We present two geometrical methods to analyse the cosmic microwave background data along a strip in the sky. These methods are motivated by the fact that the temperature fluctuation field, on large angular scales, is not ergodic on the cosmic photosphere. This property is examined in the context of different experimental configurations. The methods involve a numerical study of the expected pip number and distribution function of pip sizes, and take into account the non-ergodicity of the temperature field. They are applied to the new measurements of the Tenerife experiment, assuming a Gaussian random field for the temperature fluctuations with power spectra poc k in a flat universe. Moreover, these geometrical methods can be readily used to test non-Gaussian random fields as representations of the cosmic microwave background temperature fluctuations. Key words: methods: data analysis - cosmic microwave background - cosmology: observations.