Editing Metric tensor (section)

====The round metric on a sphere====
The unit sphere in {{math|'''ℝ'''<sup>3</sup>}} comes equipped with a natural metric induced from the ambient Euclidean metric, through the process explained in the [[#Induced_metric|induced metric section]]. In standard spherical coordinates {{math|(''θ'', ''φ'')}}, with {{math|''θ''}} the [[colatitude]], the angle measured from the {{mvar|z}}-axis, and {{mvar|φ}} the angle from the {{mvar|x}}-axis in the {{mvar|xy}}-plane, the metric takes the form

:<math>g = \begin{bmatrix} 1 & 0 \\ 0 & \sin^2 \theta\end{bmatrix} \,.</math>

This is usually written in the form

:<math>ds^2 = d\theta^2 + \sin^2\theta\,d\varphi^2\,.</math>