# Gaussian curvature $G$

How a surface curves in 2 dimensions. If negative, the shape is saddle-like (some directions upwards, others downwards); if positive, all directions are the same way (a ball, a mountain top, a valley); if zero, at least one direction is straight/non-curving. Calculated for a single point.

$$G=k_\text{smallest}\cdot k_\text{largest}$$

The $k$’s are the smallest and largest 1D curvatures (principle curvatures) that pass through the point.

• Scalar property
• Symbol: $G$
• SI-unit: Inverse metres $\mathrm{m^{-2}}$