# Hermite Constant

The Hermite constant was named after Charles Hermite. It determines how much maximum, an element of a lattice, could be short enough in the Euclidean space. It is known in dimensions 1–8 and 24. For n = 2, the Hermite constant is written as: γ2=2/√3.

Constant Name

Hermite Constant

Symbol : γ2

Value : 1.15470 05383 79251 52901

The Hermite constant was named after Charles Hermite. It determines how much maximum, an element of a lattice, could be short enough in the Euclidean space. It is known in dimensions 1–8 and 24. For n = 2, the Hermite constant is written as: γ2=2/√3.

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For n value, the Hermite constant is defined as: γn=(supf minxi f(x1, x2,..xn))/[discriminant(f)]1/n. It is also represented as: γn=4(∂n/Vn)2/n
where ∂n is the maximum lattice.
For a large value of n, the Hermite Constant is defined as: 1/2∏e≤(γn/n)≤1.744.../2∏e

For n value, the Hermite constant is defined as: γn=(supf minxi f(x1, x2,..xn))/[discriminant(f)]1/n. It is also represented as: γn=4(∂n/Vn)2/n
where ∂n is the maximum lattice.
For a large value of n, the Hermite Constant is defined as: 1/2∏e≤(γn/n)≤1.744.../2∏e