# Maximum Volume of Unit Radius Sphere in Fractional Dimensions

## Theorem

The volume of a unit sphere in $x$-dimensional Euclidean space for real $x$ occurs when $x$ is given as:

$x = 5 \cdotp 25694 \, 64048 \, 60 \ldots$

The corresponding volume at that dimension is given by:

$V = 5 \cdotp 27776 \, 80211 \, 13400 \, 997 \ldots$

## Historical Note

This result has been attributed to David Breyer Singmaster.