently enough in mathematical contexts that a special name for them is convenient. For example, the densest lattice packing of unit spheres in four dimensions places a sphere at every point whose coordinates are either all integers or all half-integers; this packing is closely related to the Hurwitz integers, which are quaternions whose real coefficients are either all integers or all half-integers. Moreover, the Pauli exclusion principle states that fermions have spins that are half-integers.