We let ℍ be the hyperbolic plane, and instead of tesselating ℍ in the usual way by copies of the fundamental region { |ℜ(*z*)| ≤ 1/2, |z| ≥ l } of PSL(2, ℤ), we construct an alternate tesselation using Farey fractions. Then Series showed that the way in which a geodesic γ cuts across the triangles of this tesselation is intimately linked to the continued fraction expansions of the endpoints of γ on the real line. We utilize this connection to provide nice visual observations of known properties of continued fractions and their relations to problems in Diophantine approximation that we saw earlier in the paper.

Measuring of the rotation rate of rigid bodies in turbulence is a direct way of probing the energy cascade at the scale of the particle. Therefore, very accurate measurements of particle rotation rates can in principle be used to find higher moments of velocity structure functions, as has previously been done using multiple-point velocity correlations. The measurements presented in this thesis are the first step along this path, and it is suggested finally that rotation rate measurements are a more intuitive and direct way to approach the subject of turbulent energy scaling for researchers and students alike.

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